Question

Two gases $A$ and $B$ present seperately in two vessels $X$ and $Y$ at the same temperature with molecular weights $M$ and $2M$ respectively are effused out. The orifice in vessel $X$ is circular while that in $Y$ is a square. If the radius of the circular orifice is equal to that of the length of the square orifice, the ratio of effusion of gas $A$ to that of gas $B$ is

• A. $\sqrt{2}\pi$
• B. $\sqrt{\frac{\pi }{2}}$
• C. $2\pi$
• D. $\sqrt{\frac{2}{\pi }}$

Answer 1

The correct option is A $\sqrt{2}\pi$

Let the radius of circular orifice in vessel X $=r$
So the the side length of square orifice in vessel Y $=r$ (given)
$\text{Rate of diffusion}\alpha \text{Area of cross-section}$
$\text{Rate of diffusion}\alpha \frac{1}{\sqrt{M}}$
$\text{Rate of diffusion}\alpha \frac{\text{Area of cross-section}}{\sqrt{M}}$
$\frac{r_x}{r_y}=\sqrt{\frac{2M}{M}}\times \frac{A_x}{A_y}$ where $A_x$ and $A_y$ are the area of cross section of orifice.
$\therefore \frac{r_x}{r_y}=\sqrt{2}\times \frac{\pi r^2}{r^2}$
$\frac{r_x}{r_y}=\sqrt{2}\times \pi$