Question

The ratio of average speed of $C{H}_4$ molecules at ${27}^{o}C$ and that of $S{O}_2$ molecules at ${127}^{o}C$ is:

• A. $1:1$
• B. $2:\sqrt{3}$
• C. $\sqrt{3}:2$
• D. $3:1$

Answer 1

The correct option is D $3:1$

We know the average speed of a molecule $=\sqrt{\frac{8RT}{\Pi M}}$.

$M=$ Molecular mass $\frac{{\overline{CH}}_{4_{300}}}{{\overline{SO}}_{2_{400}}}=\frac{\sqrt{\frac{8R\times 300}{\Pi 16}}}{\sqrt{\frac{8R\times 400}{\Pi 64}}}$

$T=$ Absolute Temperature $=\frac{300}{16}\times \frac{64}{400}$

$R=$ Universal gas constant $=3:1$