The solid curves in figure shows analytical curves for T S = R -1 S as a function of pH and magnetic field, using equation 23 for the rate constant, with parameters given in table III. The protonation rate constant k p = 10 7 M -1 s -1 was chosen to obtain a rough qualitative match with experiment. This value is reasonably consistent with known protonation rate constants for carboxylic acids in solution, determined by NMR spectroscopy and fluorescence spectroscopy .