Kinetic Molecular Theory of Gases
The kinetic molecular theory is a molecluar level representation and a mathematical way of describing tand accounting for the physical behavior of gases. The kinetic molecular theory is a model. The assumption of this theory include:
1. Gas molecules move in a continuous, random, straight-line, motion.
2. Volume of gas molecules are negligible compared to the volume of the entire container
3. Collisions between gas molecules are elastic
4. The average kinetic energy of any gas is proportional to the temperature (in units of Kelvin).
5. No attractive forces exist between gas molecules
The average kinetic energy of a gas is proportional to the temperature. So that if we compare two gases, say He and NH3, at the same temperature, each gas will have the same average KE.
av KEgasA = av KEgasB
(1/2)mAvA2 = (1/2)mBvB2
If we compare He and NH3, mHe is less than the mNH3
therefore the average speed of the He molecules must be greater than the average speed of the NH3 molecules.
In order for the av KE of each gas to be equal, the lighter HE molecules travel faster (more collisions), yet they hit the walls of the container with a lighter force than the NH3 molecules. The NH3 molecules are traveling a bit slower (not as many collisions), but they hit the walls of the container with more force - the two factors of speed and mass of each gas balance each other.
We need to discuss the fact that at a specific temperature, all of the gas molecules do not have the same speed. In fact, there is a distribution of speeds.
As the temperature is increased the average speed of a sample of O2 molecules increases. There is a difference bewteen average speed and root-mean-square speed.
Note that <v2> does not equal <v>2!!!
Use the root mean square speed! ---> vrms = (<v2>)(.5) (an exponent to one-half is the same operation as a square root radical).
Also that at a specific temperature, different gases have different average speeds.
Consider a mixture of Helium and Neon at some temperature, T.
This says that if we compare the average speed of two gases at the same temperature, the av KE is the same. The only way for this to be true since the masses are different is for the light molecules to be moving at a faster average speed than the heavier molecules. If an increase in temperature occurs, the number of molecules stays constant, the molecules go faster, the average kinetic energy increases.