06/20/22 1 Chapter 12 Chapter 12 The Behavior of Gases The Behavior of Gases Chemistry
Dec 29, 2015
04/19/231
Chapter 12Chapter 12The Behavior of GasesThe Behavior of Gases
Chemistry
04/19/232
The Kinetic Theory RevisitedThe Kinetic Theory Revisited
Have you ever noticed that a balloon shrinks when it gets cold and expands when it is warmed? You saw a balloon shrink to nothing when placed in liquid nitrogen and then expand when removed from the liquid nitrogen!
04/19/233
The Kinetic Theory RevisitedThe Kinetic Theory RevisitedGases consist of hard spherical particlesThese particles are so small that in relation
to the distances between them that their individual volumes can be assumed to be insignificant.
There is considerable empty space between the particles
Between the particles is empty space. No attractive or repulsive forces exist between the particles.
04/19/234
The Kinetic Theory RevisitedThe Kinetic Theory Revisited
The particles move in constant random motion. They travel in straight paths, independently of
each other. The gas particles change direction only from collision with one another or with other objects.
Gases fill their containers regardless of the shape and volume of the containers.
Uncontained gases diffuse into space without limit.
04/19/235
The Kinetic Theory RevisitedThe Kinetic Theory Revisited
All collisions are perfectly elastic. This means that during collisions kinetic energy is transferred without loss from one particle to another and the total kinetic energy remains the same.
04/19/236
The Kinetic Theory RevisitedThe Kinetic Theory Revisited
Compressibility is a measure of how much the volume of matter decreased under pressure.
Gases are easily compressed (unlike solids or liquids)
Compressibility is why air bags work.
04/19/237
The Kinetic Theory RevisitedThe Kinetic Theory Revisited
Remember that the average kinetic energy of a collection of gas particles is directly proportional to the Kelvin temperature of a gas
04/19/238
The Kinetic Theory RevisitedThe Kinetic Theory Revisited
The four variables that describe a gas are:
– Pressure in kilopascals, kPa
– Volume in liters, L
– Temperature in Kelvin degrees – K has no° sign
– Number of moles, n
04/19/239
Factors Affecting Gas PressureFactors Affecting Gas Pressure
The limitation of how many gas particles can be added to a container is the strength of the container.
Halving the number of gas particles, halves the pressure.
04/19/2310
Factors Affecting Gas PressureFactors Affecting Gas Pressure
Raising the temperature of a gas in a closed container increases the pressure.
The speed and kinetic energy increases as the temperature increases. Faster moving particles impact the walls of the container with more energy, exerting greater pressure.
Doubling the Kelvin temperature doubles the gas pressure.
04/19/2311
Factors Affecting Gas PressureFactors Affecting Gas Pressure
Heating an aerosol can can cause the can to burst. Why?
As the temperature increases the gas pressure increases. At some point, the aerosol can cannot withstand the increased pressure and it bursts open.
04/19/2312
Factors Affecting Gas PressureFactors Affecting Gas Pressure
You can raise the pressure of a contained gas by decreasing the volume. The more gas is compressed, the greater the gas pressure.
Reducing the volume by half doubles the gas pressure.
Doubling the volume halves the gas pressure.
04/19/2313
Boyle’s LawBoyle’s LawP P αα 1/V 1/VThis means Pressure and This means Pressure and
Volume are INVERSELY Volume are INVERSELY PROPORTIONAL if moles PROPORTIONAL if moles and temperature are and temperature are constant (do not change).constant (do not change).
For example, P goes up as V For example, P goes up as V goes down.goes down.
PP11VV11 = P = P22 V V22
Robert Boyle Robert Boyle (1627-1691).(1627-1691).
04/19/2314
The Gas Laws –Boyle’s LawThe Gas Laws –Boyle’s Law
Boyle’s Law is the pressure-volume relationship
Boyle’s Law states that for a given mass of gas at constant temperature, the volume of the gas varies inversely with pressure. In an inverse relationship the product of the two variable quantitative is constant.
