Characteristic of Gases. The Nature of Gases Gases expand to fill their containers Gases are fluid – they flow Gases have low density – 1/1000 the density.
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Characteristic of
Gases
The Nature of Gases
bull Gases expand to fill their containersbull Gases are fluid ndash they flowbull Gases have low densityndash 11000 the density of the equivalent liquid
or solid
bull Gases are compressiblebull Gases effuse and diffuse
Gases Are Fluids
bull Gases are considered fluids
bull The word fluid means ldquoany substance that can flowrdquo
bull Gas particles can flow because they are relatively far apart and therefore are able to move past each other easily
Gases Have Low Densitybull Gases have much lower densities than
liquids and solids do - WHY ndash Because of the relatively large distances
between gas particles most of the volume occupied by a gas is empty space
bull The low density of gases also means that gas particles travel relatively long distances before colliding with each other
Gases are Highly Compressible
bull Suppose you completely fill a syringe with liquid and try to push the plunger in when the opening is plugged ndash You cannot make the space the liquid takes up become
smaller bull The space occupied by the gas particles is very
small compared with the total volume of the gasbull Applying a small pressure will move the gas
particles closer together and will decrease the volume
Gases Completely Fill a Container
bull A solid has a certain shape and volume
bull A liquid has a certain volume but takes the shape of the lower part of its container
bull In contrast a gas completely fills its container
bull Gas particles are constantly moving at high speeds and are far apart enough that they do not attract each other as much as particles of solids and liquids do
bull Therefore a gas expands to fill the entire volume available
Gas Pressure
Gas Pressurebull Earthrsquos atmosphere commonly known as air is a
mixture of gases mainly nitrogen and oxygen
bull As gas molecules are pulled toward the surface of Earth they collide with each other and with the surface of Earth more often Collisions of gas molecules are what cause air pressure
Measuring Pressure
Pressure = Area
Force Newton (N)
m2 cm2
Units of Pressure
1 atm = 760 torr = 1013 kPa = 760 mmHg
Standard Temperature Pressure (STP)
1 atm 0degC 224 L 1 mole
100 atm 760 mmHg = 760 x 10^2 mmHg
1 Covert 100 atm to mmHg
1 atm
300atm 1013 kPa = 304 kPa
2 Covert 300 atm to kPa
1 atm
3 What is 1000 KPa in atm
1000 kPa
1013 kPa = 09872 atm
1 atm
bull Measures atmospheric pressure
bull The atmosphere exerts pressure on the surface of mercury in the dish
bull This pressure goes through the fluid and up the column of mercury
bull The mercury settles at a point where the pressure exerted downward by its weight equals the pressure exerted by the atmosphere
Measuring Pressure Using Barometer
Gas Theory
Kinetic Molecular Theorybull Particles of matter are ALWAYS in motionbull Volume of individual particles is zerobull Collisions of particles with container walls cause
pressure exerted by gasbull Particles exert no forces on each otherbull Average kinetic energy is proportional to Kelvin
temperature of a gas
bull Ideal gas- imaginary perfect bull gas fitting the theory
Checking for understandingList 5 characteristics of gases12345
List 5 characteristics of gases according to the KMT12345
Gas Laws
Measurable Properties of GasesGases are described by their measurable
properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship
Boylersquos Lawbull Pressure and Volume are inversely
proportional at constant temperaturebull Pressure = Volume bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the
variable you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atm while the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=
P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=
P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=
P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Temeperature-Volume Relationship Charlersquos
Lawbull Volume and temperature are
proportional at constant pressurebull volume = temperature (K)bull Volume = temperature (K)
= kVT
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constantV1= 665 mL V2= mLT1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 KV1
T1
= V2
T2
V1
T1
=V2T2 =(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
= V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293
K T2= degC
V1
T1
= V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Temperature-Pressure Relationships Gay-Lussacrsquos
Lawbull Pressure and temperature are
proportional at constant volumebull pressure = temperature (K)bull pressure = temperature (K)
= kPT
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation
1 An aerosol can containing gas at 101 kPa and 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
=11 x 10^2 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
=49 x 10^2 K or 22 x10^2 degC
P2= 203 kPa
T1
Volume-Molar Relationships Avogadrorsquos
Lawbull Volume and number of moles (n) are
proportional at constant temperature and pressure
bull volume = number of molesbull volume = number of molesbull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
Checking for understandingState the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos LawAvogadrorsquos Law
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull The passage of gas particles through a small opening is called effusion
Effusion
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A
and B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar massbull Particles of low molar mass travel faster
than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
The Nature of Gases
bull Gases expand to fill their containersbull Gases are fluid ndash they flowbull Gases have low densityndash 11000 the density of the equivalent liquid
or solid
bull Gases are compressiblebull Gases effuse and diffuse
Gases Are Fluids
bull Gases are considered fluids
bull The word fluid means ldquoany substance that can flowrdquo
bull Gas particles can flow because they are relatively far apart and therefore are able to move past each other easily
Gases Have Low Densitybull Gases have much lower densities than
liquids and solids do - WHY ndash Because of the relatively large distances
between gas particles most of the volume occupied by a gas is empty space
bull The low density of gases also means that gas particles travel relatively long distances before colliding with each other
Gases are Highly Compressible
bull Suppose you completely fill a syringe with liquid and try to push the plunger in when the opening is plugged ndash You cannot make the space the liquid takes up become
smaller bull The space occupied by the gas particles is very
small compared with the total volume of the gasbull Applying a small pressure will move the gas
particles closer together and will decrease the volume
Gases Completely Fill a Container
bull A solid has a certain shape and volume
bull A liquid has a certain volume but takes the shape of the lower part of its container
bull In contrast a gas completely fills its container
bull Gas particles are constantly moving at high speeds and are far apart enough that they do not attract each other as much as particles of solids and liquids do
bull Therefore a gas expands to fill the entire volume available
Gas Pressure
Gas Pressurebull Earthrsquos atmosphere commonly known as air is a
mixture of gases mainly nitrogen and oxygen
bull As gas molecules are pulled toward the surface of Earth they collide with each other and with the surface of Earth more often Collisions of gas molecules are what cause air pressure
Measuring Pressure
Pressure = Area
Force Newton (N)
m2 cm2
Units of Pressure
1 atm = 760 torr = 1013 kPa = 760 mmHg
Standard Temperature Pressure (STP)
1 atm 0degC 224 L 1 mole
100 atm 760 mmHg = 760 x 10^2 mmHg
1 Covert 100 atm to mmHg
1 atm
300atm 1013 kPa = 304 kPa
2 Covert 300 atm to kPa
1 atm
3 What is 1000 KPa in atm
1000 kPa
1013 kPa = 09872 atm
1 atm
bull Measures atmospheric pressure
bull The atmosphere exerts pressure on the surface of mercury in the dish
bull This pressure goes through the fluid and up the column of mercury
bull The mercury settles at a point where the pressure exerted downward by its weight equals the pressure exerted by the atmosphere
Measuring Pressure Using Barometer
Gas Theory
Kinetic Molecular Theorybull Particles of matter are ALWAYS in motionbull Volume of individual particles is zerobull Collisions of particles with container walls cause
pressure exerted by gasbull Particles exert no forces on each otherbull Average kinetic energy is proportional to Kelvin
temperature of a gas
bull Ideal gas- imaginary perfect bull gas fitting the theory
Checking for understandingList 5 characteristics of gases12345
List 5 characteristics of gases according to the KMT12345
Gas Laws
Measurable Properties of GasesGases are described by their measurable
properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship
Boylersquos Lawbull Pressure and Volume are inversely
proportional at constant temperaturebull Pressure = Volume bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the
variable you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atm while the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=
P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=
P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=
P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Temeperature-Volume Relationship Charlersquos
Lawbull Volume and temperature are
proportional at constant pressurebull volume = temperature (K)bull Volume = temperature (K)
= kVT
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constantV1= 665 mL V2= mLT1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 KV1
T1
= V2
T2
V1
T1
=V2T2 =(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
= V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293
K T2= degC
V1
T1
= V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Temperature-Pressure Relationships Gay-Lussacrsquos
Lawbull Pressure and temperature are
proportional at constant volumebull pressure = temperature (K)bull pressure = temperature (K)
= kPT
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation
1 An aerosol can containing gas at 101 kPa and 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
=11 x 10^2 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
=49 x 10^2 K or 22 x10^2 degC
P2= 203 kPa
T1
Volume-Molar Relationships Avogadrorsquos
Lawbull Volume and number of moles (n) are
proportional at constant temperature and pressure
bull volume = number of molesbull volume = number of molesbull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
Checking for understandingState the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos LawAvogadrorsquos Law
