Elsevier

Fluid Phase Equilibria

Volume 518, 15 August 2020, 112628
Fluid Phase Equilibria

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

https://doi.org/10.1016/j.fluid.2020.112628Get rights and content

Highlights

  • Water activities of Na2MoO4+PEG 4000+H2O system were studied from 313.15–333.15 K.

  • Good agreement between experimental and correlated water activities was obtained by Pitzer model.

  • Physical properties of Na2MoO4+PEG 4000+H2O system were determined from 313.15–333.15 K.

  • Good agreement between experimental and calculated data of physical properties was obtained by Othmer's rule.

  • Pitzer and UNIQUAC models, operate independently of the molar mass of the PEG used.

Abstract

Thermodynamic and physical properties of water activity, density, sound velocity, refractive index and viscosity of unsaturated solutions of Na2MoO4 + PEG 4000 + H2O system and the constituent binary systems at 313.15, 323.15 and 333.15 K were studied. The concentration range of the solutions was from 0.02 to 0.17 mass fraction of Na2MoO4 and from 0.05 to 0.30 mass fraction of poly(ethylene glycol) with an average molar mass of 4000 g/mol. Water activities were correlated with the modified Pitzer model and physical properties were correlated by the Othmer's rule, obtaining in all cases a good agreement between the experimental and correlated data. Water activity predictions for the Na2MoO4 + PEG 2000 + H2O and Na2MoO4 + PEG 4000 + H2O systems were performed with the modified Pitzer and extended UNIQUAC models, respectively, showing that both thermodynamic models can operate independently of the molar mass of the polymer used.

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:lnγ±=lnγ±LR+lnγ±SR,where the superscripts, LR and SR, stand for long-range and short-range contributions, respectively.

For the non-ionic components,lnγiLR=2AVidb3[1+bI12(1+bI12)12ln(1+bI12)],whereI=0.5jwNm'jZj2,m'j=njns,ns=nw+Mini1000,and 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.

References (36)

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