Accepted Manuscript Determination of water activity, osmotic coefficients, activity coefficients, solubility and excess Gibbs free energies of NaClsucrose-H2O mixture at 298.15 K Brahim Messnaoui, Abdelfetah Mounir, Abderrahim Dinane, Samaouali Abderrahim, Bahija Mounir PII: DOI: Reference: S0167-7322(18)35854-9 https://doi.org/10.1016/j.molliq.2019.03.156 MOLLIQ 10697 To appear in: Journal of Molecular Liquids Received date: Revised date: Accepted date: 25 November 2018 24 March 2019 26 March 2019 Please cite this article as: B. Messnaoui, A. Mounir, A. Dinane, et al., Determination of water activity, osmotic coefficients, activity coefficients, solubility and excess Gibbs free energies of NaCl-sucrose-H2O mixture at 298.15 K, Journal of Molecular Liquids, https://doi.org/10.1016/j.molliq.2019.03.156 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. ACCEPTED MANUSCRIPT PT 1 RI Determination of Water Activity, Osmotic Coefficients, Activity SC Coefficients, solubility and Excess Gibbs Free Energies of Messnaoui1 Brahim Abdelfetah 4 5 Mounir2, Dinane3,4*, Abderrahim Samaouali MA Abderrahim , Bahija Mounir 1 NU NaCl-Sucrose-H2O Mixture at 298.15 K Laboratoire d’Analyse et Conception des Procédés Industriels, Ecole Nationale des Sciences Appliquées ENSA- Safi, Université Cadi Ayyad Marrakech, Route Sidi Bouzid, Safi 46000, Institut Supérieur des Professions Infirmières et Techniques de Santé Marrakech, Rue PT E 2 D Maroc. Abdelouahab Derraq, Marrakech 40000, Maroc. 3 Ecole Royale Navale, Département de Recherches et Projets, Laboratoire de Thermodynamique, Boulevard Sour Jdid, Casablanca 20000, Maroc. 4 Laboratoire Matériaux, Substances Naturelles, Environnement & Modélisation (LMSNEM), AC 5 CE Equipe de Thermodynamique et Energétique, Centre de Recherches en Energie, Département de Physique, Faculté de Sciences, Université Mohammed V, Agdal, B.P.1014, 10090, Rabat, Morocco. Faculté Polydisciplinaire de Taza, Université Sidi Mohamed Ben Abdellah, Fès, Route d’Oujda, B.P. 1223 Taza, Maroc. * Corresponding author: (A. Dinane) E-mail: [email protected] Tel.: 212 64 27 21 99 ACCEPTED MANUSCRIPT 2 Abstract The relative humidities on ternary NaCl-sucrose-H2O solution of 0.5, 1.0, 2.0, 4.0 and 5.5 mol.kg-1 of sucrose have been determined by the hygrometric method at 298.15 K in the molality range from 0.5 to 6.0 mol.kg-1 of NaCl. The obtained data allow the deduction of the water activities and osmotic PT coefficients. The experimental results are compared with the predictions of the RI extended composed additivity (ECA) rule, the Lin et al. equation, and Lietzke SC and Stoughton (LS II) models. The obtained results were interpreted by using Pitzer-Simonson-Clegg model. The four mixture parameters are determined NU and used to predict the activity coefficients of NaCl and sucrose in the mixed solution. The solubility, excess Gibbs energy and The Gibbs energies of PT E D MA transfer of sodium chloride are also calculated for this system. Key words CE water activity; osmotic coefficient; activity coefficient; excess Gibbs energy; AC NaCl-sucrose-H2O; solubility; Pitzer-Simonson-Clegg model. ACCEPTED MANUSCRIPT 3 1. Introduction Electrolyte and non electrolyte solutions play an important role in several fields of science and technology such as biology, chemical and pharmaceutical industries, biochemical systems, and in other applications. Atmospheric aerosol is composed of solid particles, mainly electrolytes suspended in the air, and RI cloud formation and climate system regulation. PT plays an important role in the environmental domain, for example