Find the number of diffusion steps required to separate the isotopic mixture initially containing some mass of helium gas and 1 mole of methane gas in a 3 litre container maintained at 24.63 atm and 3

Question

Find the number of diffusion steps required to separate the isotopic mixture initially containing some mass of helium gas and 1 mole of methane gas in a 3 litre container maintained at 24.63 atm and 300 K to the final mass ratio of helium to methane gas equal to 1:32.

TestHub · Accepted Answer

Total moles = PV/RT = 24.63 × 3/(0.0821 × 300) = 3.0 mol, so He = 2.0 mol and CH₄ = 1.0 mol.

Initial mass ratio He:CH₄ = (2 × 4):(1 × 16) = 1:2.

Each diffusion step divides the He:CH₄ ratio by sqrt(M_CH₄/M_He) = sqrt(16/4) = 2.

(1/2) × (1/2)ⁿ = 1/32 ⇒ 2ⁿ⁺¹ = 32 ⇒ n + 1 = 5 ⇒ n = 4.

Chemistry - Ideal Gas Question with Solution | TestHub

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