The rms speed of oxygen at room temperature i | vedclass

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(B) The root mean square (rms) speed of a gas molecule is given by the formula $V_{rms} = \sqrt{\frac{3RT}{M_0}}$, where $R$ is the universal gas cons

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$2000$

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(B) The root mean square (rms) speed of a gas molecule is given by the formula $V_{rms} = \sqrt{\frac{3RT}{M_0}}$, where $R$ is the universal gas constant, $T$ is the absolute temperature, and $M_0$ is the molar mass of the gas.Since $R$ and $T$ are constant for both gases, we have $V_{rms} \propto \frac{1}{\sqrt{M_0}}$.Therefore, the ratio of the rms speeds of hydrogen $(H_2)$ and oxygen $(O_2)$ is given by:$\frac{(V_{rms})_{H_2}}{(V_{rms})_{O_2}} = \sqrt{\frac{M_{O_2}}{M_{H_2}}} = \sqrt{\frac{32}{2}} = \sqrt{16} = 4$.Given $(V_{rms})_{O_2} = 500 \,m/s$, we find:$(V_{rms})_{H_2} = 4 	imes 500 \,m/s = 2000 \,m/s$.

The rms speed of oxygen at room temperature is about $500 \,m/s$. The rms speed of hydrogen at the same temperature is about (in $\,m/s$)

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