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull The passage of gas particles through a small opening is called effusion
Effusion
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A
and B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar massbull Particles of low molar mass travel faster
than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Gases Are Fluids
bull Gases are considered fluids
bull The word fluid means ldquoany substance that can flowrdquo
bull Gas particles can flow because they are relatively far apart and therefore are able to move past each other easily
Gases Have Low Densitybull Gases have much lower densities than
liquids and solids do - WHY ndash Because of the relatively large distances
between gas particles most of the volume occupied by a gas is empty space
bull The low density of gases also means that gas particles travel relatively long distances before colliding with each other
Gases are Highly Compressible
bull Suppose you completely fill a syringe with liquid and try to push the plunger in when the opening is plugged ndash You cannot make the space the liquid takes up become
smaller bull The space occupied by the gas particles is very
small compared with the total volume of the gasbull Applying a small pressure will move the gas
particles closer together and will decrease the volume
Gases Completely Fill a Container
bull A solid has a certain shape and volume
bull A liquid has a certain volume but takes the shape of the lower part of its container
bull In contrast a gas completely fills its container
bull Gas particles are constantly moving at high speeds and are far apart enough that they do not attract each other as much as particles of solids and liquids do
bull Therefore a gas expands to fill the entire volume available
Gas Pressure
Gas Pressurebull Earthrsquos atmosphere commonly known as air is a
mixture of gases mainly nitrogen and oxygen
bull As gas molecules are pulled toward the surface of Earth they collide with each other and with the surface of Earth more often Collisions of gas molecules are what cause air pressure
Measuring Pressure
Pressure = Area
Force Newton (N)
m2 cm2
Units of Pressure
1 atm = 760 torr = 1013 kPa = 760 mmHg
Standard Temperature Pressure (STP)
1 atm 0degC 224 L 1 mole
100 atm 760 mmHg = 760 x 10^2 mmHg
1 Covert 100 atm to mmHg
1 atm
300atm 1013 kPa = 304 kPa
2 Covert 300 atm to kPa
1 atm
3 What is 1000 KPa in atm
1000 kPa
1013 kPa = 09872 atm
1 atm
bull Measures atmospheric pressure
bull The atmosphere exerts pressure on the surface of mercury in the dish
bull This pressure goes through the fluid and up the column of mercury
bull The mercury settles at a point where the pressure exerted downward by its weight equals the pressure exerted by the atmosphere
Measuring Pressure Using Barometer
Gas Theory
Kinetic Molecular Theorybull Particles of matter are ALWAYS in motionbull Volume of individual particles is zerobull Collisions of particles with container walls cause
pressure exerted by gasbull Particles exert no forces on each otherbull Average kinetic energy is proportional to Kelvin
temperature of a gas
bull Ideal gas- imaginary perfect bull gas fitting the theory
Checking for understandingList 5 characteristics of gases12345
List 5 characteristics of gases according to the KMT12345
Gas Laws
Measurable Properties of GasesGases are described by their measurable
properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship
Boylersquos Lawbull Pressure and Volume are inversely
proportional at constant temperaturebull Pressure = Volume bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the
variable you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atm while the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=
P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=
P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=
P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Temeperature-Volume Relationship Charlersquos
Lawbull Volume and temperature are
proportional at constant pressurebull volume = temperature (K)bull Volume = temperature (K)
= kVT
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constantV1= 665 mL V2= mLT1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 KV1
T1
= V2
T2
V1
T1
=V2T2 =(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
= V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293
K T2= degC
V1
T1
= V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Temperature-Pressure Relationships Gay-Lussacrsquos
Lawbull Pressure and temperature are
proportional at constant volumebull pressure = temperature (K)bull pressure = temperature (K)
= kPT
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation
1 An aerosol can containing gas at 101 kPa and 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
=11 x 10^2 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
=49 x 10^2 K or 22 x10^2 degC
P2= 203 kPa
T1
Volume-Molar Relationships Avogadrorsquos
Lawbull Volume and number of moles (n) are
proportional at constant temperature and pressure
bull volume = number of molesbull volume = number of molesbull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
Checking for understandingState the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos LawAvogadrorsquos Law
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull The passage of gas particles through a small opening is called effusion
Effusion
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A
and B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar massbull Particles of low molar mass travel faster
than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Gases Have Low Densitybull Gases have much lower densities than
liquids and solids do - WHY ndash Because of the relatively large distances
between gas particles most of the volume occupied by a gas is empty space
bull The low density of gases also means that gas particles travel relatively long distances before colliding with each other
Gases are Highly Compressible
bull Suppose you completely fill a syringe with liquid and try to push the plunger in when the opening is plugged ndash You cannot make the space the liquid takes up become
smaller bull The space occupied by the gas particles is very
small compared with the total volume of the gasbull Applying a small pressure will move the gas
particles closer together and will decrease the volume
Gases Completely Fill a Container
bull A solid has a certain shape and volume
bull A liquid has a certain volume but takes the shape of the lower part of its container
bull In contrast a gas completely fills its container
bull Gas particles are constantly moving at high speeds and are far apart enough that they do not attract each other as much as particles of solids and liquids do
bull Therefore a gas expands to fill the entire volume available
Gas Pressure
Gas Pressurebull Earthrsquos atmosphere commonly known as air is a
mixture of gases mainly nitrogen and oxygen
bull As gas molecules are pulled toward the surface of Earth they collide with each other and with the surface of Earth more often Collisions of gas molecules are what cause air pressure
Measuring Pressure
Pressure = Area
Force Newton (N)
m2 cm2
Units of Pressure
1 atm = 760 torr = 1013 kPa = 760 mmHg
Standard Temperature Pressure (STP)
1 atm 0degC 224 L 1 mole
100 atm 760 mmHg = 760 x 10^2 mmHg
1 Covert 100 atm to mmHg
1 atm
300atm 1013 kPa = 304 kPa
2 Covert 300 atm to kPa
1 atm
3 What is 1000 KPa in atm
1000 kPa
1013 kPa = 09872 atm
1 atm
bull Measures atmospheric pressure
bull The atmosphere exerts pressure on the surface of mercury in the dish
bull This pressure goes through the fluid and up the column of mercury
bull The mercury settles at a point where the pressure exerted downward by its weight equals the pressure exerted by the atmosphere
Measuring Pressure Using Barometer
Gas Theory
Kinetic Molecular Theorybull Particles of matter are ALWAYS in motionbull Volume of individual particles is zerobull Collisions of particles with container walls cause
pressure exerted by gasbull Particles exert no forces on each otherbull Average kinetic energy is proportional to Kelvin
temperature of a gas
bull Ideal gas- imaginary perfect bull gas fitting the theory
Checking for understandingList 5 characteristics of gases12345
List 5 characteristics of gases according to the KMT12345
Gas Laws
Measurable Properties of GasesGases are described by their measurable
properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship
Boylersquos Lawbull Pressure and Volume are inversely
proportional at constant temperaturebull Pressure = Volume bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the
variable you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atm while the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=
P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=
P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=
P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Temeperature-Volume Relationship Charlersquos
Lawbull Volume and temperature are
proportional at constant pressurebull volume = temperature (K)bull Volume = temperature (K)
= kVT
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constantV1= 665 mL V2= mLT1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 KV1
T1
= V2
T2
V1
T1
=V2T2 =(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
= V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293
K T2= degC
V1
T1
= V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Temperature-Pressure Relationships Gay-Lussacrsquos
Lawbull Pressure and temperature are
proportional at constant volumebull pressure = temperature (K)bull pressure = temperature (K)
= kPT
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation
1 An aerosol can containing gas at 101 kPa and 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
=11 x 10^2 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
=49 x 10^2 K or 22 x10^2 degC
P2= 203 kPa
T1
Volume-Molar Relationships Avogadrorsquos
Lawbull Volume and number of moles (n) are
proportional at constant temperature and pressure
bull volume = number of molesbull volume = number of molesbull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
Checking for understandingState the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos LawAvogadrorsquos Law
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull The passage of gas particles through a small opening is called effusion
Effusion
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A
and B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar massbull Particles of low molar mass travel faster
than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Gases are Highly Compressible
bull Suppose you completely fill a syringe with liquid and try to push the plunger in when the opening is plugged ndash You cannot make the space the liquid takes up become
smaller bull The space occupied by the gas particles is very