P1 V1 = P2 V2
04/19/2315
The Gas Laws –Boyle’s LawThe Gas Laws –Boyle’s Law
Now, let's look at how these ideas relate to diving. It is well known among divers that diving at the surface can be more dangerous than deeper diving. We can understand this by first noting that for every 10 meters you descend in the water, the pressure increases by about 1 atm.
04/19/2316
The Gas Laws –Boyle’s LawThe Gas Laws –Boyle’s Law
04/19/2317
The Gas Laws –Boyle’s LawThe Gas Laws –Boyle’s Law
Therefore, when you hold your breath, you create a closed system with your lungs and thus Boyle's law will hold. If you are down at 90 meters (at 10 atm) and you rise 10 meters to 80 meters (at 9 atm), the pressure has decreased by about 10%, and since PV is a constant your lungs expand by about 10% (probably not too bad).
04/19/2318
The Gas Laws –Boyle’s LawThe Gas Laws –Boyle’s Law
Now if you are at 10 meters (at 2 atm), and you rise 10 meters to the surface (at 1 atm) the pressure had decreased by 50% and expanding your lungs by this factor could cause significant damage, maybe death!
04/19/2319
The Gas Laws –Boyle’s LawThe Gas Laws –Boyle’s Law
04/19/2320
The Gas Laws –Boyle’s LawThe Gas Laws –Boyle’s Law
A balloon contains 30.0 L of helium gas at 103 kPa. What is the volume when the balloon rises to an altitude where the pressure in only 25.0 kPa?
04/19/2321
The Gas Laws –Boyle’s LawThe Gas Laws –Boyle’s LawKnowns: P1 = 103 kPa V1 = 30.0 L
P2 = 25.0 kPa V2 = UNK
P1 V1 = P2 V2 (Rearrange for V2)
V2 = P1 V1 V2 = 103 kPa 30.0 L =
P2 25.0 kPa124 L1.24 102 L
04/19/2322
Charles’s LawCharles’s Law
Timberlake, Chemistry 7th Edition, page 259
Raising the temperature of a gas increases the pressure if the volume is held constant.
The molecules hit the walls harder.
TemperatureTemperature
If you start with 1 liter of gas at 1 atm pressure and 300 K
and heat it to 600 K one of 2 things happens
300 K
Either the volume will increase to 2 liters at 1 atm
300 K600 K
300 K 600 K
….or the pressure will increase to 2 atm.
04/19/2327
Charles’s Charles’s LawLawIf n and P are constant, If n and P are constant,
then V then V αα T TV and T are directly V and T are directly
proportional.proportional.VV11 V V22
==
TT11 T T22
If one temperature goes up, the If one temperature goes up, the
volume goes up!volume goes up!
Jacques Charles Jacques Charles (1746-1823). (1746-1823).
04/19/2328
Charles’s LawCharles’s Law
Timberlake, Chemistry 7th Edition, page 259
04/19/2329
Charles’s LawCharles’s Law
04/19/2330
Gay-Lussac’s LawGay-Lussac’s LawIf n and V are If n and V are
constant, constant, then P then P αα T T
P and T are directly P and T are directly proportional.proportional.
PP11 P P22
==
TT11 T T22
If one temperature goes up, If one temperature goes up,
the pressure goes up!the pressure goes up!
Joseph Louis Gay-Joseph Louis Gay-Lussac (1778-1850)Lussac (1778-1850)
04/19/2331
Combined Gas LawCombined Gas LawThe good news is that you don’t
have to remember all three gas laws! Since they are all related to each other, we can combine them into a single equation. BE SURE YOU KNOW THIS EQUATION!
P1 V1 P2 V2
= T1 T2
04/19/2332
Kelvin vs. CelsiusKelvin vs. Celsius
Remember that all gas laws must be applied in Kelvin
If your given a problem in Celsius Temp you must convert it to Kelvin
K = C + 273 degrees
04/19/2333
And now, we pause for this And now, we pause for this commercial message from STPcommercial message from STP
OK, so it’s really not THIS kind of STP…
STP in chemistry stands for Standard Temperature and
Pressure
Standard Pressure = 101.3 kPa, 1 atm, or
760 mm Hg
Standard Temperature = 0 deg
C (273 K)
04/19/2334
Ideal Gas EquationIdeal Gas Equation
5.4
Charles’ law: V T(at constant n and P)
Avogadro’s law: V n(at constant P and T)
Boyle’s law: V (at constant n and T)1P
V nT
P
V = constant x = RnT
P
nT
PR is the gas constant
PV = nRT
04/19/2335
The conditions 0 0C and 101.3 kPa are called standard temperature and pressure (STP).
