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. `(2K_(p)//P)^(1//3)`
B. `(2K_(p)//P_^(1//2)`
C. `(K_(p)//P)`
D. `(2K_(p)//P)`

Answer

A

Explanation

`{:(2AB_(2)(g),hArr,2AB(g),+,B_(2)(g)),(1,,0,,0),(1-x,,x,,x//2):}`
`:.` `K_(p) = (x^(2)x)/(2(1-x)^(2)).[(P)/(1+(x)/(2))]=(x^(2).P)/(2)`
`(1 - x ~~ 1` and `1 + (x)/(2) ~~1`, since `x ltlt 1)`
Or `P = 3sqrt((2K_(p))/(P))`