NMR Spectroscopy and Chemical Exchange Reactions

When a proton is transferred from one molecule to another in solutions, it usually finds itself in a different magnetic environment. As a result, if finite amounts of both reactant and product are present in solution at equilibrium, the proton can produce two lines in the NMR spectrum, one corresponding to the proton donor and the other to the proton acceptor. A second feature of this system relates to the rate with which the proton is exchanged between the donor and acceptor. If the frequency with which the proton is transferred is comparable to the radio frequency associated with the NMR spectrometer, then the lines corresponding to the two species are broadened. The extent of line broadening can be used to determine the rate constants associated with the exchange process [31]. 

When a chemical exchange reaction occurs in solution, it can lead to a broadening of the related NMR peaks, as described in the following discussion. Consider first of all a proton exchange reaction between protons in different environments denoted as HA and HB  

Since the protons are in different environments they are expected to produce two distinct lines in the NMR spectrum. The intensities of these lines reflect the relative concentrations of the protons at equilibrium. On the basis of the theory of chemical relaxation (section 7.6), the relaxation time associated with proton 

and are the rate constants associated with the forward and backward reactions in equilibrium (7.9.1). The experiment is usually designed so that the total proton concentration is very small with respect to the concentration of other solution components, for example, the solvent. Then the expression for the relaxation time can be rewritten as 

At this point it is necessary to relate the relaxation time for the chemical process to the spin-spin relaxation process which is always present when the system absorbs energy from the radio frequency wave. Both processes lead to broadening of the NMR absorption peak. If T, is the total relaxation time for process i, it may be estimated from T2 and x,- using the relationship 

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