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 cccr 2 A B_ 2(g) & & 2 A B_ (g) & + & B_ 2(g) & 2 & & 0 & & 0 & (initially) 2(1-x) & & 2 x & & x & (at equilibrium) array ) ( aligned Amount of moles at equilibrium & =2(1-x)+2 x+x & =2+x aligned ) ( aligned & K_p= [p_ A B ]^2 [p_ B₂ ] [p_ A B₂ ]^2 & K_p= ( 2 x 2+x P )^2 ( x 2+x P ) ( 2(1-x) 2+x P )^2 = 4 x^3 2+x P 4(1-x)^2 & K_p= 4 x^3 P 2 1 4 ( 1-x 1 & 2+x 2) & x= ( 8 K_p 4 P )^ 1 / 3 x= ( 2 K_p P )^ 1 / 3 aligned )