the corresponding products C and D. Both factors are taken into account by the difference in the energies of the transition states (ΔΔG‡ in the figure below). The reaction coordinate free energy profile of a typical reaction under Curtin-Hammett control is represented by the following figure: The ratio of products only depends on the value labeled ΔΔG‡ in the figure: C will be the major product, because the energy of TS1 is lower than the energy of TS2. A common but false assertion is that the product distribution does not in any way reflect the relative free energies of substrates A and B; in fact, it reflects the relative free energies of the substrates and the relative activation energies. This misunderstanding may stem from failing to appreciate the distinction between "the difference of energies of activation" and "the difference in transition state energies". Although these quantities may at first appear synonymous, the latter takes into account the equilibrium constant for interconversion of A and B, while the former does not. Mathematically, the product ratio can be expressed as a function of K, k1, and k2 or in terms of the corresponding energies ΔG°, ΔG1‡, and ΔG2‡. By combining terms, the product ratio can be rewritten in terms of the quantity ΔΔG‡ alone, where ΔΔG‡ = (ΔG2‡ – ΔG1‡) + ΔG°. Inspection of the energy diagram (shown above) makes it apparent that ΔΔG‡ is precisely the difference in transition state energies. Derivation A generic reaction under Curtin–Hammett can be described by the following parameters: \bf{C}\ \it <-[k_{\rm 1}] \bf{A} \it\ <=> [{K}]\ \bf{B}\ \it-> [k_{\rm 2}]\ \bf D In order for rapid equilibration to be a good assumption, the rate of conversion from the less stable of A or B to the product C or D must be at least 10 times slower than the rate of equilibration between A and B. The rate of formation for compound C from A is given as , and that of D from B as , with the second approximate equality following from the assumption of rapid equilibration. Under this assumption, the ratio of the products is then . In other words, because equilibration is fast compared to product formation, throughout the reaction. As a result, also remains roughly constant throughout the reaction. In turn, integration with respect to time implies that likewise takes on an approximately constant value through the course of the