Question

Indicate the correct statement for equal volumes of $N_2\left(g\right)$ and $C{O}_2\left(g\right)$ at ${25}^{\circ }\text{C}$ and 1 atm.

• A. The average translational kinetic energy per molecule is the same for $N_2$ and $C{O}_2$.
• B. The $V_{rms}$ remains same 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 kinetic energy of both $N_2$ and $C{O}_2$ is the same.

Answer 1

Answer: (A), (C), (D)

The correct options are
A The average translational kinetic energy per molecule is the same for $N_2$ and $C{O}_2$.
C The density of $N_2$ is less than that of $C{O}_2$.
D The total translational kinetic energy of both $N_2$ and $C{O}_2$ is the same.

$\Rightarrow K{E}_{Tran}=\frac{3}{2}RT\therefore \text{same}KE$
$\Rightarrow u_{rms}=\sqrt{\frac{3RT}{M}}\therefore$ different for both
$\Rightarrow d=\frac{PM}{RT}\therefore C{O}_2\left(44\right)$ is denser than $N_2\left(28\right)$
$\Rightarrow$ Since P, V, T are the same, 'n' are equal,
$\therefore K{E}_{\text{total}}=\frac{3}{2}nRT=\frac{3}{2}PV,$ are equal.
$\therefore \left[A\right],\left[C\right],\left[D\right]$