Question

Two gases $A$ and $B$ present separately in two vessels $X$ and $Y$ at the same temperature and pressure 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 that the length of the square orifice the ratio of rates of effusion of gas $A$ to that of gas $B$ is:

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

Answer 1

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

$\frac{r_x}{r_y}=\sqrt{\frac{2M}{M}}\times \frac{A_x}{A_y}$ where $A_x$ and $A_y$ are the area of cross section of orifice.

$\frac{r_x}{r_y}=\sqrt{2}\times \frac{\pi r^2}{l^2}=\pi \sqrt{2}$

$r$=radius of a radius orifice

$l$= length of square orifice.

Hence,option A is correct.