# Graham's Law

Diffusion of gases can be described as the process by which a gas spreads to occupy the available and accessible space, thereby creating a uniform pressure throughout the space the gas occupies. A gas having a higher partial pressure will travel or diffuse toward regions of gases having a lower partial pressure, until an equilibrium is reached. To analyze the diffusion of gases, it is much simpler to think in terms of effusion. The difference between diffusion and effusion is that diffusion is the movement of gas through the entire volume of the container, whereas effusion is the movement of gas through a tiny hole of the container.

The figure depicts the effusion of gas molecules through a small hole in a container.

According to Graham's law of effusion, the effusion rate of a gas is inversely related to the square root of the molecular weight of the gas. This is true provided that we have the same pressure and temperature conditions. Graham's law can be expressed as shown below:

Graham's law can also be applied to diffusion.

Example

Calculate the ratio of effusion of the gases oxygen and hydrogen. Assume that the two gases are in the same container having a tiny hole in it.

Solution

First, we have to consider the fact that according to Graham's law, the rate of effusion is inversely proportional to the square of molecular weight of the gas, which is effused. This can be represented as follows. Keep in mind that both gases are diatomic.

So the ratio of the rates of effusion of hydrogen and oxygen is 4 : 1.

We should think about the implications of this ratio. This means that the hydrogen molecules will effuse four times faster than the oxygen molecules.