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

Question

Find the number of diffusion steps required to separate the isotopic mixture initially containing some mass of hydrogen gas and 1 mole of deuterium gas in a 3 litre container maintained at 24.63 atm and 300 K to the final mass ratio of hydrogen to deuterium gas equal to 1:4.

TestHub · Accepted Answer

Total moles = PV/RT = 24.63 × 3/(0.0821 × 300) = 3.0 mol, so H2 = 2.0 mol and D2 = 1.0 mol.

Initial mass ratio H2:D2 = (2 × 2):(1 × 4) = 1:1. Required final mass ratio = 1:4.

Each diffusion step enriches the lighter component by the Graham factor √(M_D2/M_H2) = √(4/2) = √(2); after n steps the H2:D2 ratio is multiplied by (1/√(2))ⁿ.

(1/√(2))ⁿ = 1/4 ⇒ 2^n/2 = 4 ⇒ n = 4.

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