At 298 K, the rate constant for a particular gas-phase reaction is k0=1.5×10−5s−1. When a heterogeneous catalyst is introduced, the rate constant increases to kcat=9.0×10−2s−1 while the overall enthalpy change of the reaction remains −45kJ mol−1.
Using the Arrhenius equation in logarithmic form, lnk=lnA−RTEa, answer the following.
(1) Part 1: (a) Assuming the frequency factor A is unchanged by the presence of the catalyst, calculate the decrease in activation energy, ΔEa, produced by the catalyst. Express your answer in kJ mol⁻¹ and use R=8.314J mol−1K−1.
(2) Part 2: (b) Sketch a qualitative potential-energy diagram that includes both the uncatalyzed and catalyzed pathways. On your diagram clearly label (i) the relative heights of the activation energy barriers, (ii) the positions of the transition states, and (iii) the enthalpy change, ΔH, common to both pathways.
(3) Part 3: (c) Explain how your calculated value of ΔEa in part (a) is reflected in the relative heights of the energy barriers on the diagram created in part (b).