air quality, SC The physicochemical properties of these solutions has been performed by several methods such as the emf techniques [1-3], isopiestic vapour pressure NU [4-7], and vapour pressure lowering [8-10]. We have developed in our previous studies the hygrometric method [11] which MA it is very adequate to determine directly the water activity of aqueous electrolyte solutions, such as binary aqueous electrolytes [12, 13], and mixed D electrolytes [14-18]. In this study, we develop the application of this method to PT E the aqueous mixture of an electrolyte and non-electrolyte in order to determine the physicochemical properties of the system NaCl-sucrose-H2O. This system CE has been extensively studied by Robinson R. A. et al. [19] using the isopiestic vapour pressure for mixed solutions of sucrose and sodium chloride at total AC molalities from 0.5152 mol.kg-1 to about 11.677 mol.kg-1 at 298.15 K. Wang J. et al. [20] have determined the mean activity coefficients by emf measurements of NaCl in aqueous solutions of 10, 20 and 30 mass% of sugar (glucose and sucrose) in the molality range from 0.006 mol.kg-1 to 2.0 rnol.kg-1 at 298.15 K. Hu Y. F. and Guo T.M. [21] have applied the Pitzer-Simonson-Clegg (PSC) equation for describing the salt activity coefficients and solubilities in ternary systems NaCl-n-H2O (n: sucrose and mannitol) at 298.15 K. Comesan J. F. et ACCEPTED MANUSCRIPT 4 al [22] have determined the water activities using an electric hygrometer for the binary system of sugar-water and for ternary system of sugar-sodium chloridewater for different types of sugar ( xylose, glucose, fructose, sucrose) at 35 °C, and their results have been correlated with an empirical equation proposed by Lin et al. [23]. Shalaev E.Yu. and Franks F. [24] have established equilibrium PT phase diagram of water-sucrose-NaCl system by DSC measurements. RI We have performed the measurement of the relative humidities of mixture of NaCl-sucrose-H2O for different molalities of the sucrose of 0.5, 1.0, 2.0, 4.0 SC and 5.5 mol.kg-1 in the molality range of NaCl from 0.5 to 6.0 mol.kg-1 at NU constant temperature of 298.15 K. From these measurements, the osmotic coefficients were deduced. Our results are compared with the values obtained MA by other methods. The solute activity coefficients, excess Gibbs energy, Gibbs energy of transfer of sodium chloride, and NaCl solubility in water-sucrose D system are calculated by using the Pitzer-Simonson-Clegg model [25-27] with 21]. PT E our new ionic Pitzer parameters and are compared with data of literature [19- CE 2. Experimental section: The apparatus used for the hygrometric method is the same to the one AC described in our previous investigations [11, 12] for the measurement of the relative humidities surrounding non-volatile electrolytes. The chosen aqueous ternary system in this study is the mixture of electrolyte with non-electrolyte as NaCl-sucrose-H2O. The procedure used is based on hygrometric measurements of the aqueous solutions. The relative humidity above the studied solution is determined from ACCEPTED MANUSCRIPT 5 measurements of the diameter of the droplet formed from previously calibrated reference solutions using a microscope equipped with a micrometric screw. The drop diameter D(aw(ref)) of the reference solution above the vessel containing the same reference solution is measured and the same diameter D(aw) above the studied solution of unknown relative humidity is then PT determined. Thus, we calculate the growth ratio K (K=D(aw(ref))/D(aw)) of the RI drop which change its diameter by evaporation