Gases and the Kinetic Molecular Theory

Speeds of gas molecules.

For a single molecule. Kinetic energy is:

KE = ½ mv2 m = mass; v = velocity

For a collection of gas molecules, the average kinetic energy is:

R = ideal gas constant = 8.314 J/Kmol

T = temperature in Kelvin

How fast do gas molecules move?

Called the root mean square speed of the gas.

What is the rms speed of O2 molecules at room temperature?

in kg/mol

Equation gives speed in meters/second.

Boltzmann Distributions

Boltzmann Distributions and Molar Mass

Boltzmann Distributions and Temperature

Gas Diffusion

Gas Effusion

Graham’s Law of Gas Effusion: used for determining molar mass of a gas

Example: A sample of ethane, C2H6, effuses through a small hole at a rate of 3.6 x 10-6 mol/hr. An unknown gas, under the sameconditions, effuses at a rate of 1.3 x 10-6 mol/hr. Calculate the molar mass of the unknown gas.

Gas Laws: The Ideal Gas Law

PV = nRT

P = pressure in atmospheresV = volume in litersN = moles of gasT = temperature in KR = gas constant = 0.08257 Latm/Kmol

Two Uses:

1. You know three of the four variables and solve for the fourth.

2. You know the change in one variable and determine the change in another.

The Ideal Gas Law: 1a: Determining one property, given the others

A sample of N2 gas has a volume of 250. mL,a pressure of 720 mm Hg, and is at 25 oC. What isthe mass of the gas?

The Ideal Gas Law: 1b: Determining one property, given the others

A sample of 2.60 g Ar gas has a pressure of 720 mm Hg, and is at 25 oC. What is the volume of the gas?

The Ideal Gas Law: 1c: Determining one property, given the others

What is the density of O2 gas at 20 oC, in grams per liter?

The General Gas Law: Determining changes in a property when a different property changes.

General idea: cancel properties that don’t change.

PV = nRT always the samePV

RnT

1 1 2 2

1 1 2 2

PV PV

nT n T

The General Gas Law: P and VA gas sample at 0.95 atm has a volume of 250 mL. What willthe pressure be if the volume is compressed to 100 mL? n and T are constant.

1 1 2 2

1 1 2 2

PV PV

nT n T

General Law:

The General Gas Law: n and VA 0.35 mol gas sample has a volume of 250 mL. What willthe volume be if 0.20 mol more gas are added? P and T are constant.

1 1 2 2

1 1 2 2

PV PV

nT n T

General Law:

The General Gas Law: T and VA gas sample has a volume of 250 mL at 100 oC. What willthe volume be if it is cooled to 10 oC? P and n are constant.

1 1 2 2

1 1 2 2

PV PV

nT n T

General Law:

The General Gas Law: T and VA car tire has a pressure of 32 psi in winter, when T = -10 oC. What will the pressure be in summer if T increases to 33 oC,but 5% of the air in the tire has leaked out? Assume V is constant.

1 1 2 2

1 1 2 2

PV PV

nT n T