For following reactions A → 700 K P r o d u c t A → 500 K P r o d u c t it was found that the E a is decreased by 30 k J / m o l in the presence of catalyst. If the rate remains unchanged, the activation energy for catalysed reaction is (Assume pre exponential factor is same)

Step-by-step solution

K c a t a l y s t = K A e - E a 1 R T 1 = A e E a 2 R T 2 E a 1 = energy of activation in presence of catalyst T 1 = 500 K T 2 = 700 K E a 1 T 1 = E a 2 T 2 but E a 1 = E a 2 - 30 E a 2 - 30 500 = E a 2 700 5 E a 2 = 7 E a 2 - 210 E a 2 = 210 2 = 105 The activation energy for catalysed reaction = ( 105 - 30 ) kJ / mol = 75 kJ / mol