The dissociation equilibrium of a gas A B 2 can be represented as 2 A B 2 ( g ) ⇌ 2 A B ( g ) + B 2 ( g ) The degree of dissociation is ' x ' and is small compared to 1. The expression

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The dissociation equilibrium of a gas A B 2 ​ can be represented as 2 A B 2 ​ ( g ) ⇌ 2 A B ( 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 isNEET 2008 (Screening)

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2 A B 2 ( g ) ​ 2 2 ( 1 − x ) ​ ⇌ ​ 2 A B ( g ) ​ 0 2 x ​ + ​ B 2 ( g ) ​ 0 x ​ (initially) (at equilibrium) ​ Amount of moles at equilibrium ​ = 2 ( 1 − x ) + 2 x + x = 2 + x ​ ​ K p ​ = [ p A B 2 ​ ​ ] 2 [ p A B ​ ] 2 [ p B 2 ​ ​ ] ​ K p ​ = ( 2 + x 2 ( 1 − x ) ​ × P ) 2 ( 2 + x 2 x ​ × P ) 2 × ( 2 + x x ​ × P ) ​ = 4 ( 1 − x ) 2 2 + x 4 x 3 ​ × P ​ K p ​ = 2 4 x 3 × P ​ × 4 1 ​ ( ∵ 1 − x ≈ 1&2 + x ≈ 2 ) x = ( 4 P 8 K p ​ ​ ) 1/3 ⇒ x = ( P 2 K p ​ ​ ) 1/3 ​

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