Question

A vessel contains two gases $A$ and $B$ in the mass ratio $2:1$ respectively. If the above gas mixture is allowed to diffuse through a hole, the molar composition of the mixture coming initially out of the hole is $1:4$. Find the simplest whole number ratio of the moles of gases $B$ and $A$ present in the vessel in the beginning respectively.

• A. $0.5$
• B. $1.0$
• C. $1.5$
• D. $2.0$

Answer 1

Answer: (A)

$0.5$

$\begin{array}{c}Giventhat\\ m_A=2,m_B=1\\ \frac{r_1}{r_2}=\sqrt{\frac{M_2}{M_1}}\\ M_2=\frac{m_B}{M_B},M_1=\frac{m_A}{M_1}\\ \frac{r_1}{r_2}=\sqrt{\frac{m_B}{M_B}\times \frac{M_1}{m_A}}\\ =\sqrt{\frac{1}{4}-\frac{4}{2}}\\ \sqrt{\frac{n_A}{n_B}}=\sqrt{0.5}\\ \frac{n_A}{n_B}=0.5\end{array}$

Hence option (A) is correct.