It has been found that for a chemical reaction with rise in temperature by 9 K the rate constant gets doubled. Assuming a reaction to be occurring at 300 K , the value of activation energy is found to be kJmol - 1 . [nearest integer] (Given ln 10 = 2 . 3 , R = 8 . 3 J K - 1 mol - 1 , log 2 = 0 . 30 )

Step-by-step solution

Arrhenius equation for the rate constant of a reaction in terms of energy of activation at two different temperatures is given by log K 2 K 1 = E a 2 . 3 R 1 T 1 - 1 T 2 Rise in temperature = 9   K Initial temperature = 300   K log K 309 K 300 = E a 2 . 3 R 1 300 - 1 309 log 2 = E a 2 . 3 R 9 300 × 309 E a = 2 . 3 × 0 . 30 × 300 × 309 9 E a = 58 . 988 × 10 3   J = 58 . 988 kJ = 59 kJ