Question

A closed vessel contains a mixture of two diatomic gases A and B molar mass of A is 16 times that of B and mass of gas A contained in the vessel is 2 times that of B, which of the following statements are correct?

• A. average kinetic energy per molecule of A is equal to that of B
• B. Root mean square value of translational velocity of B is four times that 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 times that of A

Answer 1

The correct option is D Number of molecules of B, in the cylinder, is eight times that of A

${\mu }_{av}=\sqrt{\frac{8RT}{\pi M}}$ 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 $A$.