The mass of molecule `A` is twice the mass of molecule B. The rms speed of A is twice the rms speed of B. If two samples of A and B contain same number of molecules. If the pressure of gas B is 2atm then what will be the pressure of gas A ( atm) . If two samplest are taken in separate containers of equal volume ?

Options

A. 16
B. 32
C. 48
D. 64

Answer

1

Explanation

Given `m_(A)=2m`
`:." "`mol. `wt. ` of `A=2xxmol." " wt." "` of `B" "….(i)`
Given`" "U_(rms)` of `A=2xxu_(rms)` of `B " " ….(ii)`
Also number of molecules of `A =` number of molecules of `B" "…..(iii)`
For gas `A" "P_(A)V_(A)=(1)/(3)M_(A)u_(rmsA)^(2)`
For gas `B" "P_(B)V_(B)=(1)/(3)M_(B)u_(rmsB)^(2)`
`:. " "(P_(A)V_(A))/(P_(B)V_(B))=(M_(A))/(M_(B))xx(u_(A)^(2))/(u_(B)^(2))" "....(iv)`
Given `" "V_(A)=V_(B)" "....(v)`
`:." "` By equation `(i),(ii),(iv)` and `(v)`
`(P_(A))/(P_(B))=2xx(2)^(2)=8`
`:." "P_(A)=8P_(B)`
Ans. 16