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At temperature ,T, a compound AB2(g) dis...

At temperature ,T, a compound `AB_2(g)` dissociates according to the reaction `2AB_2 (g) ltimplies 2AB(g)+B_2(g)` with a degree of dissociation, x, which is small compared with unity.Deduce the expression for `K_P`, in terms of x and the total pressure , P.

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`{:(,2AB_(2)(g),hArr,2AB(g),+,B_(2)(g),),(t=0,a_(0)"(let)",,-,,-,),(t=eq,a_(0)-2x,,2x,,x,"where " alpha=(2x)/(a_(0)),n_(T)=a_(0)+x):}`
`K_(p)=((P_(AB))^(2)(P_(B_(2))))/((P_(AB_(2)))^(2))=(((2x)/(a_(0)+x).P)^(2)((x)/(a_(0)+x).P))/(((a_(0)-2x)/(a_(0)+x).P)^(2))`
`K_(p)=(4x^(3)P)/((a_(0)+x)(a_(0)-2x)^(2))=(4x^(3)P)/(a_(0)^(3))" " (x lt a_(0))`
`K_(p)= 4P((x)/(a_(0)))^(3)=4P ((alpha)/(2))^(3) rArr alpha=((2K_(p))/(P))^(1//3)`
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