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At what temperature, the rate of effusion of $\mathrm{N}_{2}$ would be 1.625 times than that of $\mathrm{SO}_{2}$ at $50^{\circ} \mathrm{C}$ ?
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$373 \mathrm{~K}$
$\quad r \propto U$ and $U=\sqrt{\frac{3 R T}{\text { M }}}$
$\frac{\mathrm{r}_{1}}{\mathrm{r}_{2}}=\sqrt{\frac{\mathrm{T}_{1} \mathrm{M}_{2}}{\mathrm{~T}_{2} \mathrm{M}_{1}}}$ or $\frac{\mathrm{r}_{\mathrm{N}_{2}}}{\mathrm{r}_{\mathrm{SO}_{2}}}=\sqrt{\frac{\mathrm{T}_{1} \times 64}{323 \times 28}}=1.625$
or $\mathrm{T}_{2}=373 \mathrm{~K}$
$\frac{\mathrm{r}_{1}}{\mathrm{r}_{2}}=\sqrt{\frac{\mathrm{T}_{1} \mathrm{M}_{2}}{\mathrm{~T}_{2} \mathrm{M}_{1}}}$ or $\frac{\mathrm{r}_{\mathrm{N}_{2}}}{\mathrm{r}_{\mathrm{SO}_{2}}}=\sqrt{\frac{\mathrm{T}_{1} \times 64}{323 \times 28}}=1.625$
or $\mathrm{T}_{2}=373 \mathrm{~K}$
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