Spectrophotometric Measurements

The most effective spectrophotometric procedures for pKa determination are based on the processing of whole absorption curves over a broad range of wavelengths, with data collected over a suitable range of pH. Most of the approaches are based on mass balance equations incorporating absorbance data (of solutions adjusted to various pH values) as dependent variables and equilibrium constants as parameters, refined by nonlinear least-squares refinement, using Gauss-Newton, Marquardt, or Simplex procedures [120-126,226].

For an ionizable molecule, the refinement model can be posed as species

j where Aik is the calculated absorbance at the k wavelength in the i spectrum. Different values of i denote spectra collected at different pH levels. The molar absorptivity of the j species at the k wavelength is denoted by Ejk, and the concentration of the j species at the i pH is cj. ''Species'' here refers to the different charge-state forms of a molecule. The values of cij are functions of the total sample concentration and the ionization constants; these are calculated as in procedures for the pH-metric refinement of constants [118]. One can estimate pKa values, intelligently guess the values of j and use these to calculate values of Aik. In the calculation, the objective is to minimize the sum of the residuals between the calculated and observed absorbances, species spectra^ obs _ 4calc\2

k i Sik where sik are the estimated uncertainties in the measured values of absorbances. Mathematically imposed constraints prevent the calculation of negative values of absorbances [227]. The "best" set of refined pKa constants are those that minimize S.

In complicated equilibria, uninformed guessing of pKa values and j can be unsettling. Elegant mathematical methods have evolved to help this process of supervised calculation. Since not all species in a multiprotic compound possess detectible UV chromophores or sometimes more than one species have nearly identical molar absorptivity curves, methods had to be devised to assess the number of spectrally active components [121]. With ill-conditioned equations, damping procedures are required [122]. Gampp et al. [127] considered principal-component analysis (PCA) and evolving factor analysis (EFA) methods in deciding the presence and stoichiometries of the absorbing species.

Tam and others [131-135,137,138,140-143,228,229] developed a very effective generalized method for the determination of ionization constants and molar absorptivity curves of individual species, using diode-array UV spectrophotometry, coupled to an automated pH titrator. Species selection was effected by target factor analysis (TFA), and EFA methods were used. Multiprotic compounds with overlapping pKa values were investigated. Binary mixtures of ionizable compounds were considered [141]. Assessment of microconstants has been reported [138,140]. The use of cosolvents allowed the deconvolutions of 12 microconstants of cetirizine, a 3-pKa molecule [142]. Validation studies, comparing the TFA method to the first derivative technique, were reported [132,137].

A 96-well microtiter plate high-throughput method, called spectral gradient analysis (SGA), based on a pH gradient flow technique with diode-array UV detection has been reported [135,136,139]. A universal buffer, consisting of citric acid, phosphate, tris(hydroxymethyl)-aminomethane, and n-butylamine, was developed in an acidified and an alkaline form [139]. Mixture of the two forms in a flowing stream produced a pH gradient very linear in time. The SGA method was successfully validated using 110 structurally unrelated compounds [135]. Poorly soluble molecules still pose a challenge to the SGA method, although this problem is being vigorously addressed by the manufacturer.

Apparently similar flowstream universal buffers have been developed by Alibrandi and others [128,129] for assessing kinetic parameters, such as the pH-dependent hydrolysis of acetylsalicylic acid. The pH-time curves are not as linear as in the SGA system. Other reports of continuous flow pH gradient spectrophotometric data have been described, with application to rank-deficient resolution of solution species, where the number of components detected by rank analysis is lower than the real number of components of the system [130]. The linear pH-time gradient was established in the flowstream containing 25 mM H3PO4 by the continuous addition of 100 mM Na3PO4.

At pION's analytical services laboratory, the pKa of a molecule (whose structure may not be known beforehand) is first measured by the TFA method, because very little sample is consumed. (Sometimes there is not much more than 1 mg of sample with which to work.) Only when the analysis of the data proves problematic do we repeat the measurement, the second time using potentiometry, where more sample is required. If any indication of precipitation is evident, either DMSO or methanol is added to the titrated solution and the titration is repeated 3 times (using the same sample), with additional water added between the repeats, to obtain different Rw values of the mixed solvent solutions. It has been our experience that if the TFA method fails and more sample is available, the follow-up pH-metric method always works.

0 0

Post a comment