John E. McMurry • Robert C. Fay

C H E M I S T R Y

Chapter 9

Gases: Their Properties and Behavior

Lecture Notes

Alan D. Earhart Southeast Community College • Lincoln, NE

Stoichiometric Relationships with Gases The reaction used in the deployment of automobile airbags is the high-temperature decomposition of sodium azide, NaN 3 , to produce N 2 gas. How many liters of N 2 at 1.15 atm and 30.0 ° C are produced by decomposition of 45.0 g NaN 3 ?

2NaN 3 (s) 2Na(s) + 3N 2 (g)

Stoichiometric Relationships with Gases 2NaN 3 (s) 2Na(s) + 3N 2 (g)

Moles of N 2 produced:

45.0 g NaN 3  mol of N2

Volume of N 2 produced:

Use Ideal Gas Law

Examples

 Consider the reaction represented by the equation P 4 (s) + 6 H 2 (g)  4H 3 (g) What is the amount of P 4 is required to react with 5.39 L of hydrogen gas at 27.0

o C and 1.25 atm?

Partial Pressure and Dalton’s Law Dalton’s Law of Partial Pressures: The total pressure exerted by a mixture of gases in a container at constant V and T is equal to the sum of the pressures of each individual gas in the container.

Mole Fraction (X) = P total = P 1 + P 2 + … + P N Moles of component Total moles in mixture

n

i

X

i =

n

total or

P

i

X

i =

P

total

Examples

 Determine the mole fractions and partial pressures of CO 2 , CH 4 , and He in a sample of gas that contains 0.250 mole of CO 2 , 1.29 moles of CH 4 , and 3.51 moles of He, and in which the total pressure is 5.78 atm

Example

 A 1.00 L vessels contain 0.215 mole of N 2 mole of H 2 gas and 0.0118 gas at 25.5

o C. Determine the partial pressure of each component and the total pressure

Example

 On a humid day in summer, the mole fraction of gaseous H 2 O (water vapor) in the air at 25.0

o C can be as high as 0.0287. Assuming a total pressure of 0.977 atm, what is the partial pressure (in atm) of H 2 O in the air?

The Kinetic-Molecular Theory of Gases 1. A gas consists of tiny particles, either atoms or molecules, moving about at random.

2. The volume of the particles themselves is negligible compared with the total volume of the gas; most of the volume of a gas is empty space.

3. The gas particles act independently of one another; there are no attractive or repulsive forces between particles.

The Kinetic-Molecular Theory of Gases

3.

Collisions of the gas particles, either with other particles or with the walls of a container, are elastic (constant temperature).

4.

The average kinetic energy of the gas particles is proportional to the Kelvin temperature of the sample.

The Kinetic-Molecular Theory of Gases Copyright © 2008 Pearson Prentice Hall, Inc.

molar mass average speed Chapter 9/12

The Kinetic-Molecular Theory of Gases

Graham’s Law: Diffusion and Effusion of Gases Diffusion: The mixing of different gases by molecular motion with frequent molecular collisions.

Graham’s Law: Diffusion and Effusion of Gases Effusion: The escape of a gas through a pinhole into a vacuum without molecular collisions.

Graham’s Law:

Rate

a

1

m

Graham’s Law: Diffusion and Effusion of Gases

 In comparing two gases at the same temperature and pressure

Rate 1 Rate 2

=

√m2 √m1

Example

 Determine how much faster Helium atoms moves, on average, than a carbon dioxide molecule at the same temperature  Determine the molar mass and identity of a gas that moves 4.67 times as fast as CO 2

The Behavior of Real Gases

The volume of a real gas is larger than predicted by the ideal gas law.

Copyright © 2008 Pearson Prentice Hall, Inc.

Chapter 9/18

The Behavior of Real Gases

Attractive forces between particles become more important at higher pressures.

The Behavior of Real Gases

van der Waals equation

Correction for intermolecular attractions.

P

+

a n

2

V

2 V - n

b

= nRT Correction for molecular volume.

Example

 A sample of 3.50 moles of NH 3 gas occupies 5.20 L at 47 o C. Calculate the pressure of the gas (in atm) using  A) the ideal gas equation  B) the van der Waals equation a = 4.17 atm •L/mol 2 b = 0.0371 L/mol