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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.
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B
Root-mean-square value of translational velocity of B is four times that of A.
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C
Pressure exerted by B is eight times of that exerted by A.
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D
Number of molecules of B, in the cylinder, is eight times that of A.
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Solution

The correct options are
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.
Since both the gases are contained in the same vessel, temperature of both the gases is same.
Average K.E per molecule of a diatomic gas is 5/2 KT. Hence, average KE per molecule of both the gases is same. Therefore, option (a) is correct.
vrms=3RTM
Hence,
(vrms)2(vrms)1=M1M2=16=4
Hence, option (b) is correct.
Let molar mass of B be M, then that of A will be equal to 16M.
Let mass of gas B in the vessel be m; then that of A will be 2m. The number of moles of a gas, in the vessel will be n=m/M. Hence, number of moles of gases A and B will be
n1=2m16M and n2=mM
Hence,
n1n2=18
Hence, option (d) is correct.
Partial pressure exerted by a gas ia
P=nRTV
Hence,
P2P1=n2n1=8
Therefore, option (c) is also correct.

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