Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

146 EXPERIMENTAL METHODS FOR FAST REACTIONSA and B are equal, zA = oB, but if they are not, the lifetimes are related by themole fractions NA and NB: ZA/NA = oS/NB.) A second case may be considered,that in which two protons in environments A and B are coupled through spin-spininteraction J. Here the spectrum comprises four lines and, if 6 >> J, the two doubletsare well-separated and have almost equal intensity. Now it is assumed thatonly one proton undergoes exchange (A, say, with the solvent). This will have asimilar effect on the doublet of B as is observed when A and B exchange, but themodification of the B spectral lines will give information about oA. The same treatmenttherefore applies, to a good approximation, with J replacing 6.The basis of kinetic measurements by NMR is a comparison of the kinetic behaviour(exchange) with nuclear properties of known frequency, 6 or J. What happensas the lifetime o changes? Fig. 15 shows the changes in two NMR lines separated by6 (or J) as the exchange rate increases. This behaviour may be classified underthree headings.(a) “Slow” exchange-the lines begin to broaden and to approach each other. Thisapproximation is given by o6 >> 1 which, on substitution into the Bloch equations,gives1/T; = 1/T2+1/ofor eachline. (T, , Ti are the transverse relaxation times in the absence and presenceof exchange, respectively. They are related to the width of the line at half height(Am, Am’) byAm, Am‘ = l/l~(T~, Ti).)Methods of evaluating o from the separation, height and width of the lines havealso been given6 ’.Fig. 15. Variation of NMR line shape with increasing [(a) to (d)] exchange rate (intensities notto scale).