Question

If the ratio of the rates of diffusion of the two gases $A$ and $B$ is $4:1$, the ratio their densities is:

• A. $1:16$
• B. $1:4$
• C. $1:8$
• D. $1:2$

Answer 1

The correct option is A $1:16$

Let rate of diffusion of gas B =x

Rate of diffusion of gas A =4x

We know that $\frac{r_A}{r_B}=\sqrt{\frac{D_B}{D_A}}$

where $r_A$ is rate of diffusion of gas A

where $r_B$ is rate of diffusion of gas B

where $D_A$ is density of gas A

where $D_B$ is density of gas B

$=\frac{4}{1}=\sqrt{\frac{D_B}{D_A}}$

$\frac{D_B}{D_A}=\frac{16}{1}$

$\frac{D_A}{D_B}=\frac{1}{16}$

Option A is correct.