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

Explanation

`{:(,2AB_(2(g)),hArr,2AB_((g)),+,B_(2(g))),("Mole before dissociation",1,,0,,0),("Mole after dissociation",(1-x),,x,,x/2):}`
Total mole at equilibrium
`(sum n)=1-x+x+(x)/(2)=1+(x)/(2)`
Now, `K_(p)=(n_(B_(2))xx(n_(AB))^(2))/((n_(AB_(2)))^(2))xx((P)/(sum n))^(Delta n)`
`K_(p)=((x)/(2).(x)^(2))/(((1-x)^(2))xx[(P)/(1+(x)/(2))]^(1)`
`K_(p)=(x^(3)P)/(2)`
(`:' x` is small, `:. 1-x~~1` and `1+(x)/(2)~~1`)
`x=3sqrt((2K_(p))/(P))`