Perturbation of Equilibrium — Applications to Carbocations

Diagrams showing equilibrium isotope effects. A. Increasingly favoring product with H, and B. Increasingly favoring product with D. 

Larger energy difference for hydrogenated case equilibrium lies further toward products for the deuterium-substituted compound 

Isotopic perturbation of equilibrium. A. The 1,1,3,3-tetramethylcyclo-hexane system. See text for discussion. B. C NMR spectra used to study equilibria given in part A. C. An isotopic perturbation of equilibrium experiment for a prototype carbenium ion. D. Isotopic perturbation of resonance for a substituted allyl cation. The equilibrium arrows are hypothetical for sake of discussion in the text. It is really resonance, not an equilibrium. 

7 allows us to relate the chemical shift separations we have discussed to the equilibrium constant for the process, K. For this case, inserting A = 9.03 ppm and S = 0.184 ppm gives K = 1.042 0.001. This corresponds to an energy difference of 0.024 kcal/mol The isotopic perturbation of equilibrium method has allowed us to measure a very small deviation of an equilibrium constant from a value of 1. 

We can see, then, that the isotopic perturbation of equilibrium method offers a way to distinguish a situation in which we have a rapidly equilibrating pair of cations from one in which we have a single static structure. As discussed in Chapters 1,2,11, and 14, this is a recurring issue in carbocation chemistry, and so the method has proven to be very useful. 

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