Find the number of diffusion steps required to separate the isotopic mixture initially containing some amount of H 2 gas and 1 mol of D 2 gas in a container of 3 litre capacity maintained at 24.6

Question

Find the number of diffusion steps required to separate the isotopic mixture initially containing some amount of $H_{2}$ gas and 1 mol of $D_{2}$ gas in a container of 3 litre capacity maintained at 24.6 atm and $2 7^{\circ} C$ to the final mass ratio $(\frac{W _{D_{2}}}{W _{H_{2}}})$ equal to $\frac{1}{4}$ .

(Given: R = 0.082 L-atm/mol-K)

TestHub · Accepted Answer

Initial moles of H₂: n H 2 ​ ​ + n D 2 ​ ​ = RT P V ​ . n H 2 ​ ​ + 1 = 0.082 × 300 24.6 × 3 ​ = 3 ⟹ n H 2 ​ ​ = 2 mol. Initial mass ratio: W H 2 ​ ​ W D 2 ​ ​ ​ = 2 × 2 1 × 4 ​ = 1 . After N steps: W H 2 ​ ​ W D 2 ​ ​ ​ = 1 × ( M D 2 ​ ​ M H 2 ​ ​ ​ ​ ) N = 4 1 ​ . 1 × ( 4 2 ​ ​ ) N = 4 1 ​ ⟹ ( 2 ​ 1 ​ ) N = 4 1 ​ ⟹ ( 2 1 ​ ) N /2 = 4 1 ​ ⟹ N /2 = 2 ⟹ N = 4 .

Chemistry - Ideal Gas Question with Solution | TestHub

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JEE Advanced (2028)