Gases. Pressure Is caused by the collisions of molecules with the walls of a container is equal to force/unit area SI units = Newton/meter 2 = 1 Pascal.

GasesGases

PressurePressureIs caused by the collisions of molecules with

the walls of a container is equal to force/unit area SI units = Newton/meter2 = 1 Pascal (Pa) 1 atmosphere = 101,325 Pa 1 atmosphere = 1 atm = 760 mm Hg = 760

torr

Measuring Measuring PressurePressure

The first device for measuring atmospheric pressure was developed by Evangelista Torricelli during the 17th century.The device was called a “barometer”

  Baro = weight   Meter = measure

An Early An Early BarometerBarometer

The normal pressure due to the atmosphere at sea level can support a column of mercury that is 760 mm high.

Standard Temperature and Standard Temperature and PressurePressure

“STP”“STP”

P = 1 atmosphere, 760 torr T = C, 273 Kelvins The molar volume of an ideal gas is 22.42 liters at STP

Converting Celsius to KelvinConverting Celsius to KelvinGas law problems involving temperature require that the temperature be in KELVINS!

Kelvins = C + 273

°C = Kelvins - 273

Boyle’s LawBoyle’s Law

Pressure is inversely proportional to volume when temperature is held constant.

2211 VPVP

A sample of helium gas at 25°C is compressed from 200 cm3 to 0.240 cm3. Its pressure is now 3.00 cm Hg. What was the original pressure of the helium?

P1V1 = P2V2

P1 = P2V2/V1

P1 = 3.00 cm Hg x 0.240 cm3/200 cm3

P1 = 3.60 x 10-3 cm Hg

P1 = ?V1 = 200 cm3

P2 = 3.00 cmV2 = 0.240 cm3 Hg

Charles’s LawCharles’s Law  The volume of a gas is directly proportional to temperature, and extrapolates to zero at zero Kelvin.

(P = constant)

2

2

1

1

T

V

T

V

Gay Lussac’s LawGay Lussac’s Law

The pressure and temperature of a gas are directly related, provided that the volume remains constant.

2

2

1

1

T

P

T

P

A sample of oxygen gas has a volume of 2.73 dm3 at 21.0 oC.  At what temperature would the gas have a volume of 4.00 dm3?

T1 = 294 KV1 = 2.73 dm3

T2 = ?V2 = 4.00 dm3

V1 = V2

T1 T2

T2 = 294 K x 4.00 dm3

       -----------------------              2.73 dm3

2.73 dm3 = 4.00 dm3

----------- -------------

294 K T2

T2  = 431 K

The Combined Gas LawThe Combined Gas Law

The combined gas law expresses the relationship between pressure, volume and temperature of a fixed amount of gas.

2

22

1

11

T

VP

T

VP

Boyle’s law, Gay-Lussac’s law, and Charles’ law are all derived from this by holding a variable constant.

A 350 cm3 sample of helium gas is collected at 22.0 oC and 99.3 kPa.  What volume would this gas occupy at STP ?

V1 = 350 cm3

P1 = 99.3 kPaT1 = 295 KV2 = ?P2 = 101.3 kPa (standard press)T2 = 273 K (standard temp))

P1 V1 = P2 V2

---------- --------------

T1 T2

(99.3 kPa )(350 cm3 ) = (101.3 kPa) V2 --------------------------------------- ___________________

( 295 K) (273 K)

V2 = 320 cm3

Avogadro’s LawAvogadro’s Law

For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas.

V = an

a = proportionality constant V = volume of the gas n = number of moles of gas

31. D 32. D 33. D 34. C 35. C 36. B 37. B

------------------------------------

Ideal Ideal GasesGases

Ideal gases are imaginary gases that perfectly fit all of the assumptions of the kinetic molecular theory.

Gases consist of tiny particles that are far apart relative to their size.

Collisions between gas particles and between particles and the walls of the container are elastic collisions

No kinetic energy is lost in elastic collisions

Ideal Gases Ideal Gases (continued)

Gas particles are in constant, rapid motion. They therefore possess kinetic energy, the energy of motion

There are no forces of attraction between gas particles

The average kinetic energy of gas particles depends on temperature, not on the identity of the particle.

The Nature of GasesThe Nature of GasesGases expand to fill their containers Gases are fluid – they flow Gases have low density

1/1000 the density of the equivalent liquid or solid

Gases are compressible Gases effuse and diffuse

– Effusion, molecules moving at a high rate of speed will eventually “collide” with a hole and escape.

• Effusion is gas escaping through a hole,

• Example: air escaping through a hole in your tire

• Diffusion, again because the molecules are moving at a high rate of speed, they will spread out– Example: perfume diffusing through air

– Example: Liquids also diffuse: food coloring in water

Ideal Gas LawIdeal Gas Law

PV = nRT P = pressure in atm V = volume in liters n = moles R = proportionality constant

= 0.08206 L atm/ mol· T = temperature in Kelvins

Holds closely at P < 1 atm

What volume is occupied by 5.03 g of O2 at 28°C and a pressure of 0.998 atm?

P = 0.998 atm

V= ?