small compared with the total volume of the gasbull Applying a small pressure will move the gas
particles closer together and will decrease the volume
Gases Completely Fill a Container
bull A solid has a certain shape and volume
bull A liquid has a certain volume but takes the shape of the lower part of its container
bull In contrast a gas completely fills its container
bull Gas particles are constantly moving at high speeds and are far apart enough that they do not attract each other as much as particles of solids and liquids do
bull Therefore a gas expands to fill the entire volume available
Gas Pressure
Gas Pressurebull Earthrsquos atmosphere commonly known as air is a
mixture of gases mainly nitrogen and oxygen
bull As gas molecules are pulled toward the surface of Earth they collide with each other and with the surface of Earth more often Collisions of gas molecules are what cause air pressure
Measuring Pressure
Pressure = Area
Force Newton (N)
m2 cm2
Units of Pressure
1 atm = 760 torr = 1013 kPa = 760 mmHg
Standard Temperature Pressure (STP)
1 atm 0degC 224 L 1 mole
100 atm 760 mmHg = 760 x 10^2 mmHg
1 Covert 100 atm to mmHg
1 atm
300atm 1013 kPa = 304 kPa
2 Covert 300 atm to kPa
1 atm
3 What is 1000 KPa in atm
1000 kPa
1013 kPa = 09872 atm
1 atm
bull Measures atmospheric pressure
bull The atmosphere exerts pressure on the surface of mercury in the dish
bull This pressure goes through the fluid and up the column of mercury
bull The mercury settles at a point where the pressure exerted downward by its weight equals the pressure exerted by the atmosphere
Measuring Pressure Using Barometer
Gas Theory
Kinetic Molecular Theorybull Particles of matter are ALWAYS in motionbull Volume of individual particles is zerobull Collisions of particles with container walls cause
pressure exerted by gasbull Particles exert no forces on each otherbull Average kinetic energy is proportional to Kelvin
temperature of a gas
bull Ideal gas- imaginary perfect bull gas fitting the theory
Checking for understandingList 5 characteristics of gases12345
List 5 characteristics of gases according to the KMT12345
Gas Laws
Measurable Properties of GasesGases are described by their measurable
properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship
Boylersquos Lawbull Pressure and Volume are inversely
proportional at constant temperaturebull Pressure = Volume bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the
variable you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atm while the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=
P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=
P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=
P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Temeperature-Volume Relationship Charlersquos
Lawbull Volume and temperature are
proportional at constant pressurebull volume = temperature (K)bull Volume = temperature (K)
= kVT
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constantV1= 665 mL V2= mLT1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 KV1
T1
= V2
T2
V1
T1
=V2T2 =(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
= V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293
K T2= degC
V1
T1
= V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Temperature-Pressure Relationships Gay-Lussacrsquos
Lawbull Pressure and temperature are
proportional at constant volumebull pressure = temperature (K)bull pressure = temperature (K)
= kPT
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation
1 An aerosol can containing gas at 101 kPa and 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
=11 x 10^2 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
=49 x 10^2 K or 22 x10^2 degC
P2= 203 kPa
T1
Volume-Molar Relationships Avogadrorsquos
Lawbull Volume and number of moles (n) are
proportional at constant temperature and pressure
bull volume = number of molesbull volume = number of molesbull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
Checking for understandingState the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos LawAvogadrorsquos Law
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull The passage of gas particles through a small opening is called effusion
Effusion
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A
and B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar massbull Particles of low molar mass travel faster
than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Gases Completely Fill a Container
bull A solid has a certain shape and volume
bull A liquid has a certain volume but takes the shape of the lower part of its container
bull In contrast a gas completely fills its container
bull Gas particles are constantly moving at high speeds and are far apart enough that they do not attract each other as much as particles of solids and liquids do
bull Therefore a gas expands to fill the entire volume available
Gas Pressure
Gas Pressurebull Earthrsquos atmosphere commonly known as air is a
mixture of gases mainly nitrogen and oxygen
bull As gas molecules are pulled toward the surface of Earth they collide with each other and with the surface of Earth more often Collisions of gas molecules are what cause air pressure
Measuring Pressure
Pressure = Area
Force Newton (N)
m2 cm2
Units of Pressure
1 atm = 760 torr = 1013 kPa = 760 mmHg
Standard Temperature Pressure (STP)
1 atm 0degC 224 L 1 mole
100 atm 760 mmHg = 760 x 10^2 mmHg
1 Covert 100 atm to mmHg
1 atm
300atm 1013 kPa = 304 kPa
2 Covert 300 atm to kPa
1 atm
3 What is 1000 KPa in atm
1000 kPa
1013 kPa = 09872 atm
1 atm
bull Measures atmospheric pressure
bull The atmosphere exerts pressure on the surface of mercury in the dish
bull This pressure goes through the fluid and up the column of mercury
bull The mercury settles at a point where the pressure exerted downward by its weight equals the pressure exerted by the atmosphere
Measuring Pressure Using Barometer
Gas Theory
Kinetic Molecular Theorybull Particles of matter are ALWAYS in motionbull Volume of individual particles is zerobull Collisions of particles with container walls cause
pressure exerted by gasbull Particles exert no forces on each otherbull Average kinetic energy is proportional to Kelvin
temperature of a gas
bull Ideal gas- imaginary perfect bull gas fitting the theory
Checking for understandingList 5 characteristics of gases12345
List 5 characteristics of gases according to the KMT12345
Gas Laws
Measurable Properties of GasesGases are described by their measurable
properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship
Boylersquos Lawbull Pressure and Volume are inversely
proportional at constant temperaturebull Pressure = Volume bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the
variable you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atm while the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=
P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=
P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=
P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Temeperature-Volume Relationship Charlersquos
Lawbull Volume and temperature are
proportional at constant pressurebull volume = temperature (K)bull Volume = temperature (K)
= kVT
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constantV1= 665 mL V2= mLT1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 KV1
T1
= V2
T2
V1
T1
=V2T2 =(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
= V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293
K T2= degC
V1
T1
= V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Temperature-Pressure Relationships Gay-Lussacrsquos
Lawbull Pressure and temperature are
proportional at constant volumebull pressure = temperature (K)bull pressure = temperature (K)
= kPT
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation
1 An aerosol can containing gas at 101 kPa and 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
=11 x 10^2 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
=49 x 10^2 K or 22 x10^2 degC
P2= 203 kPa
T1
Volume-Molar Relationships Avogadrorsquos
Lawbull Volume and number of moles (n) are
proportional at constant temperature and pressure
bull volume = number of molesbull volume = number of molesbull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
Checking for understandingState the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos LawAvogadrorsquos Law
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull The passage of gas particles through a small opening is called effusion
Effusion
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A
and B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar massbull Particles of low molar mass travel faster
than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Gas Pressure
Gas Pressurebull Earthrsquos atmosphere commonly known as air is a
mixture of gases mainly nitrogen and oxygen
bull As gas molecules are pulled toward the surface of Earth they collide with each other and with the surface of Earth more often Collisions of gas molecules are what cause air pressure
Measuring Pressure
Pressure = Area
Force Newton (N)
m2 cm2
Units of Pressure
1 atm = 760 torr = 1013 kPa = 760 mmHg
Standard Temperature Pressure (STP)
1 atm 0degC 224 L 1 mole
100 atm 760 mmHg = 760 x 10^2 mmHg
1 Covert 100 atm to mmHg
1 atm
300atm 1013 kPa = 304 kPa
2 Covert 300 atm to kPa
1 atm
3 What is 1000 KPa in atm
1000 kPa
1013 kPa = 09872 atm
1 atm
bull Measures atmospheric pressure
bull The atmosphere exerts pressure on the surface of mercury in the dish
bull This pressure goes through the fluid and up the column of mercury
bull The mercury settles at a point where the pressure exerted downward by its weight equals the pressure exerted by the atmosphere
Measuring Pressure Using Barometer
Gas Theory
Kinetic Molecular Theorybull Particles of matter are ALWAYS in motionbull Volume of individual particles is zerobull Collisions of particles with container walls cause
pressure exerted by gasbull Particles exert no forces on each otherbull Average kinetic energy is proportional to Kelvin
temperature of a gas
bull Ideal gas- imaginary perfect bull gas fitting the theory
Checking for understandingList 5 characteristics of gases12345
List 5 characteristics of gases according to the KMT12345
Gas Laws
Measurable Properties of GasesGases are described by their measurable
properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship
Boylersquos Lawbull Pressure and Volume are inversely
proportional at constant temperaturebull Pressure = Volume bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the
variable you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atm while the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=
P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=
P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=
P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Temeperature-Volume Relationship Charlersquos
