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At certain temperature compound AB(2)(g)...

At certain temperature 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 of `K_(p)` in terms of `alpha` and initial pressure P is :

A

`(2K_(p)//P)^(1//2)`

B

`(K_(p)//P)`

C

`(2K_(p)//P)`

D

`(2K_(p)//P)^(1//3)`

Text Solution

Verified by Experts

The correct Answer is:
D
`underset(2(1-x))underset(2)(2AB_(2)(g))hArrunderset(2x)underset(0)(2AB(g))+underset(x)underset(0)(B_(2)(g))underset("at eq.")underset("initially")(.)`
Total amount of moles at equilibrium
`2=x(1-x)+2x+x=2+x`
`K_(p)=([P_(AB)]^(2)[P_(B_(2))])/([P_(AB_(2))]^(2))`
`K_(p)=([(2x)/(2+x)xxP]^(2)xx[(x)/(2+x)xxP])/([(2(1-x))/(2+x)xxP]^(2))`
`K_(p)=((4x^(3))/(2+x)xxP)/(4(1-x)^(2))`
`K_(p)=(4x^(3)xxP)/(2)xx(1)/(4)("As "1-x ~=1 and 2+x~=2)`
`x=(8K_(p)//4P)^(1//3)=(2K_(p)//P)^(1//3)`
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