A chemist is evaluating three metal complexes (M₁, M₂, and M₃) as potential catalysts for the gas-phase conversion of P to R via intermediate Q. The relevant energies for each pathway are listed in the table. All energies are given in kJ mol⁻¹ relative to reactant P.
Transition State 1
Intermediate Q
Transition State 2
Product R
Uncatalyzed
+110
+45
+ ninety
–25
Pathway with M₁
+75
+30
+72
–25
Pathway with M₂
+85
+20
+60
–25
Pathway with M₃
+70
+50
+68
–25
For safe operation, the chemist requires that the energy difference between any intermediate and the next higher transition state in the same pathway be at least 50 kJ mol⁻¹ to minimize accumulation of reactive intermediates.
(a) For each catalyzed pathway, determine the overall activation energy (the highest transition state energy relative to reactant P).
(b) For each catalyst, evaluate whether the safety criterion concerning the intermediate is satisfied. Show your reasoning.
(c) Taking both activity (rate enhancement) and safety into account, identify which catalyst, if any, should be selected. Provide a well-reasoned justification referencing your calculations.