Lawbull Volume and temperature are
proportional at constant pressurebull volume = temperature (K)bull Volume = temperature (K)
= kVT
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constantV1= 665 mL V2= mLT1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 KV1
T1
= V2
T2
V1
T1
=V2T2 =(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
= V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293
K T2= degC
V1
T1
= V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Temperature-Pressure Relationships Gay-Lussacrsquos
Lawbull Pressure and temperature are
proportional at constant volumebull pressure = temperature (K)bull pressure = temperature (K)
= kPT
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation
1 An aerosol can containing gas at 101 kPa and 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
=11 x 10^2 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
=49 x 10^2 K or 22 x10^2 degC
P2= 203 kPa
T1
Volume-Molar Relationships Avogadrorsquos
Lawbull Volume and number of moles (n) are
proportional at constant temperature and pressure
bull volume = number of molesbull volume = number of molesbull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
Checking for understandingState the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos LawAvogadrorsquos Law
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull The passage of gas particles through a small opening is called effusion
Effusion
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A
and B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar massbull Particles of low molar mass travel faster
than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Gas Pressurebull Earthrsquos atmosphere commonly known as air is a
mixture of gases mainly nitrogen and oxygen
bull As gas molecules are pulled toward the surface of Earth they collide with each other and with the surface of Earth more often Collisions of gas molecules are what cause air pressure
Measuring Pressure
Pressure = Area
Force Newton (N)
m2 cm2
Units of Pressure
1 atm = 760 torr = 1013 kPa = 760 mmHg
Standard Temperature Pressure (STP)
1 atm 0degC 224 L 1 mole
100 atm 760 mmHg = 760 x 10^2 mmHg
1 Covert 100 atm to mmHg
1 atm
300atm 1013 kPa = 304 kPa
2 Covert 300 atm to kPa
1 atm
3 What is 1000 KPa in atm
1000 kPa
1013 kPa = 09872 atm
1 atm
bull Measures atmospheric pressure
bull The atmosphere exerts pressure on the surface of mercury in the dish
bull This pressure goes through the fluid and up the column of mercury
bull The mercury settles at a point where the pressure exerted downward by its weight equals the pressure exerted by the atmosphere
Measuring Pressure Using Barometer
Gas Theory
Kinetic Molecular Theorybull Particles of matter are ALWAYS in motionbull Volume of individual particles is zerobull Collisions of particles with container walls cause
pressure exerted by gasbull Particles exert no forces on each otherbull Average kinetic energy is proportional to Kelvin
temperature of a gas
bull Ideal gas- imaginary perfect bull gas fitting the theory
Checking for understandingList 5 characteristics of gases12345
List 5 characteristics of gases according to the KMT12345
Gas Laws
Measurable Properties of GasesGases are described by their measurable
properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship
Boylersquos Lawbull Pressure and Volume are inversely
proportional at constant temperaturebull Pressure = Volume bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the
variable you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atm while the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=
P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=
P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=
P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Temeperature-Volume Relationship Charlersquos
Lawbull Volume and temperature are
proportional at constant pressurebull volume = temperature (K)bull Volume = temperature (K)
= kVT
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constantV1= 665 mL V2= mLT1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 KV1
T1
= V2
T2
V1
T1
=V2T2 =(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
= V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293
K T2= degC
V1
T1
= V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Temperature-Pressure Relationships Gay-Lussacrsquos
Lawbull Pressure and temperature are
proportional at constant volumebull pressure = temperature (K)bull pressure = temperature (K)
= kPT
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation
1 An aerosol can containing gas at 101 kPa and 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
=11 x 10^2 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
=49 x 10^2 K or 22 x10^2 degC
P2= 203 kPa
T1
Volume-Molar Relationships Avogadrorsquos
Lawbull Volume and number of moles (n) are
proportional at constant temperature and pressure
bull volume = number of molesbull volume = number of molesbull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
Checking for understandingState the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos LawAvogadrorsquos Law
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull The passage of gas particles through a small opening is called effusion
Effusion
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A
and B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar massbull Particles of low molar mass travel faster
than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Measuring Pressure
Pressure = Area
Force Newton (N)
m2 cm2
Units of Pressure
1 atm = 760 torr = 1013 kPa = 760 mmHg
Standard Temperature Pressure (STP)
1 atm 0degC 224 L 1 mole
100 atm 760 mmHg = 760 x 10^2 mmHg
1 Covert 100 atm to mmHg
1 atm
300atm 1013 kPa = 304 kPa
2 Covert 300 atm to kPa
1 atm
3 What is 1000 KPa in atm
1000 kPa
1013 kPa = 09872 atm
1 atm
bull Measures atmospheric pressure
bull The atmosphere exerts pressure on the surface of mercury in the dish
bull This pressure goes through the fluid and up the column of mercury
bull The mercury settles at a point where the pressure exerted downward by its weight equals the pressure exerted by the atmosphere
Measuring Pressure Using Barometer
Gas Theory
Kinetic Molecular Theorybull Particles of matter are ALWAYS in motionbull Volume of individual particles is zerobull Collisions of particles with container walls cause
pressure exerted by gasbull Particles exert no forces on each otherbull Average kinetic energy is proportional to Kelvin
temperature of a gas
bull Ideal gas- imaginary perfect bull gas fitting the theory
Checking for understandingList 5 characteristics of gases12345
List 5 characteristics of gases according to the KMT12345
Gas Laws
Measurable Properties of GasesGases are described by their measurable
properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship
Boylersquos Lawbull Pressure and Volume are inversely
proportional at constant temperaturebull Pressure = Volume bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the
variable you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atm while the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=
P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=
P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=
P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Temeperature-Volume Relationship Charlersquos
Lawbull Volume and temperature are
proportional at constant pressurebull volume = temperature (K)bull Volume = temperature (K)
= kVT
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constantV1= 665 mL V2= mLT1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 KV1
T1
= V2
T2
V1
T1
=V2T2 =(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
= V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293
K T2= degC
V1
T1
= V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Temperature-Pressure Relationships Gay-Lussacrsquos
Lawbull Pressure and temperature are
proportional at constant volumebull pressure = temperature (K)bull pressure = temperature (K)
= kPT
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation
1 An aerosol can containing gas at 101 kPa and 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
=11 x 10^2 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
=49 x 10^2 K or 22 x10^2 degC
P2= 203 kPa
T1
Volume-Molar Relationships Avogadrorsquos
Lawbull Volume and number of moles (n) are
proportional at constant temperature and pressure
bull volume = number of molesbull volume = number of molesbull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
Checking for understandingState the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos LawAvogadrorsquos Law
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull The passage of gas particles through a small opening is called effusion
Effusion
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A
and B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar massbull Particles of low molar mass travel faster
than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
100 atm 760 mmHg = 760 x 10^2 mmHg
1 Covert 100 atm to mmHg
1 atm
300atm 1013 kPa = 304 kPa
2 Covert 300 atm to kPa
1 atm
3 What is 1000 KPa in atm
1000 kPa
1013 kPa = 09872 atm
1 atm
bull Measures atmospheric pressure
bull The atmosphere exerts pressure on the surface of mercury in the dish
bull This pressure goes through the fluid and up the column of mercury
bull The mercury settles at a point where the pressure exerted downward by its weight equals the pressure exerted by the atmosphere
Measuring Pressure Using Barometer
Gas Theory
Kinetic Molecular Theorybull Particles of matter are ALWAYS in motionbull Volume of individual particles is zerobull Collisions of particles with container walls cause
pressure exerted by gasbull Particles exert no forces on each otherbull Average kinetic energy is proportional to Kelvin
temperature of a gas
bull Ideal gas- imaginary perfect bull gas fitting the theory
Checking for understandingList 5 characteristics of gases12345
List 5 characteristics of gases according to the KMT12345
Gas Laws
Measurable Properties of GasesGases are described by their measurable
properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship
Boylersquos Lawbull Pressure and Volume are inversely
proportional at constant temperaturebull Pressure = Volume bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the
variable you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atm while the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=
P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=
P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=
P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Temeperature-Volume Relationship Charlersquos
Lawbull Volume and temperature are
proportional at constant pressurebull volume = temperature (K)bull Volume = temperature (K)
= kVT
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constantV1= 665 mL V2= mLT1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 KV1