or condensation. The variation SC of the ratio K allows to determine the water activity (equivalent to the relative humidity [11]) of studied solution using the variation of K versus the water NU activity of reference solution of sodium chloride and lithium chloride [14,15]. The reference relative humidity is taking as 0.84 or 0.98 for dilute solution. MA The solutions were prepared from the anhydrous materials from Panreac, Merck and Fluka (Table 1) with deionized distilled water (conductivity < 5.10-6 D S·cm-1). We checked the prepared molalities by measuring the refractive index PT E with uncertainty of u(n) = 2.10-4. Thus the uncertainty of the molality data was u(m) = 0.01 mol·kg-1. The uncertainty of the relative humidity is mainly due to CE the measurements of the drop diameters and was estimated to be u(rh) = 0.0005 for aw > 0.95 and u(rh) = 0.002 for aw < 0.95. The relative humidity in AC the experiments is equivalent to the water activity aw [11]. The controlled temperature in the box of measurement is fixed at T=298.15 K with uncertainty of u(T) = 0.02 K INSERT TABLE 1 3. Theory and models In the literature we find several models to represent the thermodynamic properties of aqueous electrolyte solutions. In order to compare our results with ACCEPTED MANUSCRIPT 6 those available in literature or those predicted by the models, we choose some models and empirical equations frequently used in calculations of the properties of electrolytes and non electrolyte mixtures. These models are cited below. 3-1. The Lin et al. rule PT Recently, Lin et al. [23] presented a very simple empirical equation for RI ternary systems. This proposed equation has the form: (1) SC a w 1 (a w1 1) (a w2 1) C12 m1m2 where mi represents the molality of species i in a multicomponent solution, C12 NU adjustable coefficient obtained from ternary mixture. The aw1 and aw2 are the water activities of aqueous binary solutions of electrolyte 1 and non electrolyte MA 2, respectively. 3-2. The ECA rule D A simple mixing equation named ECA “Extended Composed Additivity” PT E rule, proposed by Dinane [14] predicts the water activity in mixed electrolyte solutions. We have applied the proposed equation for the aqueous mixture of CE an electrolyte and non electrolyte in the case of the studied system water (1)- AC sucrose (2)-sodium chloride (MX) by: aw 1 aw(MX) aw(2) mMX m2 mMX m2 m , (2) where mMX, m2 and aw(MX), aw(2) are, the molalities of electrolyte component MX and non-electrolyte 2, their water activities in the binary solutions, respectively. m is the total molality of the mixture. The parameters and , characterise the deviation from ideality in the mixture of electrolyte MX and ACCEPTED MANUSCRIPT 7 non-electrolyte 2 for concentrated solution. They are estimated by a graphical procedure with an equation derived from Eq. (2) a w λ mδ , mMX m2 (3) where Δ aw is the difference between the experimental and calculated values of PT water activity aw. The quantity on the left was plotted against the total molality RI to obtain a linear plot with intercept and slope . 3-3. The LS model SC The LS II equation given by Lietzke and Stoughton [28,29] for the NU prediction of the osmotic coefficients of the aqueous mixtures of electrolytes is applied in the case of mixed electrolyte and non-electrolyte such the studied MA system water (1)-sucrose (2)-sodium chloride (MX) by: ( MXmMX m2 ) MXmMXMX m22 , (4) D where MX represent the number of ions when the molecule of considered PT E electrolyte component MX is dissociated completly, mMX its molality, and MX is the osmotic coefficient of the binary solution of component MX at the total CE molality of the mixture. m2 is the molality of non electrolyte and 2 its osmotic AC coefficient in the binary solution at the total molality of the mixture. 