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(A) The formula for the $r.m.s.$ speed of a gas molecule is given by $v_{rms} = \sqrt{\frac{3RT}{M}}$,where $R$ is the universal gas constant,$T$ is t

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$H_2$

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(A) The formula for the $r.m.s.$ speed of a gas molecule is given by $v_{rms} = \sqrt{\frac{3RT}{M}}$,where $R$ is the universal gas constant,$T$ is the absolute temperature,and $M$ is the molar mass of the gas.Given $v_{rms} = 1930 \, m/s$,$T = 300 \, K$ (room temperature),and $R = 8.314 \, J/(mol \cdot K)$.Squaring both sides: $v_{rms}^2 = \frac{3RT}{M}$.Rearranging for $M$: $M = \frac{3RT}{v_{rms}^2}$.Substituting the values: $M = \frac{3 	imes 8.314 	imes 300}{1930^2} \approx \frac{7482.6}{3724900} \approx 0.002008 \, kg/mol$.This is approximately $2 	imes 10^{-3} \, kg/mol$,which corresponds to $2 \, g/mol$.The molar mass of $H_2$ is $2 \, g/mol$. Therefore,the gas is $H_2$.

At room temperature,a diatomic gas is found to have an $r.m.s.$ speed of $1930 \, m/s$. The gas is

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