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

According to Graham's law of diffusion;

At constant temperature and pressure, the rate of diffusion of a gas is inversely proportional to the square root of its molar mass.

The molar mass of helium, m2= 4.

Therefore, r1/r2 = 1/4 since the gas diffuses 0.25 times as fast as helium.

Therefore;

Therefore, the molar mass of the gas is 64.

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64.0 g/mol.

Explanation:

∨ ∝ 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.

the answer

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