• # question_answer Indicate the correct statement for a 1-L sample of ${{N}_{2}}(g)$ and $C{{O}_{2}}(g)$ at 298 K and 1 atm pressure A)                 The average translational KE per molecule is the same in ${{N}_{2}}$ and $C{{O}_{2}}$ B)                 The rms speed remains constant for both ${{N}_{2}}$ and $C{{O}_{2}}$ C)                 The density of ${{N}_{2}}$ is less than that of $C{{O}_{2}}$ D)                 The total translational KE of both ${{N}_{2}}$ and $C{{O}_{2}}$ is the same

Correct Answer: A

Solution :

Kinetic energies per molecule will be same because it is proportional to absolute temperature only.                    $\frac{{{d}_{{{N}_{2}}}}}{{{d}_{C{{O}_{2}}}}}=\frac{{{M}_{{{N}_{2}}}}}{{{M}_{C{{O}_{2}}}}}=\frac{28}{44}$i.e. $d{{N}_{2}}<dC{{O}_{2}}$ Total translational kinetic energy will also be same because at same temperature & pressure number of molecules present in same volume would be same (according to Avogadro's Law)

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