If hydrogen effuses four times faster than an unknown gas, the molar mass of the unknown gas must be_______________?
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Answer: B. 32 gmol-1
Explanation
Graham's law of effusion states that the rate of gas effusion is inversely proportional to square root of molar mass. Since hydrogen gas effuses four times faster than the unknown gas, the unknown gas must be sixteen times heavier. Multiplying the molar mass of diatomic hydrogen by sixteen yields the correct molar mass of thirty-two grams per mole. Graham's law allows chemists to determine unknown molecular weights by measuring relative gas effusion or diffusion rates. Diatomic hydrogen is the lightest known gas with a standard molar mass of approximately two grams per mole. Kinetic energy principles dictate that lighter molecules travel at higher average speeds than heavier molecules at equal temperatures.
A molar mass of 16 g/mol would correspond to methane, which does not satisfy the fourfold effusion rate difference. Option C suggests 48 g/mol, which fails to match the mathematical ratio required by Graham's law calculations. Option D suggests 64 g/mol, representing an excessively heavy gas that would effuse at a much slower rate.
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