Question

If the number of molecules of $S{O}_2$ (molecular weight =64) effusing through an orifice of unit area of cross-section in unit time at $0^{o}C$ and 1 atm pressure is n. The number of He molecules (atomic weight=4) effusing under similar conditions at ${273}^{o}C$ and $0.25atm$ is:

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

Answer 1

The correct option is A $\frac{n}{\sqrt{2}}$

The number of molecules of $S{O}_2$ (molecular weight =64) effusing through an orifice of unit area of the cross-section in unit time at $0^{o}C$ and 1 atm pressure is n. This represents the rate of effusion of $S{O}_2$.

Let x be the rate of effusion of He.

The expression for the relative rates of effusion of two gases is $\frac{r_1}{r_2}=\frac{p_1}{p_2}\sqrt{\frac{T_2{M}_2}{T_1{M}_1}}$.

Here, 1 represents $S{O}_2$ and 2 represents $He$.

Substitute values in the above expression.

$\frac{n}{x}=\frac{1}{0.25}\sqrt{\frac{2\times 273\times 4}{273\times 64}}$

Hence, $x=\frac{n}{\sqrt{2}}$.

So, the correct option is $A$