Question

A gaseous mixture of $O_2$ and $X$ containing $20$ % of $X$, diffuses through a small hole in $234s$ while pure $O_2$ take $224s$ to diffuse through the same hole. The molecular mass of the mixture is:

• A. $34.9$
• B. $46.6$
• C. $32$
• D. $44$

Answer 1

Answer: (A)

$34.9$

The rate of diffusion is the ratio of quantity diffused to time.

The rate of diffusion is inversely proportional to square root of molecular mass. When same quantity of two gases diffuses,

$\frac{t_{mixture}}{t_{O2}}=\sqrt{\frac{M_{mixture}}{M_{O2}}}$
$\frac{234}{224}=\sqrt{\frac{M_{mixture}}{32}}$
$1.0446=\sqrt{\frac{M_{mixture}}{32}}$
$1.091=\frac{M_{mixture}}{32}$

$M_{mixture}=34.9$ g/mol

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