Infrared titration of phosphoric acid

The titration of phosphoric acid by sodium hydroxide was performed by infrared (IR) spectroscopy with the objective of obtaining the infrared spectra of the pure ionic species and determining their abundance as a function of pH. In the series of spectra, taken in the pH range of 0.18-13.4, the subtraction of neutral water, acidic water, and basic water was made. Factor analysis (FA) was then applied to the series of spectra to obtain the objective. First, we found the four most abundant species : H3PO4 (pH 0-4), H2PO4- (pH 0-9), HPO4-2 (pH 4-14), and PO4-3 (pH 9-14). Secondly, we found three complexes in small quantities : H3PO4-H2PO4-(pH 0-4),H2PO4--HPO42- (pH 4-9), and HPO42--PO4-3 (pH 9-14). The equilibrium constants of these species with the parent molecules are 0.65, 0.63, and 0.4 L/mol, respectively. Thirdly, we found residual water that was closely bound to the ionic species which formed hydrates. The pK(a) values obtained from the IR titration were used to obtain the theoretical concentration of the four principal species as a function of pH. The resulting distribution curve was found to be coincident with the distribution curve obtained by IR.