Question

A closed vessel contains a mixture of two diatomic gases $A$ and $B$. Molar mass $A$ is 16 times that of $B$ and mass of gas $A$ contained in the vessel is 2 times that of $B$. The following statements are given:

• A. Average kinetic energy per molecule of $B$ is equal to that of $A$
• B. Root mean square value of translation velocity of $B$ is four times of $A$.
• C. Pressure exerted by $B$ is eight times of that exerted by $A$
• D. Number of molecules of $B$ in the cylinder is eight time that of $A$.

Answer 1

The correct option is D Number of molecules of $B$ in the cylinder is eight time that of $A$.

As we know,

${\mu }_{av}=\sqrt{\frac{8RT}{\pi M}}$ and ${\mu }_{rms}=\sqrt{\frac{3RT}{M}}$

As given, $M_A=16M_B$

So, $\frac{v_{rmsB}}{v_{rmsA}}=\sqrt{\frac{M_A}{M_B}}=4$

Also as mass of gas $A$ contained in the vessel is 2 times that of $B$, $\frac{n_B}{n_A}=8$

Number of molecules of $B$ in the cylinder is eight times that of $A$.