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 no. of molecules, what will be the ratio of P of two samples in separate containers of equal volume.

Explanation

Given, `M_(A) =2M_(B)`
`therefore` Mol wt. of `A=2xx` mol wt. of B `" …(1)"`
`U_("rma")` of `A=2xxU_("rms")` of B `" …(2)"`
Also, the no. of molecules of A =NO. of Molecules of B `" ….(3)"`
For gas `A P_(A) V_(A) =(1)/(3) M_(A) U_("rms")^(2) A`
`(P_(A)V_(A))/(P_(B)V_(B))=(M_(A))/(M_(B))xx(U_(A))/(U_(B))" .....(4)"`
Given `V_(A) =V_(B)" .....(5)"`
`therefore` By equation (1) (2) (4) & (5)
`(P_(A))/(P_(B)) =2xx(2)^(2)=8`
`P_(A) =8P_(B)`