Measurement and modelling of water activity, density, sound velocity, refractive index and viscosity of the Na2MoO4 + poly(ethylene glycol) + H2O system in the temperature range from 313.15 to 333.15 K
Introduction
Aqueous two-phase systems (ATPS) have been investigated as alternative systems of extraction, which have numerous advantages such as low cost, low viscosity, short process time, low energy consumption and are environmentally friendly [1].
The study of the physical and chemical properties of aqueous polymer-salt solutions is very useful in chemical engineering to understand the fundamentals of separation processes and fluid transport, among others. Physical properties, such as density and viscosity, are also indispensable for pipe sizing, mass balance calculations, and equipment design [2]. Regarding thermodynamic properties, the activity is an important and key thermodynamic property because it is closely related with the other thermodynamic properties such as osmotic coefficients, activity coefficients, among others. Due to this, the thermodynamic representation for water activity of (polymer + salt) aqueous two-phase systems is of great importance [3].
Thermodynamic properties of sodium molybdate have been scarcely studied [[4], [5], [6]]. Same occurs with the physical and thermodynamic properties of sodium molybdate in aqueous PEG solutions: Barrueto et al. [1] determined the liquid-liquid equilibrium and physical properties of the Na2MoO4 + PEG 4000 +H2O system in the temperature range from 288.15 to 308.15 K, where liquid-liquid equilibrium was correlated by the extended UNIQUAC model. Jiménez [5] measured and correlated using the UNIQUAC model, the water activities of unsaturated solutions of the Na2MoO4 + PEG 2000 + H2O system in the temperature range from 303.15 to 333.15 K. However, it is necessary to give greater emphasis to the study of this system due to its interesting applications in mining and biotechnology industries [5].
In addition, some authors have studied the modeling of aqueous PEG solutions: Ninni et al. [7] measured water activities of binary and ternary poly(ethylene glycol)s (PEGs) solutions at 298.15 K, and correlated these data by the group contribution method UNIFAC. Eliassi et al. [8], correlated water activities for aqueous solutions of poly(ethylene glycol) (PEG) with number average molecular weights of 300, 400, 4000, and 6000 at 308.15, 318.15, 328.15, and 338.15 K in a wide concentration range. Through these experimental data, Flory-Huggins interaction parameters were calculated. Sadeghi [9,10] and Sadeghi et al. [[11], [12], [13]] reported experimental water activities of diverse ternary systems containing polymer + salt + water, incorporating in some studies the correlation of experimental data with the Wilson model and the extended form of Chen's non-random two liquid (NRTL) model. Cortes et al. [14], Salabat et al. [15], Jahani et al. [16,17], and Zafarani-Moattar et al. [18] have reported similar studies of ternary systems.
The Pitzer model of virial coefficients [19] has been used widely in the prediction and correlation of solubilities in systems that contain one salt (or more) in a single solvent, generally water, however, the original form of this model is not successfully applied for mixed-solvent electrolyte solutions. Due to this, Wu et al. [20] proposed a modified Pitzer model for the prediction of the liquid – liquid equilibrium of polymer + salt + water ternary systems. Later, Lovera et al. [21], successfully applied the modified Pitzer model for the correlation of the solid–liquid equilibrium of the LiCl + PEG 4000 + H2O, NaCl + PEG 4000 + H2O, and KCl + PEG 4000 + H2O systems at 25 °C.
In the present article, the water activity and the physical properties of unsaturated solutions of the ternary Na2MoO4 + PEG 4000 + H2O system and the constituent binary systems at T = (313.15, 323.15, and 333.15) K were studied. The interval concentrations of Na2MoO4 were between 0.02 and 0.17 mass fraction, and for PEG 4000, the interval concentrations were between 0.05 and 0.30 mass fraction. The modified Pitzer model [20,21] was used to correlate the water activities, and the Othmer's rule [2,22] to correlate the physical properties such as density, sound velocity, refractive index and viscosity.
