Chapter 9Gases: Their Properties and Behavior

C H E M I S T R Y

Methanol (CH3OH) can be synthesized by the following reaction:

CO(g) + 2 H2(g) CH3OH(g)

What volume (in Liters) of hydrogen gas, measured at a temperature of 355K and a pressure of 738 mmHg, is required to synthesize 35.7 g of methanol?

ExamplesConsider the reaction represented by the equation

P4(s) + 6 H2(g) 4H3(g)

What is the amount of P4 is required to react with 5.39 L of hydrogen gas at 27.0oC and 1.25 atm?

Ptotal = P1 + P2 + … + PN

Mole Fraction (X) =

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.

Xi = Ptotal

PiXi =

ntotal

nior

Total moles in mixture

Moles of component

ExamplesDetermine the mole fractions and partial pressures of

CO2, CH4, and He in a sample of gas that contains 0.250 mole of CO2, 1.29 moles of CH4, and 3.51 moles of He, and in which the total pressure is 5.78 atm

ExampleA 1.00 L vessels contain 0.215 mole of N2 gas and 0.0118

mole of H2 gas at 25.5oC. Determine the partial pressure of each component and the total pressure

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.

averagespeed

molarmass

Diffusion: The mixing of different gases by molecular motion with frequent molecular collisions.

Graham’s Law:

Effusion: The escape of a gas through a pinhole into a vacuum without molecular collisions.

Rate1

m

Graham’s Law: Diffusion and Effusion of GasesIn comparing two gases at the same temperature and

pressure

√m2

√m1

Rate 1

Rate 2

=

ExampleDetermine 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 CO2

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

Attractive forces between particles become more important at higher pressures.

PV2

n2

= nRT+ V - n

van der Waals equation

ba

Correction for intermolecular attractions.

Correction for molecular volume.

ExampleA sample of 3.50 moles of NH3 gas occupies 5.20 L at

47oC. Calculate the pressure of the gas (in atm) usingA) the ideal gas equationB) the van der Waals equation

a = 4.17 atm •L/mol2 b = 0.0371 L/mol