Explain how the rate of diffusion of a gas is related to its molar mass.

Carbon dioxide gas (CO2) effuses 3.2 times faster than an unknown gas. Determine the molar mass of the unknown gas. Show your work or explain your answer, giving specific values used to determine the answer.

1 - Rate2 is the rate of effusion for the second gas. M2 is the molar mass of gas 2. In the same conditions of temperature and pressure, the molar mass is proportional to the mass density. Therefore, the rates of diffusion of different gases are inversely proportional to the square roots of their mass densities.

Explanation:

2 - According to Graham's law of diffusion:

R1/R2 = √M.M2 / √ M.M1

where

R1 = rate if diffusion of the first gas

R2 = rate of diffusion of the second gas

M.M2 = molar mass of the second gas

M.M1 = molar mass of the first gas

The first gas is CO2 and CO2 has a molar mass of 44

R1/R2 = 3.2

Substitute all the values into the equation:

3.2 = √M.M2 / √44

Squaring both sides:

3.2^2 = M.M2 / 44

Cross multiply as follows:

M.M2 = 3.2*3.2*44

= 450.56