KMT

Kinetic Molecular Theory

A simple microscopic model:

1) Gases are composed of molecules that are in continuous motion, traveling in a straight lines and changing directions only when they collide with other molecules or with the walls of a container.

2) Molecules composing the gas are negligibly small compared to the distances between them

3) Pressure exerted by a gas in a container results from collisions between the gas molecules and the container walls.

4) Gas molecules exert no attractive or repulsive forces on each other or the container walls; therefore, their collisions are elastic and do not involve a loss of energy

5) Average kinetic energy of the gas molecules is proportional to the kelvin temperature of the gas.

Maxwell-Boltzmann distribution

Describes the molecular speed distribution of molecules in the gas, where some have a very slow speed and some have a very high speed, but the overwhelming majority has an intermediate speed.

KE = 1/2(m*(v^2))

Kinetic energy formula

urms

The symbol that represents the root mean squared speed of a particle

Root mean square speed

The square root of the average of the squares of the speeds with n representing the number of particles.

M

Symbol that represents molar mass in the units of kg/mol

KE(average) = 1/2(M*(urms^2))

Formula for the average kinetic energy of the mole of particles.

KE(average) = 3/2(RT)

The equation that describes the directly proportional relationship of the average kinetic energy of a mole of gas molecules to the temperature of the gas.

8.314 J/mol•K

The appropriate gas constant value to use in the proportional relationship of the average kinetic energy and the temperature of the gas

1/2(M*(urms^2)) = 3/2(RT)

First combination of equation.

urms = ((3RT)/(M))^1/2

Second combination of equation

lighter molecules, heavier molecules

Gases composed of _______________ have more high-speed particles and a higher urms.

Gases composed of _______________ have more low-speed particles and a lower urms.

Effusion rate is directly proportional to urms

Another part of the Graham’s law

M = (3RT)/(urms^2)

Formula to find molar mass

(effusion rate A)/(effusion rate B) = (urms A)/(urms B) = (MB/MA)^1/2

Mathematical representation of the another part of the Graham’s law