T1
= V2
T2
V1
T1
=V2T2 =(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
= V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293
K T2= degC
V1
T1
= V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Temperature-Pressure Relationships Gay-Lussacrsquos
Lawbull Pressure and temperature are
proportional at constant volumebull pressure = temperature (K)bull pressure = temperature (K)
= kPT
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation
1 An aerosol can containing gas at 101 kPa and 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
=11 x 10^2 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
=49 x 10^2 K or 22 x10^2 degC
P2= 203 kPa
T1
Volume-Molar Relationships Avogadrorsquos
Lawbull Volume and number of moles (n) are
proportional at constant temperature and pressure
bull volume = number of molesbull volume = number of molesbull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
Checking for understandingState the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos LawAvogadrorsquos Law
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull The passage of gas particles through a small opening is called effusion
Effusion
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A
and B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar massbull Particles of low molar mass travel faster
than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
bull Measures atmospheric pressure
bull The atmosphere exerts pressure on the surface of mercury in the dish
bull This pressure goes through the fluid and up the column of mercury
bull The mercury settles at a point where the pressure exerted downward by its weight equals the pressure exerted by the atmosphere
Measuring Pressure Using Barometer
Gas Theory
Kinetic Molecular Theorybull Particles of matter are ALWAYS in motionbull Volume of individual particles is zerobull Collisions of particles with container walls cause
pressure exerted by gasbull Particles exert no forces on each otherbull Average kinetic energy is proportional to Kelvin
temperature of a gas
bull Ideal gas- imaginary perfect bull gas fitting the theory
Checking for understandingList 5 characteristics of gases12345
List 5 characteristics of gases according to the KMT12345
Gas Laws
Measurable Properties of GasesGases are described by their measurable
properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship
Boylersquos Lawbull Pressure and Volume are inversely
proportional at constant temperaturebull Pressure = Volume bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the
variable you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atm while the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=
P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=
P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=
P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Temeperature-Volume Relationship Charlersquos
Lawbull Volume and temperature are
proportional at constant pressurebull volume = temperature (K)bull Volume = temperature (K)
= kVT
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constantV1= 665 mL V2= mLT1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 KV1
T1
= V2
T2
V1
T1
=V2T2 =(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
= V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293
K T2= degC
V1
T1
= V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Temperature-Pressure Relationships Gay-Lussacrsquos
Lawbull Pressure and temperature are
proportional at constant volumebull pressure = temperature (K)bull pressure = temperature (K)
= kPT
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation
1 An aerosol can containing gas at 101 kPa and 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
=11 x 10^2 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
=49 x 10^2 K or 22 x10^2 degC
P2= 203 kPa
T1
Volume-Molar Relationships Avogadrorsquos
Lawbull Volume and number of moles (n) are
proportional at constant temperature and pressure
bull volume = number of molesbull volume = number of molesbull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
Checking for understandingState the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos LawAvogadrorsquos Law
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull The passage of gas particles through a small opening is called effusion
Effusion
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A
and B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar massbull Particles of low molar mass travel faster
than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Gas Theory
Kinetic Molecular Theorybull Particles of matter are ALWAYS in motionbull Volume of individual particles is zerobull Collisions of particles with container walls cause
pressure exerted by gasbull Particles exert no forces on each otherbull Average kinetic energy is proportional to Kelvin
temperature of a gas
bull Ideal gas- imaginary perfect bull gas fitting the theory
Checking for understandingList 5 characteristics of gases12345
List 5 characteristics of gases according to the KMT12345
Gas Laws
Measurable Properties of GasesGases are described by their measurable
properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship
Boylersquos Lawbull Pressure and Volume are inversely
proportional at constant temperaturebull Pressure = Volume bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the
variable you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atm while the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=
P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=
P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=
P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Temeperature-Volume Relationship Charlersquos
Lawbull Volume and temperature are
proportional at constant pressurebull volume = temperature (K)bull Volume = temperature (K)
= kVT
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constantV1= 665 mL V2= mLT1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 KV1
T1
= V2
T2
V1
T1
=V2T2 =(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
= V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293
K T2= degC
V1
T1
= V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Temperature-Pressure Relationships Gay-Lussacrsquos
Lawbull Pressure and temperature are
proportional at constant volumebull pressure = temperature (K)bull pressure = temperature (K)
= kPT
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation
1 An aerosol can containing gas at 101 kPa and 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
=11 x 10^2 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
=49 x 10^2 K or 22 x10^2 degC
P2= 203 kPa
T1
Volume-Molar Relationships Avogadrorsquos
Lawbull Volume and number of moles (n) are
proportional at constant temperature and pressure
bull volume = number of molesbull volume = number of molesbull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
Checking for understandingState the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos LawAvogadrorsquos Law
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull The passage of gas particles through a small opening is called effusion
Effusion
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A
and B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar massbull Particles of low molar mass travel faster
than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Kinetic Molecular Theorybull Particles of matter are ALWAYS in motionbull Volume of individual particles is zerobull Collisions of particles with container walls cause
pressure exerted by gasbull Particles exert no forces on each otherbull Average kinetic energy is proportional to Kelvin
temperature of a gas
bull Ideal gas- imaginary perfect bull gas fitting the theory
Checking for understandingList 5 characteristics of gases12345
List 5 characteristics of gases according to the KMT12345
Gas Laws
Measurable Properties of GasesGases are described by their measurable
properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship
Boylersquos Lawbull Pressure and Volume are inversely
proportional at constant temperaturebull Pressure = Volume bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the
variable you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atm while the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=
P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=
P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=
P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Temeperature-Volume Relationship Charlersquos
Lawbull Volume and temperature are
proportional at constant pressurebull volume = temperature (K)bull Volume = temperature (K)
= kVT
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constantV1= 665 mL V2= mLT1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 KV1
T1
= V2
T2
V1
T1
=V2T2 =(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
= V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293
K T2= degC
V1
T1
= V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Temperature-Pressure Relationships Gay-Lussacrsquos
Lawbull Pressure and temperature are
proportional at constant volumebull pressure = temperature (K)bull pressure = temperature (K)
= kPT
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation
1 An aerosol can containing gas at 101 kPa and 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
=11 x 10^2 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
=49 x 10^2 K or 22 x10^2 degC
P2= 203 kPa
T1
Volume-Molar Relationships Avogadrorsquos
Lawbull Volume and number of moles (n) are
proportional at constant temperature and pressure
bull volume = number of molesbull volume = number of molesbull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
Checking for understandingState the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos LawAvogadrorsquos Law
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull The passage of gas particles through a small opening is called effusion
Effusion
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A
and B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar massbull Particles of low molar mass travel faster
than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Checking for understandingList 5 characteristics of gases12345
List 5 characteristics of gases according to the KMT12345
Gas Laws
Measurable Properties of GasesGases are described by their measurable
properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship
Boylersquos Lawbull Pressure and Volume are inversely
proportional at constant temperaturebull Pressure = Volume bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the
variable you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atm while the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=
P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=
