Question

The rate of diffusion of two gases $A$ and $B$ is in the ratio of $1:2$ and the $B$ and $C$ in the ratio $1:8$, the rate of diffusion of $C$ with respect to $A$ is

• A. $1:12$
• B. $12$
• C. $1:16$
• D. $16$

Answer 1

The correct option is D $16$

We know that,
Rate of diffusion $\left(r\right)\propto \frac{1}{\sqrt{M}}$
Where $M$ is molar mass of gas.
$\therefore \frac{r_A}{r_B}=\sqrt{\frac{M_B}{M_A}}=\frac{1}{2}$
$\Rightarrow \frac{M_B}{M_A}=\frac{1}{4}$
Also,
$\frac{r_B}{r_C}=\sqrt{\frac{M_C}{M_B}}=\frac{1}{8}$
$\Rightarrow \frac{M_C}{M_B}=\frac{1}{64}$

$\therefore \frac{M_C}{M_A}=\frac{M_B}{M_A}\times \frac{M_C}{M_B}=\frac{1}{4}\times \frac{1}{64}$
So, $\frac{r_C}{r_A}=\sqrt{\frac{M_A}{M_C}}=\sqrt{4\times 64}=16$