Answer to Question #288470 in General Chemistry for yane

Question

Oxygen (O₂) gas is observed to diffuse through a capillary for 18 seconds. How long will it take for methane gas (CH₄) to diffuse through the same orifice under identical conditions of temperature and pressure?

Answer 1

It is based on Graham's law of diffusion rates: "The rate of diffusion of a gas is inversely proportional to the square root of it's molar mass."

The formula for comparing the diffusion rates of two gases:

r₁/r₂ = (M₂/M₁)^1/2

​r stands for rate of diffusion and M stands for molar mass of the gas and the subscripts 1 and 2 are referring two different gases.

Let's say 1 is for oxygen and 2 is for methane. Molar mass of oxygen is 32 and molar mass of methane is 16.

Rate is how much volume diffused per unit time, so:

(V₁/t₁) / (V₂/t₂) = (M₂/M₁)^1/2

Since the volumes are same, the formula could be written as:

t₂/t₁ = (M₂/M₁)^1/2

​t₂/18 sec = (16/32)^1/2

t₂ = 12.7 sec