P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=
P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Temeperature-Volume Relationship Charlersquos
Lawbull Volume and temperature are
proportional at constant pressurebull volume = temperature (K)bull Volume = temperature (K)
= kVT
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constantV1= 665 mL V2= mLT1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 KV1
T1
= V2
T2
V1
T1
=V2T2 =(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
= V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293
K T2= degC
V1
T1
= V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Temperature-Pressure Relationships Gay-Lussacrsquos
Lawbull Pressure and temperature are
proportional at constant volumebull pressure = temperature (K)bull pressure = temperature (K)
= kPT
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation
1 An aerosol can containing gas at 101 kPa and 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
=11 x 10^2 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
=49 x 10^2 K or 22 x10^2 degC
P2= 203 kPa
T1
Volume-Molar Relationships Avogadrorsquos
Lawbull Volume and number of moles (n) are
proportional at constant temperature and pressure
bull volume = number of molesbull volume = number of molesbull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
Checking for understandingState the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos LawAvogadrorsquos Law
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull The passage of gas particles through a small opening is called effusion
Effusion
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A
and B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar massbull Particles of low molar mass travel faster
than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Gas Laws
Measurable Properties of GasesGases are described by their measurable
properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship
Boylersquos Lawbull Pressure and Volume are inversely
proportional at constant temperaturebull Pressure = Volume bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the
variable you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atm while the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=
P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=
P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=
P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Temeperature-Volume Relationship Charlersquos
Lawbull Volume and temperature are
proportional at constant pressurebull volume = temperature (K)bull Volume = temperature (K)
= kVT
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constantV1= 665 mL V2= mLT1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 KV1
T1
= V2
T2
V1
T1
=V2T2 =(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
= V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293
K T2= degC
V1
T1
= V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Temperature-Pressure Relationships Gay-Lussacrsquos
Lawbull Pressure and temperature are
proportional at constant volumebull pressure = temperature (K)bull pressure = temperature (K)
= kPT
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation
1 An aerosol can containing gas at 101 kPa and 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
=11 x 10^2 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
=49 x 10^2 K or 22 x10^2 degC
P2= 203 kPa
T1
Volume-Molar Relationships Avogadrorsquos
Lawbull Volume and number of moles (n) are
proportional at constant temperature and pressure
bull volume = number of molesbull volume = number of molesbull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
Checking for understandingState the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos LawAvogadrorsquos Law
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull The passage of gas particles through a small opening is called effusion
Effusion
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A
and B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar massbull Particles of low molar mass travel faster
than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Measurable Properties of GasesGases are described by their measurable
properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship
Boylersquos Lawbull Pressure and Volume are inversely
proportional at constant temperaturebull Pressure = Volume bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the
variable you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atm while the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=
P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=
P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=
P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Temeperature-Volume Relationship Charlersquos
Lawbull Volume and temperature are
proportional at constant pressurebull volume = temperature (K)bull Volume = temperature (K)
= kVT
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constantV1= 665 mL V2= mLT1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 KV1
T1
= V2
T2
V1
T1
=V2T2 =(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
= V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293
K T2= degC
V1
T1
= V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Temperature-Pressure Relationships Gay-Lussacrsquos
Lawbull Pressure and temperature are
proportional at constant volumebull pressure = temperature (K)bull pressure = temperature (K)
= kPT
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation
1 An aerosol can containing gas at 101 kPa and 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
=11 x 10^2 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
=49 x 10^2 K or 22 x10^2 degC
P2= 203 kPa
T1
Volume-Molar Relationships Avogadrorsquos
Lawbull Volume and number of moles (n) are
proportional at constant temperature and pressure
bull volume = number of molesbull volume = number of molesbull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
Checking for understandingState the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos LawAvogadrorsquos Law
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull The passage of gas particles through a small opening is called effusion
Effusion
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A
and B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar massbull Particles of low molar mass travel faster
than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship
Boylersquos Lawbull Pressure and Volume are inversely
proportional at constant temperaturebull Pressure = Volume bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the
variable you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atm while the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=
P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=
P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=
P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Temeperature-Volume Relationship Charlersquos
Lawbull Volume and temperature are
proportional at constant pressurebull volume = temperature (K)bull Volume = temperature (K)
= kVT
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constantV1= 665 mL V2= mLT1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 KV1
T1
= V2
T2
V1
T1
=V2T2 =(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
= V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293
K T2= degC
V1
T1
= V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Temperature-Pressure Relationships Gay-Lussacrsquos
Lawbull Pressure and temperature are
proportional at constant volumebull pressure = temperature (K)bull pressure = temperature (K)
= kPT
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation
1 An aerosol can containing gas at 101 kPa and 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
=11 x 10^2 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
=49 x 10^2 K or 22 x10^2 degC
P2= 203 kPa
T1
Volume-Molar Relationships Avogadrorsquos
Lawbull Volume and number of moles (n) are
proportional at constant temperature and pressure
bull volume = number of molesbull volume = number of molesbull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
Checking for understandingState the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos LawAvogadrorsquos Law
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull The passage of gas particles through a small opening is called effusion
Effusion
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A
and B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar massbull Particles of low molar mass travel faster
than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Pressure-Volume Relationship
Boylersquos Lawbull Pressure and Volume are inversely
proportional at constant temperaturebull Pressure = Volume bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the
variable you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atm while the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=
P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=
P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=
P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Temeperature-Volume Relationship Charlersquos
Lawbull Volume and temperature are
proportional at constant pressurebull volume = temperature (K)bull Volume = temperature (K)
= kVT
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constantV1= 665 mL V2= mLT1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 KV1
T1
= V2
T2
V1
T1
=V2T2 =(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
= V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293
K T2= degC
V1
T1
= V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Temperature-Pressure Relationships Gay-Lussacrsquos
Lawbull Pressure and temperature are
proportional at constant volumebull pressure = temperature (K)bull pressure = temperature (K)
= kPT
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation
1 An aerosol can containing gas at 101 kPa and 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
=11 x 10^2 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
=49 x 10^2 K or 22 x10^2 degC
P2= 203 kPa
T1
Volume-Molar Relationships Avogadrorsquos
Lawbull Volume and number of moles (n) are
proportional at constant temperature and pressure
bull volume = number of molesbull volume = number of molesbull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
Checking for understandingState the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos LawAvogadrorsquos Law
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull The passage of gas particles through a small opening is called effusion
Effusion
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A
and B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar massbull Particles of low molar mass travel faster
than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the
variable you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atm while the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=
