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 t

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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 is

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2 A B 2 ( g ) ​ ⇌ 2 A B ( g ) ​ + B 2 ( g ) ​ Initial Equilibrium ​ 2 2 ( 1 − x ) ​ 0 2 x ​ 0 x ​ ​ Moles at equilibrium = 2 ( 1 − x ) + 2 x + x = 2 − 2 x + 2 x + x = x + 2 K p ​ ​ = [ P A B 2 ​ ​ ] [ P A B ​ ] 2 [ P B 2 ​ ​ ] ​ = [ x + 2 2 ( 1 − x ) ​ × p ] 2 ( x + 2 2 x ​ × p ) 2 ( 2 + x x ​ × p ) ​ = 4 ( 1 − x ) 2 x + 2 4 x 3 ​ × p ​ = 2 4 x 2 × p ​ × 4 1 ​ ​ ​ x = ( p 2 K p ​ ​ ) 1/3 (as 1 − x ≈ 1 , 2 + x ≈ 2 )

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