Chemistry: Effusion and Diffusion

Effusion and Diffusion

Other important behaviors of gases explained by the Kinetic Molecular Theory are effusion and diffusion. Effusion is the rate at which a gas escapes through a small hole in a container. Diffusion is the rate at which a gas travels across a room. Both of these phenomena are illustrated by the following figure.

Figure 15.4(a) Effusion is when a gasescapes through a small hole in a container. (b) Diffusion is the rate at which a gas travels across the room.

The relative rates at which two gases effuse or diffuse is explained by Graham's Law, shown here:

• ^r₁⁄_r2 = √^M₂⁄_M

The rate of motion of gas 1 is r₁, and M₁ denotes its molecular weight (in kg). Likewise, r₂ and M₂ stand for the rate of motion and molecular weight of gas 2. Let's see an example of how this equation is used:

Example: If I pop a balloon of methane and a balloon of carbon dioxide at the same time, which gas will diffuse to the other end of the room more quickly?

Solution: We'll let r₁ represent the rate of diffusion of methane and r₂ represent the rate of diffusion of carbon dioxide. Plugging the molecular weights of both gases into this equation, we find that:

• r_CH4⁄r_CO2 = √^{0.0440kg / mol}⁄_0.0180kg / mol

We have determined that methane will travel across the room 1.56 times faster than carbon dioxide, making it the first to hit the opposite wall.