PV = nRT
R = PVnT
=(101.3kPa)(22.414L)
(1 mol)(273.15 K)
R = 8.31 L • kPa / (mol • K)
5.4
Experiments show that at STP, 1 mole of an ideal gas occupies 22.414 L.
04/19/2336
Density (d) Calculations
d = mV =
PMRT
m is the mass of the gas in g
M is the molar mass of the gas
Molar Mass (M ) of a Gaseous Substance
dRTP
M = d is the density of the gas in g/L
5.4
04/19/2337
A 2.10-L vessel contains 4.65 g of a gas at 1.00 atm and 27.00C. What is the molar mass of the gas?
5.3
dRTP
M = d = mV
4.65 g2.10 L
= = 2.21 g
L
M =2.21
g
L
101.3 kPa
x 8.31 x 300.15 KL•kPamol•K
M = 54.6 g/mol
04/19/2338
Gas Stoichiometry
What is the volume of CO2 produced at 370 C and 1.00 atm when 5.60 g of glucose are used up in the reaction:
C6H12O6 (s) + 6O2 (g) 6CO2 (g) + 6H2O (l)
g C6H12O6 mol C6H12O6 mol CO2 V CO2
5.60 g C6H12O6
1 mol C6H12O6
180 g C6H12O6
x6 mol CO2
1 mol C6H12O6
x = 0.187 mol CO2
V = nRT
P
0.187 mol x 8.31 x 310.15 KL•kPamol•K
101.3 kPa= = 4.76 L
5.5
04/19/2342
Gas diffusion is the gradual mixing of molecules of one gas with molecules of another by virtue of their kinetic properties.
5.7
NH3
17 g/molHCl
36 g/mol
NH4Cl
04/19/2343
GAS DIFFUSION AND GAS DIFFUSION AND EFFUSIONEFFUSION diffusiondiffusion is the is the
gradual mixing of gradual mixing of molecules of molecules of different gases.different gases.
effusioneffusion is the is the movement of molecules movement of molecules through a small hole through a small hole into an empty into an empty container.container.
04/19/2344
GAS DIFFUSION AND GAS DIFFUSION AND EFFUSIONEFFUSION
Graham’s law governs Graham’s law governs effusion and diffusion of effusion and diffusion of gas molecules. gas molecules. KE=1/2 mv2
Thomas Graham, 1805-1869. Thomas Graham, 1805-1869. Professor in Glasgow and London.Professor in Glasgow and London.
Rate of effusion is Rate of effusion is inversely proportional inversely proportional to its molar mass.to its molar mass.
Rate of effusion is Rate of effusion is inversely proportional inversely proportional to its molar mass.to its molar mass.
M of AM of B
Rate for B
Rate for A
04/19/2345
GAS DIFFUSION AND GAS DIFFUSION AND EFFUSIONEFFUSION
Molecules effuse thru holes in a Molecules effuse thru holes in a rubber balloon, for example, at a rubber balloon, for example, at a rate (= moles/time) that israte (= moles/time) that is
proportional to Tproportional to T inversely proportional to M.inversely proportional to M.Therefore, He effuses more rapidly Therefore, He effuses more rapidly
than Othan O22 at same T. at same T.
HeHe
04/19/2346
Gas DiffusionGas Diffusionrelation of mass to rate of diffusionrelation of mass to rate of diffusionGas DiffusionGas Diffusionrelation of mass to rate of diffusionrelation of mass to rate of diffusion
HCl and NH3 diffuse from opposite ends of tube.
Gases meet to form NH4Cl
HCl heavier than NH3
Therefore, NH4Cl forms closer to HCl end of tube.
HCl and NH3 diffuse from opposite ends of tube.
Gases meet to form NH4Cl
HCl heavier than NH3
Therefore, NH4Cl forms closer to HCl end of tube.