Kinetic Theory of Gases

Ideal Gas Equation PV = n R T (using moles) P V = N k B T (using molecules) – P: pressure (Pa) – V: volume (m 3 ) – N: number of molecules – k B : Boltzman’s constant 1.38 x J/K – T: temperature (K)

Sample problem Suppose a near vacuum contains 25,000 molecules of helium in one cubic meter at 0 o C. What is the pressure?

Sample problem Can you find a relationship between the Universal Gas Law constant R (8.31 J/mol K) and Boltzman’s constant k B (1.38 x J/K) ?

Kinetic Theory of Gases 1.Gases consist of a large number of molecules that make elastic collisions with each other and the walls of the container. 2.Molecules are separated, on average, by large distances and exert no forces on each other except when they collide. 3.There is no preferred position for a molecule in the container, and no preferred direction for the velocity.

Simulations nThI.html nThI.html atory/GLP.htm atory/GLP.htm

Average Kinetic Energy of a Gas K ave = 3/2 k B T – K ave : average kinetic energy (J) – k B : Boltzmann’s Constant (1.38 x J/K) – T: Temperature (K) The molecules have a range of kinetic energies; K ave is just the average of that range.

Sample Problem What is the average kinetic energy and the average speed of oxygen molecules in a gas sample at 0 o C?

Sample Problem Suppose nitrogen and oxygen are in a sample of gas at 100 o C. – A) What is the ratio of the average kinetic energies for the two molecules? – B) What is the ratio of their average speeds?