Experiment and correlation of osmotic coefficient for aqueous solution of carboxylic acids using NRTL nonrandom factor model

Using isopiestic method, osmotic data are measured at 298.15 K for carboxylic acid systems such as acetic, propionic, butyric, formic, malic, malonic and tartaric acids at a wide range of concentration that very rare data are available for these systems. The NRTL-NRF model of Haghtalab and Vera was already modified and applied for aqueous phosphoric acid solution [A. Haghtalab, M. Nosrati, Fluid Phase Equilib., 152, 1(1998) 43–55]. In this work the model is applied for calculation of osmotic coefficients of the other weak electrolyte systems such as carboxylic acids. Using a numerical version of Marquardt–Levenbergʹs optimization method, the interaction energy parameters of the NRTL-NRF model are calculated through minimization of the root mean square deviation between the calculated and experimental osmotic coefficient so that the corresponding equilibrium reaction of acidʹs dissociation is satisfied. Agreement of the calculated osmotic coefficient values with experimental data is very good over the whole range of concentration. In addition, molality of the undissociated electrolyte (mE) is simultaneously calculated during the process of the parameter optimization. Using the present model, the pH values for each aqueous carboxylic electrolyte solution are calculated so that the calculated results are in very good agreement with experiment.