A researcher proposes the following three-step catalytic mechanism for the…

CHEMISTRY · Multi-part · AP · Chemistry · Kinetics · Kinetics

Problem

A researcher proposes the following *three-step* catalytic mechanism for the decomposition of compound X (g) to form products Y (g) and Z (g): Step 1 X+Cat→XCX + \text{Cat} \to XC   ΔH1=+65 kJ mol−1\Delta H_1 = +65\,\text{kJ mol}^{-1}  Ea1=90 kJ mol−1E_{a1} = 90\,\text{kJ mol}^{-1} Step 2 XC→Y+Cat-ZXC \to Y + \text{Cat-Z}  ΔH2=−20 kJ mol−1\Delta H_2 = -20\,\text{kJ mol}^{-1}  Ea2=75 kJ mol−1E_{a2} = 75\,\text{kJ mol}^{-1} Step 3 Cat-Z→Z+Cat\text{Cat-Z} \to Z + \text{Cat}  ΔH3=−55 kJ mol−1\Delta H_3 = -55\,\text{kJ mol}^{-1}  Ea3=40 kJ mol−1E_{a3} = 40\,\text{kJ mol}^{-1} For comparison, the uncatalyzed single-step decomposition of X has an activation energy of 185 kJ mol−1185\,\text{kJ mol}^{-1} and an overall ΔH\Delta H of −10 kJ mol−1-10\,\text{kJ mol}^{-1}. (1) Part 1: (a) Using the numerical information above, construct a *scaled* potential-energy diagram (qualitative sketch) for both the catalyzed and uncatalyzed pathways on the same axes. Label all transition states, intermediates, and indicate the positions where the catalyst is regenerated. (2) Part 2: (b) From your diagram, determine which elementary step is the slowest in the catalyzed mechanism and justify your choice. (3) Part 3: (c) Discuss how replacing Cat with a modified catalyst Cat* that lowers Ea2E_{a2} by 15 kJ mol−115\,\text{kJ mol}^{-1} (without affecting the other steps) would influence the rate-determining step and the overall reaction rate.

Related theory

Browse the problem library