A researcher investigates the competitive formation of two esters, F and G
CHEMISTRY · Multi-part · AP · Chemistry · Thermodynamics and Electrochemistry · Thermodynamics and Electrochemistry
Problem
A researcher investigates the competitive formation of two esters, F and G, from the same acyl cation intermediate in solution. Independent kinetic experiments yield the following pseudo-first-order rate constants at two temperatures when the concentration of nucleophile is held constant:
kF(s−1)kG(s−1)
298 K 6.2×10−31.1×10−4
318 K 3.4×10−27.5×10−4
Assume that each pathway is first order with respect to the acyl cation and that pre-exponential factors are temperature-independent over this range. Separate thermodynamic studies indicate that at 298 K the free energies of the isolated esters satisfy ΔG∘(G)−ΔG∘(F)=−7.5kJmol−1.
(a) Using the Arrhenius equation in its linearized form, determine the activation energy for formation of each ester. Show all steps of your calculation.
(b) Identify which ester is the kinetic product at 298 K and justify quantitatively.
(c) Explain, with reference to both your activation energies and the given ΔG∘ difference, which ester will predominate after the reaction mixture is heated at 350 K for 48 h.
(d) Propose a temperature–time protocol that would maximize the isolated yield of ester F within an 8 h laboratory period. Justify your plan using the kinetic and thermodynamic data.