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The dissociation equilibrium of a gas AB...

The dissociation equilibrium of a gas `AB_2` can be represented as, `2AB_2(g) hArr 2AB (g) +B_2(g)`. The degree of disssociation is 'x' and is small compared to 1. The expression relating the degree of dissociation (x) with equilibrium constant `k_p` and total 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
`2AB_(2)hArr2AB+B_(2)`
`{:(1,0,0,),("At eqm.",1-x,x,x//2):}`
`K_(p)=((P_(AB))^(2)(P_(B_(2))))/((P_(AB_(2)))^(2))impliesK_(p)=([(x)/((1+x//2))xxP]^(2)[(x//2)/(1+x//2)xxP])/([(1-x)/(1+x//2)xxP]^(2))`
`impliesK_(p)=(x^(3)P)/(2(1+x//2)(1-x)^(2))`
`1-x-=1" "1+x//2-=1`
`K_(p)=(x^(3)P)/(2)impliesx=((2K_(p))/(P))^(1//3)`
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Knowledge Check

  • The dissociation equilibrium of a gas AB_(2) can be represented as, 2AB_(2)(g)iff2AB(g)+B_(2)(g) . The degree of dissociation is x and is small compared to 1. The expression relating the degree of dissociation (x) with equilibrium constant k_(p) and total pressure P is :

    A
    `(k_(p))/(P)`
    B
    `(2k_(p))/(P)`
    C
    `((2k_(p))/(P))^(1//3)`
    D
    `((2k_(p))/(P))^(1//2)`

  • The dissociation of a gas AB_(2) at equilibrium can be represented as : 2AB_(2)(g) hArr 2AB(g)+B_(2)(g) The degree of dissociation is x and is small compared to I. The expression relating the degree of dissociation (x) with equilibrium constant K_(p) and total pressure P is :

    A
    `(2K_(1)//P)`
    B
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  • The dissociation equilibrium of a gas AB_(2) can be represented as : 2AB_(2) hArr 2AB(g) +B_(2)(g) The degree of dissocaition x is very small as compared to 1. The expression which relates the degree of dissociation (x) with equilibrium constant (K_(p)) and total pressure (p) is :

    A
    `(2 K_(p) //P)^(1//2)`
    B
    `(K_(p)//P)`
    C
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    D
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