Chemistry 5

Chapter-6

Gases

Part-3

9 October 2002

Chemistry Research: Some History

George B. Kistiakowsky

Dudley R. Herschbach

How does a gas behave at the molecular scale?

Key Observations/Assumptions• Structure

• Motion

• Forces

• Collisions

• Energy

Kinetic-Molecular Theory

Gas consists of large number of molecules or atoms whose size is negligible relative to volume

Gas molecules are in constant random motion, and travel in straight-line trajectories between collisions.

Gas molecules do not influence one another; assume attractive and repulsive forces are negligible except during collisions.

Gas molecules collide with each other and container walls. Individual molecules gain/lose energy during collisions, although total energy is conserved; collisions are elastic.

The average kinetic energy of gas molecules is proportional to the absolute temperature. At a given temperature, all gases havethe same average kinetic energy (but not speed).

Molecular collisions & pressure

Since P = F/A, what are forces of collisions?• kinetic energy:

• frequency of collisions:

• impact force

Origin of Pressure

Like any moving object, gas molecules have a translational kinetic energy, ek:

ek = ½mu2

where m is mass and u is speed.

The number of collisions/second or frequency will affect total pressure. The collision frequency is related to speed of molecules and number per unit volume:

collision freqency = u(N/V)

The momentum transfer that occurs when a gas molecule collides with the wall is called an impulse, and is directly proportional to mass and velocity of molecules:

impulse ∝ mu

Root mean square speed,(u2)1/2

Putting all together:

Pressure: Molecular Theory

Since we are deriving properties based on kinetic energy, which is ∝ u2, it is the average of the square of speed that is important:

u2 = (u12 + u2

2 + … uN2)/N

The pressure, P, is then going to be the product of the impulse and collision frequency terms for three dimensions

P = (impulse)x(collision frequency)

P = 1/3 (N/V)mu2

How do properties of ideal gas molecules affect properties such a speed?

Distributions vs. Mass

Molecular Speeds

Assume we have a mole of gas, thenPV = nRT = RT and N = NA

Substitute into expression for pressure, and solve for u:PV = (1/3)NAmu2

3RT = NAmu2

but NAm = molar mass, M

urms = (3RT/M)1/2

Note: R = 8.314 J/mol-K, where J = kg(m/s)2

How does temperature affect the average kinetic energy of gas molecules?

Distributions vs. Temperature

Temperature

urms = (3RT/M)1/2

Solve for TT = (M/3R)u2

That is, temperature and kinetic energy are directly related.

Effusion

Demonstration--Observations•

•

Graham’s Law:

Effusion of a Gas

is defined as the escape of gas molecules from a container via atiny orifice into vacuum.

Large and small metal balls are given an average kinetic energy by shaking.We see that the rate of small balls exiting the orifice is greater than that of the larger ball, which are traveling more slowly.

The rates of effusion of two different gases are inversely proportional to the square roots of their molar masses.

What is diffusion?

What can we say about diffusion of different gases?

Diffusion

Diffusion of a gas corresponds to gradual mixing of two or more gases due to random molecular motions of the gas molecules.

Diffusion rates of gases will depend on the molecular mass of the gas molecules.However, we cannot simply apply Graham’s law to diffusion since molecules of diffusing gas undergo collision during the process such that their average diffusion rate is much lower than speed (in absence of collisions).