For a hypothetical gas phase reaction A ( g ) + B ( g ) C ( g ) + D ( g ) , the forward rate constant ( k _ f ) is 2.0 10⁻³ ~s ⁻¹ and the backward rate constant ( k _ b ) is 1.0 10⁻³ ~s ⁻¹ . At a given instant, the concentrations of the reacting species are [ A ] = 0.1 ~M , [ B ] = 0.2 ~M , [ C ] = 0.2 ~M , and [ D ] = 0.4 ~M . What is the value of the equilibrium constant ( K _ c ) and the predicted direction in whi

Step-by-step solution

The equilibrium constant K _ c is the ratio of the forward and backward rate constants: K _ c = k _ f k _ b = 2.0 10⁻³ 1.0 10⁻³ = 2.0 The reaction quotient Q _ c at the given instant is calculated as: Q _ c = [ C ][ D ] [ A ][ B ] = 0.2 0.4 0.1 0.2 = 0.08 0.02 = 4.0 Comparing Q _ c and K _ c , we find that Q _ c > K _ c ( 4.0 > 2.0 ). Since the reaction quotient is greater than the equilibrium constant, the reaction will proceed in the backward direction to reach equilibrium. Answer: 2.0 , Backward direction