Question

The rate of diffusion of methane at a given temperature is twice that of gas $X$. The molecular mass of gas $X$ is :

• A. $64.0$
• B. $32.0$
• C. $4.0$
• D. $8.0$

Answer 1

Answer: (A)

$64.0$

The rate of diffusion of methane at a given temperature is twice that of gas X.

$r_{C{H}_4}=2r_X$
The rate of diffusion is inversely proportional to the square root of its molar mass.

$\frac{r_{C{H}_4}}{r_X}=\sqrt{\frac{M_X}{M_{C{H}_4}}}$
$\frac{2r_X}{r_X}=\sqrt{\frac{M_X}{16}}$
$4=\frac{M_X}{16}$
The molecular mass of gas $X$ is $M_X=64.0$ g/mol

Hence, the correct option is A.