An unknown gas diffuses 0.25 times as fast as helium. What is it's molar mass? What steps are to be done?

64.0 g/mol.

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 unknown gas.

∨₂ is the rate of effusion of He gas.

M₁ is the molar mass of the unknown gas.

M₂ is the molar mass of He gas (M₂ = 4.0 g/mol).

∨₁/∨₂ = 0.25.

∵ ∨₁/∨₂ = √ (M₂/M₁)

∴ (0.25) = √ (4.0 g/mol) / (M₁)

By squaring the both sides:

∴ (0.25) ² = (4.0 g/mol) / (M₁)

∴ M₁ = (4.0 g/mol) / (0.25) ² = 64.0 g/mol.