The dissociation equilibrium of a gas A B₂ can be represented as 2 A B₂(g) 2 A B(g)+B₂(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

Step-by-step solution

( array cccc & 2 A B₂(g) & & 2 A B(g) & + & B₂(g) Initial moles & 1 & & 0 & & 0 At equilibrium & 2(1-x) & & 2 x & & x array ) where, x= degree of dissociation aligned Total moles at equilibrium & =2-2 x+2 x+x & =(2+x) aligned aligned & So, _ A B₂ = 2(1-x) p (2+x) & _ A B = 2 x p (2+x) aligned aligned p_ B₂ & = x p (2+x) K_p & = (p_ A B )^2 (p_ B₂ ) (p_ A B₂ )^2 aligned = ( 2 x p 2+x )^2 ( x 2+x p ) ( 2(1-x) (2+x) p )^2 = x^3 p (2+x)(1-x)^2 aligned [ x 1 and 2 , so & (1-x)=1,(2+x)=2] & = x^3 p 2 aligned x= ( 2 K_p p