Elsevier

Fluid Phase Equilibria

Volume 327, 15 August 2012, Pages 38-44
Fluid Phase Equilibria

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

https://doi.org/10.1016/j.fluid.2012.05.002Get rights and content

Abstract

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–Levenberg's 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 acid's 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.

Highlights

► Using isopiestic method, osmotic coefficient of carboxylic acids is measures. ► The NRTL-NRF model is extended for weak acids using dissociation constant. ► Osmotic coefficients are correlated for several weak acids such as acetic acid. ► The calculated pHs of carboxylic acids were in very good agreement with experiment.

Introduction

Weak organic electrolytes such as carboxylic acids are broadly exist in food industries such as tomato paste, fruit juices, candies, coffee extract, fermented milk, and yoghurt [1]. Acetic, citric, malic, tartaric, and malonic acids are the examples of very common edible organic compounds that are widely used in different food industries [2]. Also, volatile fatty acids such as formic, acetic, propionic and butyric acid are main intermediates in the process of anaerobic digestion [3], [4]. Experiments for measurement of osmotic coefficient of water for the carboxylic acid solutions are needed to evaluate pH and activity of water in such aqueous acid mixtures. At infinite dilution, all weak acids behave as same as a strong electrolyte that they are completely dissociated into anion and cation species. Thermodynamic modeling of weak acid is rare so that only for phosphoric acid correlation of osmotic coefficient data was already obtained [5]. Moreover, experimental data for thermodynamic properties of phosphoric acid such as osmotic coefficient, pH, vapor pressure, conductivity and degree of dissociation were already proposed by few investigators [6], [7], [8], [9], [10], [11], [12]. Experimental osmotic coefficient data of citric acid, as another common weak electrolyte in food industries, was presented by Apelblat et al. [13].

In this work, using the isopiestic method the osmotic coefficient of several carboxylic acids is measured at 298.15 K at a wide range of concentration. The extended NRTL-NRF model, which developed previously for phosphoric acid, is used to correlation of the osmotic coefficient data [5]. The NRTL-NRF equation is a Wilson-type local composition model that first proposed by Haghtalab and Vera [14], [15] for modeling of activity coefficient of electrolyte solutions and then, it was modified for electrolyte solutions and applied to aqueous two-phase partitioning of polymer–salt systems [16], [17]. The model is a modification of NRTL model that take into account nonrandomness of species in a solution through parameter of nonrandom factor by assuming random state of central cells as a reference state. The advantage of NRTL-NRF model respect to the other local composition models is its application in correlation and prediction of thermodynamic properties of electrolyte solutions up to their saturation point where salts are precipitated. Another point that it makes NRTL-NRF model superior is using the random state of ions as a reference state that is more realistic since in the alternative local composition models it is assumed pure ions as a reference state that it violates the principle of electroneutrality of electrolyte solutions. In this investigation, following our previous work [5] the model is extended to apply for carboxylic acid systems. The interaction parameters of the model are calculated through minimization of the root mean square deviation between the calculated and experimental osmotic coefficient along with satisfying the acid's dissociation constant of the weak acid equilibrium reaction.

Section snippets

Materials and apparatus

The pure carboxylic acids plus sodium chloride were obtained from Merck Company. Prior the isopiestic experiments, all materials are degassed and de-moisturized at 353.15 K (80 °C). Doubled distilled and de-ionized water is used for preparation of the organic acid solutions. During preparation of the mixture, temperature was decreased from 353.15 K to 298.15 K. An ANDHR–202 analytical weighting scale balance having accuracy of ±0.01 mg and a Metrohm pH meter with buffer solutions at pH = 4.00, 7.00,

Modeling of a weak acid

Most of weak acids dissociate in several incomplete stages; however, the first step has mainly the highest dissociation constant (α). Table 1 illustrates the dissociation constants, chemical formula, and molecular weight of the organic acids investigated in this study. Polycarboxylic acids i.e. malonic, malic, tartaric and citric acids dissociate more than one stage. However, the second and third dissociation constants are such small that it could be neglected compared to constant of the first

Results and discussion

The relation ϕs = ϕrνrmr/(νsms) is used to calculate the osmotic coefficient of unknown solution sample where ϕr and mr are the osmotic and molality of the reference NaCl solution and “ν” stand for the stochiometric number of the reference solution with a value of 2 and for the weak electrolyte was considered as unity. The osmotic coefficient of the reference solutions was calculated using the exact interpolation of experimental osmotic coefficient data available for NaCl [20] as shown in Fig. 1.

Conclusion

In this work, the isopiestic method was used for measurement of the osmotic coefficient of carboxylic acids such as formic, acetic, propionic, butyric, malonic, malic, tartaric and citric. The extended NRTL-NRF model was applied for correlation of osmotic coefficient data of the carboxylic acids and the binary interaction parameters were obtained for those mentioned acids. Finally, one can conclude that the NRTL-NRF model can be applied successfully for prediction of pH and concentration of

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