Question

T'(K) k(s-1 400 0.000659 The rate of a certain reaction was studied at various temperatures. The table shows temperature (T) and rate constant (k) data collected during the experiments. Plot the data to answer the questions. 420 0.00327 440 0.0181 What is the value of the activation energy, Eq, for this reaction? 460 0.0589 480 0.213 500 0.615 520 1.66 1 Ea = kJ · mol-1 540 3.99 560 9.64 OG TOOLS What is x102 Itial factor (sometimes called the irequency factor), A, for this reaction? 580 20.1 A = 5-1

Answer 1

According to arhenius theory, expression for the rate constant is as follows: Here, k → rate constant A → Arrhenius constant E → activation energy T → absolute temperature Take logarithms on both sides of the equation Inka = In A (1) for uncatalyzed RT Ink, =ln A- (2) for catalyzed RT Subtract the 1st equation from the 2nd equation toute - Hand - ( 1 - **) (14->) In hy - ELE. ką RT RT ka 1 In = +(8,-€.) (3) Initi al temperature, 7; = 400 K Rate constant of the reaction at Ti, k = 0.000659 s-1 Final temperature, T =420 K Rate constant of the reaction at Ty, kg = 0.00327 s-1 Gas constant, R = 8.314 JK-mol-1 According to Arhenius theory, In E R (一) 1 0.00327 s- 1 In 0.000659 3-1 8.314 JK-mol-1 420K 420 K 1.602 = (1.19x10* K-1) 8.314 JK-mol-1 J Activation energy, 1 kJ E = 1.12x10 = 112 kJ/mol mol 103 J X Temperature, T = 400 K Rate constant, k = 0.000659 s-1 Gas constant, R = 8.314 x 10-3 kJK-mol-1 Activatation of the reaction, E = 112 kJ/mol Rate constant, k = Ae k Arrhenius factor, A = = koe? 112 k tol = 0.0006595-1) (8314x10 WK-'701'Y400 K) = (0.000659 $-4)233.8 = (0.000659 s-^)(4.24x1044) = 2.79x1011 3-1