Question

A vessel initially contains two gases A and ab in the mass ratio 2:1 respectively. If the above gas mixture is allowed to effuse through a hole then the molar composition of the mixture coming initially out of the hole is 1:4. Thus:

• A. the simplest whole number ratio of the moles of gases A and B present in the vessel in the beginning respectively is 1:2
• B. the simplest whole number ratio of the moles of gases A and B present in the vessel in the beginning respectively is 1:8
• C. if the mass ratio of gases A and B required in the final concentrated sample is 1:32 then the number of successive steps of effusion to be carried out is 5
• D. none of these

Answer 1

The correct option is A the simplest whole number ratio of the moles of gases A and B present in the vessel in the beginning respectively is 1:2

Let the masses be $2x$ and $x$

$n$ of gas $1.\frac{2x}{M_1}$

$n$ of gas $2.=\frac{x}{M_2}$

Now, rate of eff $\propto \frac{n}{U_m}$

$\therefore \frac{n_1}{U{m}_1}\times \frac{\sqrt{M_2}}{n_2}=\frac{1}{4}$

$\Rightarrow \frac{2x}{M_1}\times \frac{M_2^{\frac{3}{2}}}{n_2}=\frac{1}{4}$

$\Rightarrow \frac{M_2}{M_1}=\frac{1}{4}$

$\therefore$ ration of mass $=\frac{2x}{{\mu }_1}\times \frac{m_2}{x}=2\times \frac{1}{12}=\frac{1}{2}$