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 ?

Options

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 time that of `A`
C. Pressure exerted by `B` is eight time of the exerted by `A`.
D. Number of moleucles of `B`, in the cylinder, is eight times that of `A`

Answer

A, B, C, D

Explanation

Since both the gases are contained in the same vessel, temperature of both the gases is same.
Average `KE` 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.
`v_(mas)=sqrt((2RT)/( M))`
Hence,
`((u_(rms))_(2))/((v_(rms))_(1))=sqrt((M_(1))/( M_(2)))=sqrt(16)=4`
Hence, option `(b)` is correct.
Let molar mass of `B` be `M`, then that of `A` will be equal to `16 M`.
Let mass of gass `B` ini 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
`n_(1)=(2m)/( 16 M) ` and `n_(2)=(m)/( M)`
Hence `(n_(1))/( n_(2))=(1)/(8)`
Hence, option `(d)` is correct.
Partial pressure exerted by a gas is
`P=(nRT)/( V)`
Hence ` (P_(2))/( P_(1))=(n_(2))/( n_(1))=8`
Therefore, option `(c)` is also correct.