Thermodynamic Modeling and Experimental Investigation of Phosphoric Acid as a Polyelectrolyte System: Comparative Assessment of Thermodynamic Models

Process, Energy, Materials and Environment Laboratory (PEME), National School of Applied Sciences of Khouribga, Sultan Moulay Slimane University, Beni-Mellal, Morocco.

Published online: 22 May 2026

Abstract

The thermodynamic behavior of phosphoric acid systems containing cadmium, calcium, and sulfate ions was investigated using the Pitzer and Debye–Hückel models over a phosphorus content ranging from 5% to 30% P2O5 and a temperature range of 25°C to 80°C. This study aims to predict pH and density and compare the performance of the two models in describing the thermodynamic behavior of the system. Experimental measurements were used to validate the models, yielding Pearson correlation coefficients of r = 0.886 for pH and r = 0.764 for density, with normalized root mean square errors (NRMSE) of 0.203 and 0.121, respectively. Both models captured the general behavior of the system; however, the Pitzer model consistently provided more accurate and robust predictions. Overall, the Pitzer model proves to be the most accurate and reliable approach for predicting the thermodynamic properties of complex phosphoric acid solutions, offering a highly relevant tool for process control and parametric optimization.