For the reaction P + Q R + S , carried out at 298 K , the equilibrium constant was found to be 169 and the initial concentrations of all reactants and products was 1.0 M . What is the equilibrium concentration of the reactants?

Step-by-step solution

The reaction is P + Q R + S . The equilibrium constant K_c = 169 . Initial concentrations are [P]₀ = 1.0 M , [Q]₀ = 1.0 M , [R]₀ = 1.0 M , [S]₀ = 1.0 M . Let x be the change in concentration at equilibrium. Since the reaction quotient Q_c = [R][S] [P][Q] = 1 1 1 1 = 1 At equilibrium: [P] = 1 - x [Q] = 1 - x [R] = 1 + x [S] = 1 + x The equilibrium constant expression is K_c = [R][S] [P][Q] = (1+x)^2 (1-x)^2 = 169 . Taking the square root of both sides: 1+x 1-x = 169 = 13 . 1 + x = 13(1 - x) 1 + x = 13 - 13x 14x = 12