Question

The molecules of gas $A$ travel four times faster than the molecules of gas $B$ at the same temperature. The ratio of molecular weights $\left(M_A/M_B\right)$ will be:

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

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

where $r_A$ is rate of diffusion of gas A

where $r_B$ is rate of diffusion of gas B

where $M_A$ is molecular gas of gas A

where $M_B$ is rate of diffusion of gas B

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

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

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

Hence, option A is correct.