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At temperature T, a compound AB(2)(g) di...

At temperature T, a compound `AB_(2)(g)` dissociates according to the reaction:
`2AB_(2)(g) hArr 2AB(g)+B_(2)(g)`
with a degree of dissociation x which is small compared to the unity. Deduce the expression for x in terms of the equilibrium constant `K_(p)` and the total pressure P.

Text Solution

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`{:("",2AB_2(g),hArr,2AB(g),+B_2(g)),("Initial (Mole)",1,"",0,0),("At eq.(mole)",1-alpha,"",alpha,alpha//2),("At eq.(p.p)",P((1-alpha)/(1+alpha//2)),"","",(Palpha//2)/((1+alpha//2))):}`
Total moles at equilibrium = `(1+alpha//2)`
`K_p=(((P.alpha)/(1+alpha//2))^2((P.alpha//2)/(1+alpha//2)))/(P^2((1-alpha)/(1+alpha//2))^2)`
`K_p=(Palpha^3)/(2(1-alpha)^2(1+alpha//2))`
But `1 gt gt alpha therefore K_p=(Palpha^3)/2`
`alpha=((2K_p)/P)^(1//3)`
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