For given two equilibria attained in a container which are correct if degree of dissociation of A and A' are `alpha` and `alpha'`.
`A(s) hArr 2B(g)+C(g), K_(p_(1))=8xx10^(-2)`
`A'(s) hArr 2B(g)+D(g), K_(P_(2))=2xx10^(-2)`

Options

A. `K_(p_(1))/K_(p_(2))=[((3alpha'+2alpha))/((3alpha+2alpha'))]^(3)xxalpha/(alpha')`
B. `P'_(C)//P'_(D)=4`
C. `P'_(B)=2P'_(C)+2P'_(D)`
D. `alpha gt alpha'`

Answer

A, B, C, D

Explanation

`{:(A(s),hArr,2B(g),+,C(g)),(,,2alpha+2alpha',,alpha),(A'(s),hArr,2B,+,D),(,,2alpha'+2alpha,,alpha'):}`
`K_(p_(1))=(2alpha+2alpha')^(2)xxalphaxx[(P)/((3alpha+2alpha'))]^(3)`
`K_(p_(2))=(2alpha+2alpha')^(2)xxalpha'xx[(P)/((3alpha'+2alpha))]^(3)`
`K_(p_(1))/K_(P_(2))=([3alpha'+2alpha]^(3))/([3alpha+2alpha]^(3))xxalpha/alpha_(1)`
Also, `K_(p_(1))=(P'_(B))^(2)xxP'_(c)`
`K_(p_(2))=(P'_(B))^(2)xxP'_(p)`
r `(P'_(c))/(P'_(D))=K_(p_(1))/K_(p_(2))=(8xx10^(-2))/(2xx10^(-2))=4`
Also, `P'_(B)=2xx(P'_(c)+P'_(D))`
`K_(p_(1)) gt K_(p_(2)) :. alpha gt alpha_(1)`