Question

Flask I contains a gaseous mixture of $He\left(g\right)$, $H_2\left(g\right)$, in the molar ratio of $1:\sqrt{2}$. The gas mixture is allowed to effuse through a fine orifice in the flask l and is collected in flask ll. What is the average molar mass of gas mixture initially collected in flask ll?

• A. 3.2
• B. 2.33
• C. 4
• D. None of these

Answer 1

The correct option is A 3.2

$\left(A\right)$ Given

$\frac{{}^n{H}_e}{{}^n{H}_2}=\frac{1}{\sqrt{2}}\Rightarrow {}^n{H}_e=\frac{{}^n{H}_2}{\sqrt{2}}$

Let ${}^n{H}_2=x$ then ${}^n{H}_e=\frac{x}{\sqrt{2}}$

mole fraction of $H_2=\frac{x}{\frac{x}{\sqrt{2}}+x}=\frac{\sqrt{2}}{1+\sqrt{2}}=Y_A$

mole fraction of $H_e=\frac{1}{1+\sqrt{2}}=Y_B$

arg molecular weight $\left(\overline{M}w\right)=M_{H_e}{Y}_B+M_{H_2}{Y}_A$