Unit 9: Gases

Dalton’s Law of Partial Pressures, Grahams Law, and Real vs. Ideal Gases

After today you will be able to…

• • • Describe Dalton’s law of partial pressures and calculate P total or a partial pressure Explain Graham’s law of effusion and calculate the rate at which gases effuse Explain what is meant by the term “real” vs. “ideal” gases

Recall, gas pressure results from

collisions of gas particles.

• Gas pressure depends on

particles.

the amount of gas and the KE of its

• Since particles in a mixture of gases at the same temperature contain the same average KE, the kind of particle is unimportant.

Example: Composition of Dry Air Component Volume Partial Pressure

Nitrogen

78.08% 79.11 kPa

Oxygen Carbon dioxide

20.95% 0.04%

MISC gases

0.93% Total 100.00% 21.22 kPa 0.04 kPa 0.95 kPa 101.32 kPa

“The total pressure of a mixture of gases is equal to the sum of the individual (partial) pressures.”

Dalton’s Law of Partial Pressures

P

total

= P

1

+ P

2

+ P

3

… Units of pressure must match!

Example: Dalton’s Law

What is the total pressure for a mixture of O 2 CO P O2 2 = if P O2 = 0.719 atm and P CO2 = 423mmHg.

0.719atm

x 760mmHg 1atm = 546mmHg

P CO2 =

423mmHg

and

P total =546mmHg + 423mmHg

P total =969mmHg

Thomas Graham (1846)

• Diffusion:

Is the tendency of gas particles to spontaneously spread out until uniformly distributed.

•

Effusion:

The escape of a gas through a tiny pinhole in a container of gas.

–

Gases with lower molar masses effuse more quickly.

“The rate of effusion of a gas is inversely proportional to the square root of the gas’s molar mass.”

Graham’s Law of Effusion

Rate A = √MM

B A Always place the larger molar mass in the numerator!

Example: Graham’s Law

Which gas effuses faster, H 2 faster?

or Cl 2 ? How much

Rate H 2 Rate Cl 2 Rate H 2 Rate Cl 2 = = √MM Cl2 √MM H2 √(70.90) √(2.02)

= 5.92x

H 2 effuses 5.92x faster than Cl 2

Real vs. Ideal Gases

• The gas laws we’ve learned in this unit are based on a gas that behaves “ideally.” • An ideal gas has: –

No molecular volume

–

No attractive forces

• In reality,

there are no perfectly ideal gases. But, under most conditions, real gases will approximate ideal gas behavior.

• However, under certain conditions,

real gases will deviate from ideal gas behavior.

Real vs. Ideal Gases

• These deviations occur for:

1. High pressure:

Gas particles are pushed closer together, more attractive forces result.

2. Low Temperature:

The gas is compressed, there are more attractive forces.

3. High molar mass:

Higher molar mass of the molecule usually means larger volume.

4. Polar molecules:

Unequal sharing of electrons creates an attraction between molecules.