Question

The temperature at which $RMS$ velocity of $O_2$ is equal to the $RMS$ velocity of $S{O}_2$ at ${327}^{\circ }C$ is:

• A. $273K$
• B. $300K$
• C. ${100}^{\circ }C$
• D. $1200K$

Answer 1

Answer: (B)

$300K$

We know,

$V_{rms}=\sqrt{\frac{3RT}{M}}$

Given that,

${\left(V^{}rms\right)}_{O_2}={\left(V_{rms}\right)}_{S{O}_2}$

$\therefore \sqrt{\frac{3RT}{32}}=\sqrt{\frac{3R\times 600}{64}}$

$\therefore \frac{T}{32}=\frac{600}{64}$

$\therefore T=300$ $K$

Note: ${327}^{o}C=(273+327)K=600K$