Mass = 5.03 g O2 / 1 mol O2 / =

/ 32 g O2 /

n= 0.157 moles

R = 0.08206 L atm mol K

T = 28°C + 273 = 301 K

PV = nRT

(0.998 atm) V = (0.157 mol) (0.08206 L atm ) ( 301 K) mol K

=3.89 L

Standard Molar Standard Molar VolumeVolume

Equal volumes of all gases at the same temperature and pressure contain the same number of molecules.

- Amedeo Avogadro

Density and the Ideal Gas Density and the Ideal Gas LawLaw

Combining the formula for density with the Ideal Gas law, substituting and rearranging algebraically:

M = Molar Mass

P = Pressure

R = Gas Constant

T = Temperature in Kelvins

dRT = molar

P mass

Gas Stoichiometry #1If reactants and products are at the same conditions of temperature and pressure, then mole ratios of gases are also volume ratios.

3 H2(g) + N2(g) 2NH3(g)

3 moles H2 + 1 mole N2 2 moles NH3 3 liters H2 + 1 liter N2 2 liters NH3

Gas Stoichiometry #2How many liters of ammonia can be produced when 12 liters of hydrogen react with an excess of nitrogen?

3 H2(g) + N2(g) 2NH3(g)

12 L H2

L H2

= L NH3 L NH3

3

28.0

Gas Stoichiometry #3Gas Stoichiometry #3How many liters of oxygen gas, at STP, can be collected from the complete decomposition of 50.0 grams of potassium chlorate?

2 KClO3(s) 2 KCl(s) + 3 O2(g)

= L O2

50.0 g KClO3 1 mol KClO3

122.55 g KClO3

3 mol O2

2 mol KClO3

22.4 L O2

1 mol O2

13.7

Gas Stoichiometry #4Gas Stoichiometry #4

PnRT

V

How many liters of oxygen gas, at 37.0C and 0.930 atmospheres, can be collected from the complete decomposition of 50.0 grams of potassium chlorate?

2 KClO3(s) 2 KCl(s) + 3 O2(g)

= “n” mol O2

50.0 g KClO3 1 mol KClO3

122.55 g KClO3

3 mol O2

2 mol KClO3 0.612 mol O2

atm0.930

K))(310Kmol

atmL1mol)(0.082(0.612

= 16.7 L

Dalton’s Law of Partial Dalton’s Law of Partial PressuresPressures

For a mixture of gases in a container,

PTotal = P1 + P2 + P3 + . . .

This is particularly useful in calculating the pressure of gases collected over water.

nTotal = n1 + n2 + n3 + . . .

Mixture of gas and water vapor.

PT = pgas + pvap(H2O)

Dalton’s law of partial pressurescollecting gases over water

Hydrogen gas is collected over water at a total pressure of 95.0 kPa and a temperature of 25 C. What is the partial pressure of hydrogen gas? According to a water vapor pressure table, the vapor pressure of water at 25C is 3.17 kPa.

Ptotal = Pgas + P water vapor 95.0 kPa = X + 3.17 kPa

X = 91.8 kPa

• e.g., If 6.00 g of O2 and 9.00 g of CH4 are placed in a 15.0-L container

• at 0ºC, what is the partial pressure of each gas and the total pressure in

• the container.

Kinetic Energy of Gas Kinetic Energy of Gas ParticlesParticles

At the same conditions of temperature, all gases have the same average kinetic energy.

2

2

1mvKE

The Meaning of TemperatureThe Meaning of Temperature

Kelvin temperature is an index of the random motions of gas particles (higher T means greater motion.)

(KE)32avg RT

Kinetic Molecular Kinetic Molecular TheoryTheory

Particles of matter are ALWAYS in motion

Volume of individual particles is zero.

Collisions of particles with container walls cause pressure exerted by gas.

Particles exert no forces on each other.

Average kinetic energy Kelvin temperature of a gas.  

Diffusion: describes the mixing of gases. The rate of diffusion is the rate of gas mixing.

DiffusionDiffusion

EffusionEffusionEffusion: describes the passage of gas into an evacuated chamber.

Kinetic Molecular Theory• Gases have certain properties that can be explained by the KMT. • Low Density, because the molecules are moving at a high rate of speed and

are not held back by electrostatic attractions, they, spread out. And because gases have small volume as well as being spread out, they have low density

• Compressibility, because the molecules have space between them, they can be forced to compress unlike liquids and solids where there is little space between the molecules

• Expansion, because the molecules are moving at a high rate of speed, they will spread out if given the opportunity

• Diffusion, again because the molecules are moving at a high rate of speed, they will spread out

– Example: perfume diffusing through air– Example: Liquids also diffuse: food coloring in water

• Effusion, molecules moving at a high rate of speed will eventually “collide” with a hole and escape.

– Effusion is gas escaping through a hole,– Example: air escaping through a hole in your tire

Rate of effusion for gas 1Rate of effusion for gas 2

2

1

MM

Distance traveled by gas 1Distance traveled by gas 2

2

1

MM

Effusion:Effusion:

Diffusion:Diffusion:

Graham’s LawGraham’s LawRates of Effusion and DiffusionRates of Effusion and Diffusion

Real GasesReal Gases

[ ]P a V nb nRTobs2( / ) n V

corrected pressurecorrected pressure corrected volumecorrected volume

PPideaidea

ll

VVideaidea

ll

Must correct ideal gas behavior when at high pressure (smaller volume) and low temperature (attractive forces become important).