Behavior of Gas Molecules: Molecular Diffusion, Mean Free Path, and Effusion

A closed bottle of perfume contains a high concentration of gaseous aromatic molecules that are constantly moving and randomly colliding. Meanwhile, the air outside of the bottle contains essentially none of these molecules.

On opening the bottle, a concentration gradient is established between these high- and low-concentration regions. The molecules continue moving randomly, with overall movement from the high-concentration region to the low-concentration region.

The spontaneous mixing and spreading of liquids or gases in response to a concentration gradient is called molecular diffusion.

Diffusion is a slow process. Even though gas particles travel at high speeds, the numerous collisions cause frequent changes in speed and direction.

The average distance a particle travels between collisions is known as its mean free path. For a gas particle, its mean free path is influenced by the particle density, which also affects the pressure.

As the particle density increases, so does the collision frequency. Thus, their mean free path is shorter. Likewise, as the particle density decreases, so does the collision frequency, leading to a longer mean free path.

Different gases diffuse at different rates, depending on the speed of the gas particles. Since the root-mean-square, or RMS, speed and the molar mass of a gas are inversely related, lighter gases diffuse faster than heavier gases.

Consider a glass tube between reservoirs of equal amounts of ammonia and hydrogen chloride gas.

When the diffusing gases meet, they react to form a ring of ammonium chloride. The ring is closer to the hydrogen chloride end of the tube because the lighter ammonia molecules traveled farther down the tube than the heavier hydrogen chloride molecules in the same amount of time.

Effusion is another process that involves the movement of gas molecules. It is the ability of gas molecules to travel through a hole whose diameter is much smaller than the mean free path of the gas itself in response to a pressure difference.

This is why helium balloons eventually deflate — the helium gradually effuses through tiny pores in the balloon material.

Like diffusion, the rate of effusion is dependent on the RMS speed and molar mass of the gas. Specifically, the rate of effusion is inversely proportional to the square root of the molar mass of the gas. Therefore, heavier gases effuse more slowly than lighter ones.

For any two gases, the ratio of their effusion rates is the square root of the inverse ratio of their molar masses. This is called Graham’s law of effusion.

Consider two balloons inflated to the same pressure — one filled with helium and the other with oxygen. Helium has a lower molar mass than oxygen, as shown by the helium balloon’s buoyancy in air.

Applying Graham’s law to helium and oxygen suggests that helium effuses 2.8 times faster than oxygen. Thus, the helium balloon deflates faster than the oxygen balloon.