The MCAT loves Graham's Law. To understand Graham's Law, make sure you have a good conceptual picture of the particle point of view within the ideal gas system. Graham demonstrated that at the same temperature the rates of effusion of two gases (gas A and gas B) are inversely proportional to the square roots of their molecular weights. The kinetic theory picture is necessary to understand why this should be so.
Through kinetic theory we understand that at the same temperature, the average kinetic energy per particle of two ideal gases is the same. The equivalence of the average kinetic energy per particle of the two gases leads to the Graham's Law relationship of effusion rates because the rate of effusion is directly proportional to molecular speed. If the average kinetic energy per particle of the two gases is the same, then the ratio of the average speed of particle A to the average speed of particle B (how many times faster is particle A than B) will be the ratio of the square root of the mass of particle B to the square root of the mass of particle A. For two gases at the same temperature, if one is four times heavier, it will have an effusion rate one half as great.
Through kinetic theory we understand that at the same temperature, the average kinetic energy per particle of two ideal gases is the same. The equivalence of the average kinetic energy per particle of the two gases leads to the Graham's Law relationship of effusion rates because the rate of effusion is directly proportional to molecular speed. If the average kinetic energy per particle of the two gases is the same, then the ratio of the average speed of particle A to the average speed of particle B (how many times faster is particle A than B) will be the ratio of the square root of the mass of particle B to the square root of the mass of particle A. For two gases at the same temperature, if one is four times heavier, it will have an effusion rate one half as great.
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