The relationship between the rate of diffusion and the molar mass is given by Graham's law. A gas diffusing 1/6 times faster than hydrogen will have a molar mass of 72.58 g/mol. Thus, option d is correct.
Graham's law states the inverse relationship between the rate of diffusion and the square root of the molar mass of the gas. It is given as,
Rate = 1 ÷ √M
The molar mass of the gas that diffuses 1/6 times faster than hydrogen is calculated as,
R₁ ÷ R₂ = √ (M₂ ÷ M₁)
Here,
The molar mass of hydrogen = M₁
The molar mass of unknown gas = M₂
Rate of diffusion of hydrogen gas = R₁
Rate of diffusion of unknown gas = R₂ = 1 / 6 R₁
Substituting values:
R₁ ÷ 1/6 R₁ = √M₂ ÷ 2
6 × 1.414
= 8.485
= 84.85 g/mol ≈ 72.58 g/mol
Therefore, option d. 72.58 g/mol is the molar mass of unkown gas.
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