Question

T(°C) 25 100 200 300 400 The rate constant for the synthesis reaction in the presence of a Fe-based catalysts has been determined at various temperatures. The table presents the results: 3.24 x 10° 2.32 x 105.81 x 1012.11x 102.64 x 101 11. Use the data provided to determine the activation energy in the presence of the Fe-based catalyst (graphing method, you will need a spreadsheet program: e.g., Excel, google sheets). 12. Estimate how many times faster the reaction is in the presence of catalyst compared to the reaction rate in its absence (E= 325 kJ/mol) at 500°c.

Answer 1

In k vs 1/T plot 0 1/T Ink 0 0.00 0.004 0.006 -2 0.008 0.01 0.012 -4 0.01 -12.97 -6 0.005 -7.45 -8 - 10 0.0033 -3.85 -12 y = -1467.3x + 1.2301 0.0025 -14 -1.33 -16 1/T 11. From Arrhenius eqn, k = Ae-Ea/RT, where Ea = Activation energy, k = rate constant, A = pre- exponential factor Now, In k = In A -E/RT Now, comparing with the graph we found that, - Ea/R = -1467.3; Ea = (1467.3 x 8.314) = 12.2 kJ/mol In A = 1.2301; A = 27640 12. Now, Kcat/k = e(Ea(cat)-Ea] /RT, here, T = 773 K, Ea = 325 kJ/mol, Ea(cat)= 12.2 kJ/mol Now, Kcat/ k = 1021