P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=
P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=
P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Temeperature-Volume Relationship Charlersquos
Lawbull Volume and temperature are
proportional at constant pressurebull volume = temperature (K)bull Volume = temperature (K)
= kVT
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constantV1= 665 mL V2= mLT1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 KV1
T1
= V2
T2
V1
T1
=V2T2 =(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
= V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293
K T2= degC
V1
T1
= V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Temperature-Pressure Relationships Gay-Lussacrsquos
Lawbull Pressure and temperature are
proportional at constant volumebull pressure = temperature (K)bull pressure = temperature (K)
= kPT
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation
1 An aerosol can containing gas at 101 kPa and 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
=11 x 10^2 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
=49 x 10^2 K or 22 x10^2 degC
P2= 203 kPa
T1
Volume-Molar Relationships Avogadrorsquos
Lawbull Volume and number of moles (n) are
proportional at constant temperature and pressure
bull volume = number of molesbull volume = number of molesbull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
Checking for understandingState the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos LawAvogadrorsquos Law
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull The passage of gas particles through a small opening is called effusion
Effusion
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A
and B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar massbull Particles of low molar mass travel faster
than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atm while the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=
P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=
P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=
P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Temeperature-Volume Relationship Charlersquos
Lawbull Volume and temperature are
proportional at constant pressurebull volume = temperature (K)bull Volume = temperature (K)
= kVT
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constantV1= 665 mL V2= mLT1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 KV1
T1
= V2
T2
V1
T1
=V2T2 =(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
= V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293
K T2= degC
V1
T1
= V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Temperature-Pressure Relationships Gay-Lussacrsquos
Lawbull Pressure and temperature are
proportional at constant volumebull pressure = temperature (K)bull pressure = temperature (K)
= kPT
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation
1 An aerosol can containing gas at 101 kPa and 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
=11 x 10^2 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
=49 x 10^2 K or 22 x10^2 degC
P2= 203 kPa
T1
Volume-Molar Relationships Avogadrorsquos
Lawbull Volume and number of moles (n) are
proportional at constant temperature and pressure
bull volume = number of molesbull volume = number of molesbull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
Checking for understandingState the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos LawAvogadrorsquos Law
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull The passage of gas particles through a small opening is called effusion
Effusion
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A
and B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar massbull Particles of low molar mass travel faster
than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=
P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=
P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Temeperature-Volume Relationship Charlersquos
Lawbull Volume and temperature are
proportional at constant pressurebull volume = temperature (K)bull Volume = temperature (K)
= kVT
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constantV1= 665 mL V2= mLT1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 KV1
T1
= V2
T2
V1
T1
=V2T2 =(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
= V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293
K T2= degC
V1
T1
= V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Temperature-Pressure Relationships Gay-Lussacrsquos
Lawbull Pressure and temperature are
proportional at constant volumebull pressure = temperature (K)bull pressure = temperature (K)
= kPT
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation
1 An aerosol can containing gas at 101 kPa and 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
=11 x 10^2 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
=49 x 10^2 K or 22 x10^2 degC
P2= 203 kPa
T1
Volume-Molar Relationships Avogadrorsquos
Lawbull Volume and number of moles (n) are
proportional at constant temperature and pressure
bull volume = number of molesbull volume = number of molesbull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
Checking for understandingState the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos LawAvogadrorsquos Law
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull The passage of gas particles through a small opening is called effusion
Effusion
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A
and B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar massbull Particles of low molar mass travel faster
than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=
P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Temeperature-Volume Relationship Charlersquos
Lawbull Volume and temperature are
proportional at constant pressurebull volume = temperature (K)bull Volume = temperature (K)
= kVT
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constantV1= 665 mL V2= mLT1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 KV1
T1
= V2
T2
V1
T1
=V2T2 =(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
= V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293
K T2= degC
V1
T1
= V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Temperature-Pressure Relationships Gay-Lussacrsquos
Lawbull Pressure and temperature are
proportional at constant volumebull pressure = temperature (K)bull pressure = temperature (K)
= kPT
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation
1 An aerosol can containing gas at 101 kPa and 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
=11 x 10^2 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
=49 x 10^2 K or 22 x10^2 degC
P2= 203 kPa
T1
Volume-Molar Relationships Avogadrorsquos
Lawbull Volume and number of moles (n) are
proportional at constant temperature and pressure
bull volume = number of molesbull volume = number of molesbull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
Checking for understandingState the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos LawAvogadrorsquos Law
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull The passage of gas particles through a small opening is called effusion
Effusion
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A
and B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar massbull Particles of low molar mass travel faster
than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Temeperature-Volume Relationship Charlersquos
Lawbull Volume and temperature are
proportional at constant pressurebull volume = temperature (K)bull Volume = temperature (K)
= kVT
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constantV1= 665 mL V2= mLT1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 KV1
T1
= V2
T2
V1
T1
=V2T2 =(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
= V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293
K T2= degC
V1
T1
= V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Temperature-Pressure Relationships Gay-Lussacrsquos
Lawbull Pressure and temperature are
proportional at constant volumebull pressure = temperature (K)bull pressure = temperature (K)
= kPT
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation
1 An aerosol can containing gas at 101 kPa and 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
=11 x 10^2 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
=49 x 10^2 K or 22 x10^2 degC
P2= 203 kPa
T1
Volume-Molar Relationships Avogadrorsquos
Lawbull Volume and number of moles (n) are
proportional at constant temperature and pressure
bull volume = number of molesbull volume = number of molesbull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
Checking for understandingState the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos LawAvogadrorsquos Law
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull The passage of gas particles through a small opening is called effusion
Effusion
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A
and B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar massbull Particles of low molar mass travel faster
than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constantV1= 665 mL V2= mLT1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 KV1
T1
= V2
T2
V1
T1
=V2T2 =(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
= V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293
K T2= degC
V1
T1
= V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Temperature-Pressure Relationships Gay-Lussacrsquos
Lawbull Pressure and temperature are
proportional at constant volumebull pressure = temperature (K)bull pressure = temperature (K)
= kPT
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation
1 An aerosol can containing gas at 101 kPa and 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
=11 x 10^2 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
=49 x 10^2 K or 22 x10^2 degC
P2= 203 kPa
T1
Volume-Molar Relationships Avogadrorsquos
Lawbull Volume and number of moles (n) are
proportional at constant temperature and pressure
bull volume = number of molesbull volume = number of molesbull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
Checking for understandingState the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos LawAvogadrorsquos Law
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull The passage of gas particles through a small opening is called effusion
Effusion
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A
and B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar massbull Particles of low molar mass travel faster
than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
= V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293
K T2= degC
V1
T1
= V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Temperature-Pressure Relationships Gay-Lussacrsquos
Lawbull Pressure and temperature are
proportional at constant volumebull pressure = temperature (K)bull pressure = temperature (K)
