We propose an approach for monitoring the concentration of dissociated carboxylic acid species in dilute aqueous solution. The dissociated acid species are quantified employing inline Raman spectroscopy in combination with indirect hard modeling (IHM) and multivariate curve resolution (MCR). We introduce two different titration-based hard model (HM) calibration procedures for a single mono- or polyprotic acid in water with well-known (method A) or unknown (method B) acid dissociation constants pKa. In both methods, spectra of only one acid species in water are prepared for each acid species. These spectra are used for the construction of HMs. For method A, the HMs are calibrated with calculated ideal dissociation equilibria. For method B, we estimate pKa values by fitting ideal acid dissociation equilibria to acid peak areas that are obtained from a spectral HM. The HM in turn is constructed on the basis of MCR data. Thus, method B on the basis of IHM is independent of a priori known pKa values, but instead provides them as part of the calibration procedure. As a detailed example, we analyze itaconic acid in aqueous solution. For all acid species and water, we obtain low HM errors of < 2.87 × 10-4mol mol-1 in the cases of both methods A and B. With only four calibration samples, IHM yields more accurate results than partial least squares regression. Furthermore, we apply our approach to formic, acetic, and citric acid in water, thereby verifying its generalizability as a process analytical technology for quantitative monitoring of processes containing carboxylic acids.
Keywords: ALS; IHM; MCR; Process analytics; Raman spectroscopy; alternating least squares; carboxylic acid; dissociation; indirect hard modeling; itaconic acid; multivariate curve modeling; pKa estimation.