Graham's law of effusion states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. In other words, the lighter the gas, the faster it will effuse.

Hydrogen gas has a molar mass of 2 g/mol, which is the lightest of all gases. Therefore, hydrogen gas will diffuse fastest.

Here is a mathematical explanation of Graham's law of effusion:

$$Rate \ of \ effusion \ \propto \ \frac{1}{\sqrt{Molar \ mass}}$$

where:

* Rate of effusion is the volume of gas that effuses through a small opening in a unit of time.

* Molar mass is the mass of one mole of gas.

For two gases A and B, Graham's law can be expressed as follows:

$$\frac{Rate \ of \ effusion \ of \ A}{Rate \ of \ effusion \ of \ B} = \sqrt{\frac{Molar \ mass \ of \ B}{Molar \ mass \ of \ A}}$$

If we let gas A be hydrogen gas (H2) and gas B be another gas with a molar mass of M, then the equation becomes:

$$\frac{Rate \ of \ effusion \ of \ H2}{Rate \ of \ effusion \ of \ gas \ B} = \sqrt{\frac{M}{2}}$$

Since the molar mass of hydrogen gas is 2 g/mol, the rate of effusion of hydrogen gas will be:

$$Rate \ of \ effusion \ of \ H2 = \sqrt{\frac{M}{2}} \times Rate \ of \ effusion \ of \ gas \ B$$

Because the molar mass of hydrogen gas is the lightest of all gases, the rate of effusion of hydrogen gas will be the fastest of all gases.