The rate of effusion of an equilibrium mixture in `1 litre` vessel of, at `300 K`, `A_(2)hArr2A` through a pinhole is `0.707` times of rate of diffusion on `O_(2)` under identical conditions of `P` and `T`. Which of the following is/are correct if at. Wt. of `A` is `46`?

Options

A. `K_(c)=25.16 mol litre^(-1)`
B. mole ration of `(A)/(A_(2))=0.643`
C. mol.wt. of mixture `=56`
D. `DeltaG^(@)=-8.01xx10^(3)J`

Explanation

(a,b,d)
`(r_(mix))/(r_(O_(2)))=sqrt((M_(O_(2)))/(M_(mix)))=sqrt((32)/(M))=0.707` or `M=64`
Let `a` mole of `A_(2)` be present in mixture, then
`64=(axx92+(100-a)xx46)/(100)`
`A=a=39.13` mole and `A_(2)=60.87` mole
`:. (A)/(A_(2))=(39.13)/(60.87)=0.643`
`K_(c)=([A]^(2))/([A_(2)])=((39.13)^(2))/(60.87)=25.16 mol litre^(-1)`
`:' DeltaG^(@)=-2.303 RT log K`
`:. DeltaG=-2.303xx8.314xxlog 25.16`
`=-8.01xx10^(3)J`