Find the number of diffusion steps required to separate the isotopic mixture initially containing so — States of Matter and Gaseous State Chemistry Question
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.
💡 Solution & Explanation
Total initial moles $n = \frac{PV}{RT} = \frac{24.63 \times 3}{0.0821 \times 300} = 3\text{ mol}$. Since $D_2 = 1\text{ mol}$, $H_2 = 2\text{ mol}$. Initial molar ratio $n_{H_2}/n_{D_2} = 2/1 = 2$. Final mass ratio $1:4$ corresponds to molar ratio $n'_{H_2}/n'_{D_2} = (1/2) / (4/4) = 0.5$. In a fractional effusion cascade designed to enrich the heavier gas by taking the residue, the ratio changes by a factor of $\alpha = \sqrt{M_{D_2}/M_{H_2}} = \sqrt{2}$ per step inversely. Ratio $= 2 \times (1/\sqrt{2})^N = 0.5 \implies (\sqrt{2})^N = 4 \implies N = 4$. Therefore, correct answer is 4.