The system shown in the figure is in equilibrium, where `A` and `B` are isomeric liquids and form an ideal solution at `TK`. Standard vapour pressures of `A` and `B` are `P_(A)^(0)` and `P_(B)^(0)`, respectively, at `TK`. We collect the vapour of `A` and `B` in two containers of volume `V`, first container is maintained at `2 T K` and second container is maintained at `3T//2`. At the temperature greater than `T K`, both `A` and `B` exist in only gaseous form.
We assume than collected gases behave ideally at `2 T K` and there may take place an isomerisation reaction in which `A` gets converted into `B` by first-order kinetics reaction given as:
`Aoverset(k)rarrB`, where `k` is a rate constant.
In container (`II`) at the given temperature `3T//2`, `A` and `B` are ideal in nature and non reacting in nature. A small pin hole is made into container. We can determine the initial rate of effusion of both gases in vacuum by the expression

`r=K.(P)/(sqrt(M_(0)))`
where `P=` pressure differences between system and surrounding
`K=` positive constant
`M_(0)=` molecular weight of the gas
If vapours are collected in a container of volume `8.21 L` maintained at `3 T//2K`, where `T=50 K`, then the ratio of initial rate of effusion of gases `A` and `B` is given as

Options

A. `2 : 1`
B. `1 : 1`
C. `4 : 3`
D. `2 : 4`

Explanation

`(r_(A))/(r_(B))=(P_(A))/(P_(B))sqrt((M_(B))/(M_(A)))=(n_(A))/(n_(B))=(2)/(1)`