At temperature T, a compound `AB_(2)(g)` dissociates according to the reaction
`2AB_(2)(g)hArr2AB(g)+B_(2)(g)`
with degree of dissociation `alpha`, which is small compared with unity. The expression for `K_(p)` in terms of `alpha` and the total pressure `P_(T)` is

Options

A. `(Px^(3))/(2)`
B. `(Px^(2))/(3)`
C. `(Px^(3))/(3)`
D. `(Px^(2))/(2)`

Explanation

`underset(1-x)underset(1)(2AB_(2(g)))hArrunderset(x)underset(0)(2AB_((g)))+underset(x//2)underset(0)(B_(2(g)))`
`:. K_(p)=(x^(2)*x)/(2(1-x)^(2))xx[(P)/(1+(x)/(2))]^(1)`
(`:' x` being small `:. 1-x~~1` and `1+(x)/(2)~~1`)
`:. K_(p)=(x^(3)*P)/(2)`