Question

Under identical conditions of pressure and temperature, $4L$ of gaseous mixture $(H_2$ and $C{H}_4)$ effuses through a hole in $5$ min whereas $4L$ of a gas $X$ ofm molecular mass $36$ takes to $10$ min to effuse through the same hole. The mole ratio of $H_2:C{H}_4$ in the mixture is:

• A. $1:3$
• B. $1:2$
• C. $2:3$
• D. $1:1$

Answer 1

The correct option is D $1:1$

Rate of diffusion is directly proportional to $\frac{1}{(\sqrt{\text{MOLECULAR WEIGHT})}}$

$\text{TIME}$$\propto$ $\sqrt{\text{MOLECULAR WEIGHT}}$

Now time is taken for mixture=5 min

time is taken for unknown gas =10 min

therefore

$\sqrt{m_1/5}=\sqrt{\frac{36}{10}}$

$\sqrt{m_1}=3$

$m_1=9$

MOLECULAR WEIGHT $m_1=\frac{n_1{M}_1+n_2{M}_2}{n_1+n_2}$

where $n_1$ and $n_2$ are number of moles of $H_2$ and $C{H}_4$ respectively

$9=\frac{n_1\times 2+n_2\times 16}{(n_1+n_2)}$

$9n_1+9n_2=2n_1+16n_2$

$7n_1=7n_2$

$n_1=n_2$

Therefore moles ratio is 1:1

Hence, the correct option is $\text{D}$