Calculate the root mean square speed $u_{\text{rms}}$ of ${\text{O}}_2$ gas at $27^{\circ }\text{C}$. (Given $R=8.314{\text{ J mol}}^{-1}{\text{ K}}^{-1}$, $M=32\times 10^{-3}{\text{ kg mol}}^{-1}$)

Solution

1. The formula for root mean square speed is $u_{\text{rms}}=\sqrt{\frac{3RT}{M}}$.
2. Convert temperature to Kelvin: $$\begin{array}{rl}T& =27+273\\ & =300\text{ K}\end{array}$$.
3. Substitute values: $u_{\text{rms}}=\sqrt{\frac{3\times 8.314\times 300}{32\times 10^{-3}}}$.
4. $$\begin{array}{rl}{u}_{\text{rms}}& =\sqrt{\frac{7482.6}{0.032}}\\ & =\sqrt{233831.25}\end{array}$$.
5. Hence the answer is (A).