The gas-phase elementary reaction C + D → CD has the following potential-energy characteristics (values are relative to the energy of separated reactants):
• Uncatalyzed pathway: transition-state energy = 120 kJ mol⁻¹; product energy = 20 kJ mol⁻¹.
• Catalyzed pathway: transition-state energy = 80 kJ mol⁻¹; product energy unchanged.
At 500 K, only 8 % of collisions have energies at or above 120 kJ mol⁻¹, and 18 % have energies at or above 80 kJ mol⁻¹. Independent experiments show that, for either pathway, only 0.12 of collisions that satisfy the energy requirement are properly oriented to react.
(a) State the numerical value of the activation energy for both the uncatalyzed and catalyzed pathways.
(b) For each pathway, compute the fraction of total collisions expected to be successful at 500 K.
(c) The reaction mixture is heated to 550 K, at which the fraction of collisions at or above 120 kJ mol⁻¹ doubles while the fraction at or above 80 kJ mol⁻¹ increases by only 50 %. Predict which pathway will now dominate the reaction rate and justify your answer using collision-theory reasoning.
(d) Propose one molecular modification to reactant C or D that could increase the orientation probability above 0.12, and explain how this change would influence the overall reaction rate.