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. Consider the following statements and mark the correct ones.

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

Answer 1

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

The correct options are
A Average kinetic energy per molecule of gas A is equal to that of gas B
B Root mean square value of translational speed of gas B is four times that of A
C Pressure exerted by gas B is eight times of that exerted by gas A
D Number of molecules of gas B in the cylinder is eight times that of gas A

A B

Molecular wt.$=16M_0$ Molecular wt.$=M_0$

mass$=2m_0$ mass $=m_0$

$n_A=\frac{n_0}{8}$ $n_B=n_0$

(A) K.E./atom=$\frac{f}{2}kT$ which will be same for both the gases as both are diatomic.

(B) $C_{rm{s}_A}=\sqrt{\frac{3RT}{16M_0}}{C}_{rm{s}_B}=\sqrt{\frac{3RT}{M_0}},(C_{rms}{)}_B=4(C_{rms}{)}_A$

(C) $(P{)}_A=\frac{\left(n_0/8\right)RT}{V},(P{)}_B=\frac{n_{0}RT}{V},\left(P_B\right)=8\left(P_A\right)$

(D) $n_B=8n_A$