Question

Which is the incorrect statement for $1 \, L$ sample of $N_{2}\left(\right.g\left.\right)$ and $CO_{2}\left(\right.g\left.\right)$ at $298 \, K$ and $1 \, atm$ pressure

• A. The average translational $KE$ per molecule is the same in $N_{2}$ and $CO_{2}$
• B. The rms speed remains same for both $N_{2}$ and $CO_{2}$
• C. The density of $N_{2}$ is less than that of $CO_{2}$
• D. The most probable velocity is different for the two gases.

Answer 1

Answer: (B)

Kinetic energies per molecule will be same because it is proportional to absolute temperature only.

$\frac{d_{N_{2}}}{d_{CO_{2}}}=\frac{M_{N_{2}}}{M_{CO_{2}}}=\frac{28}{44}$ i.e., $\text{d}_{\text{N}_{2}} < \text{d}_{\text{C} \text{O}_{2}}$ .

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)

Hint : rms speed has relation, $\frac{U_{SO_{2}}}{U_{O_{2}}}=\sqrt{\frac{M_{O_{2}} T_{SO_{2}}}{M_{SO_{2}} T_{O_{2}}}}$