Question

At what temperature, the rate of effusion of $N_2$ would be $1.625$ times than that of ${SO}_2$ at ${50}^{o}C$?

• A. $110K$
• B. $173K$
• C. $373K$
• D. $273K$

Answer 1

The correct option is C $373K$

The rate of effusion is directly proportional to the square root of temperature and inversely proportional to the square root of molecular weight.
$r\propto U;U=\sqrt{\frac{3RT}{M}}$
$r\propto \sqrt{\frac{T}{M}}$
$\therefore \frac{r_{N_2}}{r_{{SO}_2}}=\sqrt{\frac{T_{N_2}{M}_{{SO}_2}}{T_{{SO}_2}{M}_{N_2}}}$
The rate of effusion of $N_2$ is $1.625$ times than that of ${SO}_2$ at ${50}^{o}C$.
or
$\frac{r_{N_2}}{r_{{SO}_2}}=\sqrt{\frac{T_1\times 64}{(50+273)\times 28}}=1.625$
$T_2=373K$
At $373K$, the rate of effusion of $N_2$ would be $1.625$ times than that of ${SO}_2$ at ${50}^{o}C$.