Untitled - Kelly Walsh High School

Gases 87
Second, the KMT relates the average kinetic energy of the gas particles to
the Kelvin temperature. We can represent the average kinetic energy per
molecule as:
where
m is the mass of the molecule
v is its velocity.
KE/molecule 1/2 mv 2
We can represent the average kinetic energy per mole of gas as:
where
R again is an ideal gas constant
T is the Kelvin temperature.
KE/mol 3/2 RT
Graham’s law defines the relationship of the speed of gas diffusion (mixing of
gases due to their kinetic energy) or effusion (movement of a gas through a tiny
opening) and the molecular mass. In general, the lighter the gas, the faster is its
rate of effusion. Normally we use a comparison of the effusion rates of two
gases with the specific relationship being:
r1/r2 2M2 /M1 where
r 1 and r 2 are the rates of effusion/diffusion of gases 1 and 2, respectively
M 2 and M 1 are the molecular (molar) masses of gases 2 and 1, respectively
We can use Graham’s law to determine the rate of effusion of an unknown gas
knowing the rate of a known one or we can use it to determine the molecular
mass of an unknown gas. For example, suppose you wanted to find the molar
mass of an unknown gas. You measure its rate of effusion versus a known gas,
H 2. The rate of hydrogen effusion was 3.728 mL/s, while the rate of the
unknown gas was 1.000 mL/s. The molar mass of H 2 is 2.016 g/mol. Substituting
into the Graham’s law equation gives:
r /r H2 unk 2Munk /MH2 (3.728 mL/s)/(1.000 mL/s) 2Munk /2.016 g/mol
M unk 28.018336 28.02 g/mol