Kinetic Molecular Theory

And Real Gases

The Ideal Gas Equation

• Describes how gases

behave, but it doesn’t

explain why they

behave as they do.

Kinetic-Molecular TheoryDescribes how gases

behave, but it doesn’t explain

why they behave as they do.

• The Kinetic Molecular

Theory is a model to help us

understand the physical

properties of gases.

• It helps us visualize what

happens to gas particles as

experimental conditions such

as pressure or temperature

change

Main Ideas of Kinetic-Molecular

Theory1. Gases consist of large numbers of

molecules that are in continuous,

random motion.

Random Walk – the pathway that a

molecule follows.

Main Ideas of Kinetic-Molecular

Theory• 2. The combined volume of all the

molecules of the gas is negligible relative

to the total volume in which the gas is

contained.

• 3. Attractive and repulsive forces between

gas molecules are negligible.

Main Ideas of Kinetic-Molecular

Theory4. Energy can be transferred between molecules during collisions, but the average kinetic energy of the molecules does not change with time, as long as the temperature of the gas remains constant.

Main Ideas of Kinetic-Molecular

Theory5. The average

kinetic energy of the

molecules is

proportional to the

absolute temperature.

Kinetic Molecular Theory

• The KMT explain both pressure and

temperature at the molecular level.

– Pressure is causes by collisions of the

molecules with the walls of the container.

• Higher frequency of collisions = greater pressure

• More forceful the collisions = greater pressure

– Temperature is a measure of the AVERAGE

kinetic energy, and therefore the average

speed.

Root Mean Square Speed, u

• Even though molecules have the same

AVERAGE kinetic energy and hence an average

speed, the individual molecules move at varying

speeds.

• KE = ½ mu2

– m is the mass of the molecule

– Mass is a constant for a particular molecule.

• Application: Lighter gases travel faster than

heavier at the same absolute temperature.

Sample 10.13

• Found in Notepack.

Molecular Effusion

The escape of

gas molecules

through a tiny

hole into an

evacuated

space.

Diffusion

The spread of one

substance

throughout a space

or throughout a

second substance.

Equation

• The following equation expresses the root

mean square speed of any gas molecule

at a specific temperature:

– u = (square root) 3RT/Molar Mass

– R = 8.31 kg-m2/s2-mol-K

– Therefore mass must me in a kg to make the

R value work.

Example 10.14

• Calculate the rms speed, u, of N2 molecule

at 25oC.

• Calculate the rms speed of an He atom at

25oC.

Graham’s Law of Effusion

• The effusion rate of a gas is inversely proportional to the square root of its molar mass.

– r1/r2 = (square root) Mass 2/Mass 1

• This implies that the rate of effusion is directly proportional to the rms speed of the molecules.

– r1/r2 = u1/u2 = (square root) 3RT/Mass 1

3RT/Mass 2

Example Problem 10.15

• Found in notepack:

• Practice Exercise in notepack.

Real Gases: Deviations from Ideal

Behavior

In the real world, the

behavior of gases

only conforms to the

ideal-gas equation at

relatively high

temperature and low

pressure. (below 10

atm)

Deviations from Ideal Behavior

The assumptions made in the kinetic-molecular

model break down at high pressure and/or low

temperature.

Real Gases

• Real molecules do have finite volume and

they do attract one another.

• We need to correct for these factors for

“real” gas conditions.

Corrections for Nonideal

Behavior

• The ideal-gas equation can be adjusted to

take these deviations from ideal behavior

into account.

• The corrected ideal-gas equation is

known as the van der Waals equation.

• It places correction factors for volume of

molecules and for molecular attraction

between molecules.

The van der Waals Equation

) (V − nb) = nRTn2a

V2(P +

Practice Problems

• Found in notepacks.