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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

`256 P^(3) alpha^(5)`

B

`4Palpha^(2)`

C

`8P^(3)alpha^(5)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
`2AB_(4)(g)hArrA_(2)(g)+4B_(2)(g)`
`{:(underset(("moles"))(t=0),a,,0,0),(t=t_(Eq),a-aalpha,,(aalpha)/2,2aalpha):}`
`K_(p)=(p_(A_(2)).p_(B_(2))^(4))/p_(AB_(4))^(2)`
`p_(A_(2))=(aalpha//2)/(a+3/2aalpha).p~~(alphap)/2, p_(B_(2))=(2aalpha)/(a+3/2aalpha).P~~2alphap`
`p_(AB_(4))=(a-aalpha)/(a+3/2aalpha).p~~p`
`K_(p)=((alphap)/2.(2alphap)^(4))/(p^(2))=8alpha^(5).p^(3)`
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