What is the rate of effusion of methane, CH₄, relative to the rate of effusion of acetylene, C₂H₂?

1.274.

Explanation:

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.

∨₁/∨₂ = √ (M₂/M₁)

∨₁ is the rate of effusion of the methane.

∨₂ is the rate of effusion of acetylene gas.

M₁ is the molar mass of methane (M₁ = 16.0 g/mol).

M₂ is the molar mass of acetylene (M₂ = 26.0 g/mol).

∴ The rate of effusion of methane, CH₄, relative to the rate of effusion of acetylene, C₂H₂ = ∨₁/∨₂ = √ (M₂/M₁) = √ (26.0 g/mol) / (16.0 g/mol) = 1.274.