Question

At what temperature in ${}^{\circ }C$, the $U_{rms}$ of $S{O}_2$ is equal to the average velocity of $O_2$ at ${27}^{\circ }C$?

• A. ${118.1}^{\circ }C$
• B. ${236.3}^{\circ }C$
• C. ${472.6}^{\circ }C$
• D. None of these

Answer 1

Answer: (B)

${236.3}^{\circ }C$

The average velocity of xoygen is $\sqrt{\frac{8RT}{\pi M}}=\sqrt{\frac{8R\times 300}{3.1416\times 32}}$......(1)

The rms velocity of sulphur dioxide is $\sqrt{\frac{3RT}{M}}=\sqrt{\frac{3RT}{64}}$......(2)

From equations (1) and (2),
$\sqrt{\frac{8R\times 300}{3.1416\times 32}}=\sqrt{\frac{3RT}{64}}$

Hence,
$T=\frac{8\times 300\times 64}{3\times 3.1416\times 32}=509.3K$

Hence, the temperature is $509.3-273=236.3{}^{0}C$.