The dissociation equilibrium of a gas (A B₂ ) 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

Step-by-step solution

2 A B_ 2(g) 2 A B_ (g) +B_ 2(g) array lccc Initial & 2 & 0 & 0 Equilibrium & 2(1-x) & 2 x & x array aligned & Moles at equilibrium =2(1-x)+2 x+x & =2-2 x+2 x+x=x+2 & aligned K_p & = [P_ A B ]^2 [P_ B₂ ] [P_ A B₂ ] = ( 2 x x+2 p )^2 ( x 2+x p ) [ 2(1-x) x+2 p ]^2 & = 4 x^3 x+2 p 4(1-x)^2 = 4 x^2 p 2 1 4 aligned aligned x= ( 2 K_p p )^ 1 / 3 (as 1-x 1,2+x 2 )