Question

Two gases $A$ and $B$ having the same volume diffuse through a porous partition in $20$ and $10$ seconds respectively. The molecular mass of $A$ is $49u$. Molecular mass of $B$ will be__________.

• A. $50.00u$
• B. $12.25u$
• C. $6.50u$
• D. $25.00u$

Answer 1

The correct option is B $12.25u$

The time taken by gas A to diffuse in terms of volume through a porous partition is 20 sec.

The time taken by gas B to diffuse in terms of volume through a porous partition is 10 sec.

The molecular mass of the substance A is 49 u.

Using Graham's Law of Diffusion, we find the ratio of the rate of diffusion with Molecular Mass.

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

$\frac{10}{20}=\sqrt{\frac{M_B}{49}}$

$M_B=\frac{49}{4}=12.25$

Therefore, the molecular mass of element B is 12.25 u.

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