The uncatalyzed gas-phase decomposition of AB2 has an activation energy of 180 kJ mol⁻¹. When a metal surface catalyst is introduced, the reaction proceeds through an adsorption–reaction–desorption pathway with the following enthalpy changes, all measured relative to the energy of separated gaseous reactants and a clean surface:
• Adsorption of AB2: ΔH = –60 kJ mol⁻¹
• Surface reaction forming A–B* + B*: ΔH‡ (from adsorbed state) = 70 kJ mol⁻¹
• Desorption of products: ΔH = +50 kJ mol⁻¹
Assume that the adsorption step is fast and reversible, the surface reaction is rate-limiting, and desorption is rapid once products are formed.
(a) Sketch a qualitative potential-energy diagram (energy on the vertical axis, reaction coordinate on the horizontal axis) for both the uncatalyzed and catalyzed pathways on the same set of axes. Clearly label reactants, adsorbed intermediate(s), transition state, products, and all given energy differences.
(b) Identify the step that determines the overall rate in the catalyzed pathway and state its corresponding activation energy, relative to the gaseous reactants.
(c) Using your diagram, explain why the catalyst lowers the observed activation energy even though the intrinsic barrier for the surface reaction (70 kJ mol⁻¹) is less than half of the gas-phase barrier (180 kJ mol⁻¹). Include in your discussion how adsorption energy influences the apparent activation energy.
(d) Predict qualitatively how the rate would change if the adsorption enthalpy became much more exothermic (e.g., –120 kJ mol⁻¹) while all other energetics stayed the same. Justify your prediction in terms of coverage and desorption.