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. The rate of diffusion of gas is inversely proportional to the mean square root of molar mass of the gas.

2. 450.56 g/mol.

Explanation:

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

Thomas Graham found that, at a constant temperature and pressure the rates of effusion of various gases are inversely proportional to the square root of their masses.

∨ ∝ 1/√M.

where, ∨ is the rate of diffusion of the gas.

M is the molar mass of the gas.

2. Carbon dioxide gas (CO₂) effuses 3.2 times faster than an unknown gas. Determine the molar mass of the unknown gas.

∵ ∨₁/∨₂ = √ (M₂/M₁).

∨₁ is the rate of effusion of CO₂ gas.

∨₂ is the rate of effusion of the unknown gas.

M₁ is the molar mass of CO₂ gas (M₁ = 44.0 g/mol).

M₂ is the molar mass of the unknown gas (M₂ = ? g/mol).

∨₁/∨₂ = 3.2.

∵ ∨₁/∨₂ = √ (M₂/M₁)

∴ (3.2) = √ (M₂) / (44.0 g/mol)

By squaring the both sides:

∴ (3.2) ² = (M₂) / (44.0 g/mol)

∴ M₂ = (3.2) ² (44.0 g/mol) = 450.56 g/mol.