Gases: Mixtures and Gases: Mixtures and MovementsMovements

Prentice-Hall Chapter 14.4Prentice-Hall Chapter 14.4

Dr. YagerDr. Yager

ObjectivesObjectives

RelateRelate the total pressure of a mixture of the total pressure of a mixture of gases to the partial pressures of the gases to the partial pressures of the component gasescomponent gases

ExplainExplain how the molar mass of a gas affects how the molar mass of a gas affects the rate at which the gas diffuses and effusesthe rate at which the gas diffuses and effuses

Dalton’s LawDalton’s Law

In a mixture of gases, the total pressure is the In a mixture of gases, the total pressure is the sum of the partial pressures of the gases.sum of the partial pressures of the gases.

The contribution each gas in a mixture makes to the total pressure is called the partial pressure exerted by that gas.

Partial PressurePartial Pressure

Dalton’s Law of Partial PressuresDalton’s Law of Partial Pressures states that, at constant volume and temperature, states that, at constant volume and temperature, the total pressure exerted by a mixture of gases the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of the is equal to the sum of the partial pressures of the component gases.component gases.

Dalton’s Law of Partial PressuresDalton’s Law of Partial Pressures

=+ +

Three gases are combined in Container T.

The partial pressure of oxygen must be 10.67 kPa or higher to support respiration in humans. The Mt. Everest climber below needs an oxygen mask and a cylinder of compressed oxygen to survive.

A gas mixture containing oxygen, nitrogen, and carbon dioxide has a total pressure of 32.9 kPa. If PO2 = 6.6 kPa, and PN2 = 23.0 kPa, what is the pressure of the carbon dioxide?

Ptotal = sum of all the partial pressures

32.9 kPa = 6.6 kPa + 23.0 kPa + pressure of CO2

3.3 kPa = pressure of CO2

Diffusion vs EffusionDiffusion vs Effusion

DiffusionDiffusion is the tendency of molecules to is the tendency of molecules to move towards areas of lower concentration.move towards areas of lower concentration.

Effusion Effusion is the movement of a gas through is the movement of a gas through a tiny hole in a container.a tiny hole in a container.

Key Idea:Key Idea:

Gases of lower molar mass diffuse and effuse Gases of lower molar mass diffuse and effuse faster than gases of higher molar mass.faster than gases of higher molar mass.

Diffusion is the tendency of molecules to move toward areas of lower concentration until the concentration is uniform throughout.

After several hours, the bromine has diffused almost

to the top of the cylinder.

Bromine vapor is diffusing upward through the air in a

graduated cylinder

Graham’s Law of EffusionGraham’s Law of Effusion

Graham’s LawGraham’s Law states that the rate of states that the rate of effusion of a gas is inversely proportional effusion of a gas is inversely proportional to the square root of the gas’ molar mass. to the square root of the gas’ molar mass.

This law can also be applied to the This law can also be applied to the diffusion of gases.diffusion of gases.

A helium filled balloon will deflate sooner than an air-filled balloon.

Helium and air molecules pass freely through pores in the balloon. Helium atoms are less massive than oxygen or nitrogen molecules.

At the same temperature (same kinetic energy):

KE = ½ mv2 m = mass, v = velocity

For constant KE, an increase in mass must be balanced by a decrease in velocity. So air molecules (oxygen, nitrogen) move more slowly than helium atoms with the same kinetic energy.

Because the rate of effusion is related only to a particle’s speed, Graham’s law can be written as follows for two gases, A and B.

Helium effuses (and diffuses) nearly three times faster than nitrogen at the same temperature.

Molar mass of N2 = 28 g

Molar mass of He = 4 g

1. What is the partial pressure of oxygen in a 1. What is the partial pressure of oxygen in a diving tank containing oxygen and helium if diving tank containing oxygen and helium if the total pressure is 800 kPa and the partial the total pressure is 800 kPa and the partial pressure of helium is 600 kPa?pressure of helium is 600 kPa?

a.a. 200 kPa200 kPa

b.b. 0.75 kPa0.75 kPa

c.c. 1.40 x 101.40 x 1044 kPa kPa

d.d. 1.33 kPa1.33 kPa

1. What is the partial pressure of oxygen in a 1. What is the partial pressure of oxygen in a diving tank containing oxygen and helium if diving tank containing oxygen and helium if the total pressure is 800 kPa and the partial the total pressure is 800 kPa and the partial pressure of helium is 600 kPa?pressure of helium is 600 kPa?

a.a. 200 kPa200 kPa

b.b. 0.75 kPa0.75 kPa

c.c. 1.40 x 101.40 x 1044 kPa kPa

d.d. 1.33 kPa1.33 kPa

2. A mixture of three gases exerts a 2. A mixture of three gases exerts a pressure of 448 kPa, and the gases are pressure of 448 kPa, and the gases are present in the mole ratio 1 : 2 : 5. present in the mole ratio 1 : 2 : 5. What are the individual gas pressures?What are the individual gas pressures?

a.a. 44 kPa, 88 kPa, and 316 kPa44 kPa, 88 kPa, and 316 kPa

b.b. 52 kPa, 104 kPa, and 292 kPa52 kPa, 104 kPa, and 292 kPa

c.c. 56 kPa, 112 kPa, and 280 kPa56 kPa, 112 kPa, and 280 kPa

d.d. 84 kPa, 168 kPa, and 196 kPa84 kPa, 168 kPa, and 196 kPa

2. A mixture of three gases exerts a 2. A mixture of three gases exerts a pressure of 448 kPa, and the gases are pressure of 448 kPa, and the gases are present in the mole ratio 1 : 2 : 5. present in the mole ratio 1 : 2 : 5. What are the individual gas pressures?What are the individual gas pressures?

a.a. 44 kPa, 88 kPa, and 316 kPa44 kPa, 88 kPa, and 316 kPa

b.b. 52 kPa, 104 kPa, and 292 kPa52 kPa, 104 kPa, and 292 kPa

c.c. 56 kPa, 112 kPa, and 280 kPa56 kPa, 112 kPa, and 280 kPa

d.d. 84 kPa, 168 kPa, and 196 kPa84 kPa, 168 kPa, and 196 kPa

3. 3. Choose the correct words for the spaces. Choose the correct words for the spaces. Graham's Law says that the rate of Graham's Law says that the rate of diffusion of a gas is __________ diffusion of a gas is __________ proportional to the square root of its proportional to the square root of its _________ mass_________ mass. .

a.a. directly, atomicdirectly, atomic

b.b. inversely, atomicinversely, atomic

c.c. inversely, molarinversely, molar

d.d. directly, molardirectly, molar

3. 3. Choose the correct words for the spaces. Choose the correct words for the spaces. Graham's Law says that the rate of Graham's Law says that the rate of diffusion of a gas is __________ diffusion of a gas is __________ proportional to the square root of its proportional to the square root of its _________ mass_________ mass. .

a.a. directly, atomicdirectly, atomic

b.b. inversely, atomicinversely, atomic

c.c. inversely, molarinversely, molar

d.d. directly, molardirectly, molar