[Single-digit Integer] Find the number of diffusion steps required to separate the isotopic mixture — States of Matter and Gaseous State Chemistry Question

💡 Solution & Explanation

Total moles $=PV/RT=24.63\times3/(0.0821\times300)=3$ mol. $n_{H_2}=3-1=2$ mol, $n_{D_2}=1$ mol. Initial ratio $=2$. Target mass ratio $H_2:D_2=1:4 \Rightarrow$ mole ratio $=\frac{1/2}{4/4}=0.5$. Graham factor $\alpha=\sqrt{M_{D_2}/M_{H_2}}=\sqrt{2}$. $(H_2/D_2)_N=2\times(\sqrt{2})^{-N}=0.5 \Rightarrow 2^{-N/2}=0.25=2^{-2} \Rightarrow N=4$. Answer: $\boxed{4}$