= kPT
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation
1 An aerosol can containing gas at 101 kPa and 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
=11 x 10^2 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
=49 x 10^2 K or 22 x10^2 degC
P2= 203 kPa
T1
Volume-Molar Relationships Avogadrorsquos
Lawbull Volume and number of moles (n) are
proportional at constant temperature and pressure
bull volume = number of molesbull volume = number of molesbull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
Checking for understandingState the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos LawAvogadrorsquos Law
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull The passage of gas particles through a small opening is called effusion
Effusion
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A
and B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar massbull Particles of low molar mass travel faster
than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293
K T2= degC
V1
T1
= V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Temperature-Pressure Relationships Gay-Lussacrsquos
Lawbull Pressure and temperature are
proportional at constant volumebull pressure = temperature (K)bull pressure = temperature (K)
= kPT
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation
1 An aerosol can containing gas at 101 kPa and 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
=11 x 10^2 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
=49 x 10^2 K or 22 x10^2 degC
P2= 203 kPa
T1
Volume-Molar Relationships Avogadrorsquos
Lawbull Volume and number of moles (n) are
proportional at constant temperature and pressure
bull volume = number of molesbull volume = number of molesbull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
Checking for understandingState the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos LawAvogadrorsquos Law
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull The passage of gas particles through a small opening is called effusion
Effusion
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A
and B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar massbull Particles of low molar mass travel faster
than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Temperature-Pressure Relationships Gay-Lussacrsquos
Lawbull Pressure and temperature are
proportional at constant volumebull pressure = temperature (K)bull pressure = temperature (K)
= kPT
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation
1 An aerosol can containing gas at 101 kPa and 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
=11 x 10^2 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
=49 x 10^2 K or 22 x10^2 degC
P2= 203 kPa
T1
Volume-Molar Relationships Avogadrorsquos
Lawbull Volume and number of moles (n) are
proportional at constant temperature and pressure
bull volume = number of molesbull volume = number of molesbull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
Checking for understandingState the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos LawAvogadrorsquos Law
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull The passage of gas particles through a small opening is called effusion
Effusion
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A
and B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar massbull Particles of low molar mass travel faster
than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Gay-Lussacrsquos Law Calculation
1 An aerosol can containing gas at 101 kPa and 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
=11 x 10^2 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
=49 x 10^2 K or 22 x10^2 degC
P2= 203 kPa
T1
Volume-Molar Relationships Avogadrorsquos
Lawbull Volume and number of moles (n) are
proportional at constant temperature and pressure
bull volume = number of molesbull volume = number of molesbull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
Checking for understandingState the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos LawAvogadrorsquos Law
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull The passage of gas particles through a small opening is called effusion
Effusion
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A
and B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar massbull Particles of low molar mass travel faster
than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
=49 x 10^2 K or 22 x10^2 degC
P2= 203 kPa
T1
Volume-Molar Relationships Avogadrorsquos
Lawbull Volume and number of moles (n) are
proportional at constant temperature and pressure
bull volume = number of molesbull volume = number of molesbull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
Checking for understandingState the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos LawAvogadrorsquos Law
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull The passage of gas particles through a small opening is called effusion
Effusion
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A
and B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar massbull Particles of low molar mass travel faster
than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Volume-Molar Relationships Avogadrorsquos
Lawbull Volume and number of moles (n) are
proportional at constant temperature and pressure
bull volume = number of molesbull volume = number of molesbull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
Checking for understandingState the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos LawAvogadrorsquos Law
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull The passage of gas particles through a small opening is called effusion
Effusion
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A
and B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar massbull Particles of low molar mass travel faster
than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
Checking for understandingState the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos LawAvogadrorsquos Law
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull The passage of gas particles through a small opening is called effusion
Effusion
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A
and B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar massbull Particles of low molar mass travel faster
than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
Checking for understandingState the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos LawAvogadrorsquos Law
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull The passage of gas particles through a small opening is called effusion
Effusion
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A
and B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar massbull Particles of low molar mass travel faster
than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Checking for understandingState the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos LawAvogadrorsquos Law
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull The passage of gas particles through a small opening is called effusion
Effusion
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A
and B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar massbull Particles of low molar mass travel faster
than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull The passage of gas particles through a small opening is called effusion
Effusion
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A
and B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar massbull Particles of low molar mass travel faster
than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Effusion
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A
and B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar massbull Particles of low molar mass travel faster
than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A
and B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar massbull Particles of low molar mass travel faster
than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Grahamrsquos Law Calculationbull At the same temperature which
molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at
room temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Daltonrsquos Lawbull The pressure of each gas in a mixture is
called the partial pressurebull The total pressure of a mixture of gases is
the sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Daltonrsquos Law Calculationbull What is the total pressure in a
balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos LawDaltonrsquos Law
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Ideal Gas
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Molecular Composition of Gases
bull No gas perfectly obeys all four of these laws under all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas bull does not condense to a liquid at low
temperatures bull does not have forces of attraction or
repulsion between the particles and is bull composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The combined gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Ideal Gas Law CalculationHow many moles of gas are contained
in 224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RTPV
n =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L) = =964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRTV
P =
(43 mol)(00821 Latmmol K) ( 278 K)(65 L)
= =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRTP
V =
(111 mol)(00821 Latmmol K) ( 216 K)(250 atm)
= =79 L
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
Checking for understanding 1 Explain how is ideal gas different from a
normal gas 2 Write the formula for ideal gas3 What variables can be determined by using the formula
- Characteristic of Gases
- The Nature of Gases
- Gases Are Fluids
- Gases Have Low Density
- Gases are Highly Compressible
- Gases Completely Fill a Container
- Gas Pressure
- Gas Pressure (2)
- Measuring Pressure
- Slide 10
- Slide 11
- Gas Theory
- Kinetic Molecular Theory
- Checking for understanding
- Gas Laws
- Slide 16
- Gas Laws ndash ABCGG LAWS
- Pressure-Volume Relationship Boylersquos Law
- For ALL calculations
- Boylersquos Law Calculation
- Slide 21
- Slide 22
- Temeperature-Volume Relationship Charlersquos Law
- Charless Law Calculation
- Slide 25
- Slide 26
- Temperature-Pressure Relationships Gay-Lussacrsquos Law
- Gay-Lussacrsquos Law Calculation
- Slide 29
- Volume-Molar Relationships Avogadrorsquos Law
- Avogadrorsquos Law
- Gas Laws (2)
- Checking for understanding (2)
- Gas Behavior ndash DiffusionEffusion
- Slide 35
- Grahamrsquos Law
- Grahamrsquos Law Calculation
- Grahamrsquos Law Calculation (2)
- Daltonrsquos Law
- Daltonrsquos Law Calculation
- Checking for understanding (3)
- Ideal Gas
- Molecular Composition of Gases
- Ideal Gas Law
- Ideal Gas Law Calculation
- Slide 46
- Slide 47
- Checking for understanding
top related