Why does a light gas escape through a tiny hole faster than a heavy gas?

The phenomenon where a light gas escapes through a tiny hole faster than a heavy gas is known as effusion. This process occurs when gas molecules pass through a hole smaller than the mean free path of the gas, allowing them to escape without colliding with other molecules.1

The rate of effusion is fundamentally linked to the kinetic energy of the gas molecules. According to the kinetic theory of gases, the average kinetic energy of a gas is determined by its temperature, expressed by the formula:

$$\frac{1}{2}m{v}^2=\frac{3}{2}kT$$

In this equation, $m$ represents the mass of the molecule and $v$ represents its speed. Because the average kinetic energy is constant for a given temperature, a molecule with a smaller mass ($m$) must have a higher speed ($v$) to maintain that energy level. Consequently, lighter molecules travel at higher average speeds than heavier ones, leading them to strike the opening and escape more frequently. This relationship is described by Graham’s law of effusion.12