Question

The rate of diffusion of a gas $X$ is $\sqrt{2}$ times that of $Y$. If the molecular weight of $X$ is $16$, the molecular weight of $Y$ is:

• A. $32$
• B. $8\sqrt{2}$
• C. $32\sqrt{2}$
• D. $16\sqrt{2}$

Answer 1

The correct option is A $32$

$R_X,R_Y$ and $M_X,M_Y$ are the rate of diffusion and molar mass of $X$ and $Y$ respectively.

So here, $\frac{R_X}{R_Y}=\sqrt{2}$

$\frac{R_X}{R_Y}=\sqrt{\frac{M_Y}{M_X}}=\sqrt{\frac{M_Y}{16}}=\sqrt{\frac{M_Y}{16}}$

$\frac{R_X}{R_Y}=\sqrt{2}=\frac{\sqrt{M_Y}}{4}$

$M_Y=(4\sqrt{2}{)}^2$
Hence, the molecular weight of $Y$ $=$ $32$ u.