In addition, and in order to know if the PEG molar mass has an impact on the modelling results performed by the modified Pitzer and UNIQUAC models, predictions of water activities of the Na2MoO4 + PEG 2000 + H2O and Na2MoO4 + PEG 4000 + H2O systems were performed by the modified Pitzer [20,21] and extended UNIQUAC [5] models, respectively, in the temperature range from 313.15 to 333.15 K. To the best of our knowledge, there has been no report on the water activities and physical properties of the Na2MoO4 + PEG 4000 + H2O systems in the temperature range from 313.15 to 333.15 K.
Section snippets
Materials
Synthesis grade samples of PEG with an average molar mass of 4000 g/mol (3500–4500 g/mol) and 2000 g/mol (1900–2200 g/mol) were procured from Sigma-Aldrich. Sodium molybdate dihydrate with a purity of >0.995 and sodium chloride with a purity of >0.995 were procured from Merck. All reagents were used without further purification. Deionized water was used in all experiments (Milli-Q, Millipore, κ = 0.054 μS cm−1). The chemical specifications are shown in Table 1.
Apparatus and procedures
A KNAUER K-7000 vapor pressure
The modified pitzer model
According to the modified Pitzer model [20], the activity coefficients, γ, may be written as:where the superscripts, LR and SR, stand for long-range and short-range contributions, respectively.
For the non-ionic components,whereand Vi is the molar volume in m3·mol− 1 of pure non-ionic species i, d is the mixed-solvent density, and A and b are Debye-Hückel constants; based on a value of 4 Å
Physical properties
Experimental values of density, sound velocity, refractive index and viscosity of unsaturated solutions of the Na2MoO4 + H2O and Na2MoO4 + PEG 4000 + H2O systems at T = (313.15, 323.15 and 333.15) K were measured. The sodium molybdate and poly(ethylene glycol) concentrations chosen to determine the physical properties were selected below the saturation concentration of sodium molybdate. Physical properties data of the PEG 4000 + H2O binary system previously reported [26] are included in
Conclusions
Water activities, vapor pressures, and physical properties of the ternary Na2MoO4 + PEG 4000 + H2O system and its constituent binary systems were studied in the temperature range from 313.15 to 333.15 K.
Temperature has no significant effect on the water activities for the Na2MoO4 + H2O and Na2MoO4 + PEG + H2O systems. However, for the polymer aqueous solutions, the temperature effect is clearly appreciated, especially at high PEG concentrations.
The experimental data of water activity of the
CRediT authorship contribution statement
Francisca J. Justel: Software, Validation, Investigation, Writing - original draft, Writing - review & editing. Grecia Villca: Investigation, Data curation, Methodology. Yecid P. Jimenez: Conceptualization, Investigation, Resources, Writing - review & editing, Supervision.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
None.
Acknowledgments
The authors thank CONICYT-Chile for financing this research through Fondecyt Project N° 11130012. Authors are also grateful of the Project ING2030 CORFO Code 16ENI2-71940. Also, the authors thank to the three anonymous reviewers for their valuable comments.
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2022, Journal of Molecular LiquidsCitation Excerpt :Water activities of the binary Na2MoO4 + H2O system at 303.15, 313.15, 323.15, and 333.15 K were determined and correlated by Pitzer’s model by Jimenez et al. [10]. Thermodynamic and physical properties of water activity, refractive index, sound velocity, density and viscosity of unsaturated solutions of Na2MoO4 + PEG 4000 + H2O system and the constituent binary systems from 313.15 to 333.15 K were studied by Justel et al. [5], where the water activities were modeled by modified Pitzer and UNIQUAC models. The solubility of sodium molybdate in the (Na+ + MoO42− + SO42−) system at T = (293.15 to 343.15) K was measured and correlated by Ning et al. [11].
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2021, Journal of Molecular LiquidsCitation Excerpt :The modified Pitzer model [3] considers the existence of short-range and long-range interactions described by binary and ternary parameters. The model, originally applied to predict liquid-liquid equilibrium of polymer-water-salt systems, has been applied by different authors to determine different thermodynamic properties of electrolyte solutions [4–8]. In order to extend the studies of electrolyte solutions, this work provides experimental data of NaCl, KCl and NH4Cl solubility in mixtures of water and ethanol covering the entire molar composition of the binary liquid solution, in the temperature range from 288.15 K to 328.15 K.