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(C) The average kinetic energy of an ideal gas molecule is given by the formula $KE_{avg} = \frac{3}{2}kT$, where $k$ is the Boltzmann constant and $T

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$A$ is true but $R$ is false

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(C) The average kinetic energy of an ideal gas molecule is given by the formula $KE_{avg} = \frac{3}{2}kT$, where $k$ is the Boltzmann constant and $T$ is the absolute temperature.Since $KE_{avg}$ depends only on the temperature $T$, if the average kinetic energy of $H_2$ and $O_2$ molecules is the same, their temperatures must be the same. Thus, Assertion $A$ is true.The root mean square (r.m.s.) speed of gas molecules is given by $v_{rms} = \sqrt{\frac{3RT}{M}}$, where $R$ is the universal gas constant, $T$ is the temperature, and $M$ is the molar mass.Since the molar mass $M$ of $H_2$ $(2 \ g/mol)$ and $O_2$ $(32 \ g/mol)$ are different, their $v_{rms}$ values will be different even at the same temperature. Thus, Reason $R$ is false.

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