Question

Under the same conditions of temperature and pressure, the ratio of times of diffusion of two gases $A$ and $B$ is $4:1$. So the ratio of the molecular weights of the gases $A$ and $B$ is:

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

Answer 1

The correct option is D $1:16$

Rate of diffusion of 2 gases is given by the formula:

$\frac{r_A}{r_B}=\sqrt{\frac{M_B}{M_A}}$

$\Rightarrow \frac{4}{1}=\sqrt{\frac{M_B}{M_A}}$

$\Rightarrow \frac{16}{1}=\frac{M_B}{M_A}$

$\Rightarrow \frac{M_A}{M_B}=\frac{1}{16}$

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