Diffusion is a process of intermixing of gases. This is a natural tendency of any gas to occupy the whole volume available to it. So even without pressure difference gases mix with each other. If the pressure difference is increased the diffusion process becomes faster.(GRAHAM’S LAW OF DIFFUSION).
Effusion is flow of a gas through small openings due to pressure difference that is it is a case of fast diffusion.
(a)    Diffusion is mixing of gas molecules by random motion under conditions where molecular collisions occur. Diffusion is the process by which molecules move and travel from one place to another without requiring bulk motion. Diffusion results in molecules moving or mixing by only using kinetic energy.
(b) Effusion is the escape of a gas through a pinhole without molecular collisions. Effusion is the process by which molecules travel through a pinhole from a place of high concentration to low concentration. The process describes the ability of gas to travel through a small hole without collisions between molecules. This occurs when the diameter of the hole is considerably smaller than the mean free path of the molecules. The mean free path is the average distance traveled by a moving particle between successive collisions.
According to Graham’s Law of diffusion the rate of diffusion depends on pressure and molecular weight of a gas. Rate of Diffusion is directly proportional to Partial Pressure of the gas and inversely proportional to the square root of molar mass of the gas. That is, greater the pressure faster is the movement of molecules and heavier the molecules, slower are their movement.
Rate of diffusion α P (partial pressure)
Also, Rate of diffusion α 1/ M
Therefore we can write:
Rate, r α P/M
Rate of diffusion may be defined in various ways. It may be number of moles transferred per unit time, Volume transferred per unit time, distance travelled per unit time and even pressure drop per unit time. While comparing the rates of two gases, we should take similar definitions of rate, it may be n/t, V/t or d/t.

Graham’s Law of diffusion can be applied to diffusion and effusion both.
Worked example 1:
What is the ratio of the rate of effusion of neon gas to that of helium gas at the same temperature and pressure? 

Worked example 2:
The pressure in a vessel that contained pure oxygen dropped from 2000 torr to 1500 torr in 55 min as the oxygen leaked through a small hole into a vacuum. When the same vessel was filled with another gas, the pressure dropped from 2000 torr to 1500 torr in 85 min. What is the molecular weight of the second gas?

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