3-4. The Pitzer-Simonson-Clegg model The Pitzer-Simonson-Clegg equations [25-27] can represent with a good accuracy the osmotic activity and activity coefficients of electrolytes in mixed solvents [21]. The excess Gibbs energy per mole is the sum of the contribution of two terms, a long-range electrostatic ex interaction g PSC : ex g PDH and a short-range ACCEPTED MANUSCRIPT 8 ex g ex g ex g PDH PSC , RT RT RT (5) where R is the universal constant of ideal gas and T is the Temperature. For water(1)-sucrose(2)-sodium chloride (MX) system, the long-range electrostatic equation of Clegg-Simonson-Pitzer is given by: RI PT ex g PSC x1 x1 W1.MX x2W2.MX x I2 x1 U 1.MX x2U 2.MX RT , (6) 0 x I2 2 2 2 1 x I x1 V1.MX x2V2.MX x1 x2 W12 U 12 x1 x2 x I Y1, 2,MX Y1, 2,MX 4 SC where x1 , x 2 , and x I are the mole fraction of water, the mole fraction of NU sucrose and the total mole fraction of ion ( xI 1 x1 x2 ), respectively. W1, MX , U 1, MX and V1, MX are the model parameters adjusted from experimental MA data of single electrolyte NaCl-water system. w12 and u12 are the model parameters for the description of sucrose-water system. W2, MX , U 2, MX , V2,MX , PT E D Y10, 2,MX and Y11, 2,MX are the model parameters used to represent the interactions arising in mixtures including both non-ionic and ionic solutes. The long-range Pitzer-Debye-Hückel term is expressed by: 1 x2 ln 1 I 1x 2 I BMX g I x 2 , 4 (7) AC CE ex 4A I g PDH x x RT Ax denotes the Debye–Hückel parameter for the osmotic coefficients (Ax= 2.917) [21], ρ is the closest approach parameter (ρ =14.0292). BMX is the Pitzer’s parameter of MX.is a standard value equal to 13.0 [21]. Ix is the ionic strength ( I x 1 zi2 xi ). 2 i 1 Hu and Guo [21] concluded that the result obtained with introduction of Sucrose physical properties, in the calculation of Debye-Hückel parameters Aφ ACCEPTED MANUSCRIPT 9 and the closest approach distance for the ions ρ, presents a large deviation from experimental data. In this work, we used the density ρA and the dielectric constant D of water for estimating the Debye-Hückel parameter Ax. The function g y I x is done as: 2 1 1 y exp y , y2 (8) PT gy The differentiation of equations (6) and (7) permits to obtain the corresponding RI expressions of activity and ionic mean coefficients of different components in SC aqueous solution. The water activity coefficient is given as: 2 AX I X3 2 I X2 BMX exp I 1x 2 x I 1 x1 W1,MX x2 W2,MX 1 I 1X 2 NU ln 1 x I2 1 2 x1 U 1,MX 2 x2 U 2,MX x I2 x1 2 3 x1 V1,MX 3 x22 V2,MX MA x 2 x2 I x 1 2 x1 Y10, 2,MX x2 1 4 x1 Y11, 2,MX 4 x2 1 x1 w12 2 x1 x2 1 x1 x2 u12 , (9) D 3 I ln 2 PT E The sucrose activity coefficient is given as: 2 AX I X3 2 I X2 BMX exp I 1x 2 x I 1 x2 W2,MX x1 W1,MX 12 1 I X CE x I2 1 2 x2 U 2,MX 2 x1 U 1,MX x I2 x2 2 3 x2 V2,MX 3 x12 V1,MX AC x 2 x1 I x 1 2 x2 Y10, 2,MX x1 1 4 x2 Y11, 2,MX 4 x1 1 x2 w12 2 x1 x2 1 x2 x1 u12 w12 u12 3 I , (10) The ionic mean activity coefficient of NaCl in sucrose-water system is given as: ACCEPTED MANUSCRIPT 10 2 I 1 2 1 2 I x ln AX ln 1 I 1x 2 x 1 I 1x 2 I x BMX g I 1x 2 exp I 1x 2 1 x I 2 , (11) 1 x I x1 W1,MX x2 W2,MX 2 x I 1 x I x1 U 1,MX x2 U 2,MX x I 2 3 x I x12 V1,MX x22 V2,MX x1 x2 1 4 I x Y10, 2,MX 3 I x2 x I3 Y11, 2,MX 4. Results and discussion SC 4-1. Water activity and osmotic coefficient RI PT x1 x2 w12 2 x1 x2 u12 W1,MX The measurements of water activities for 0.5, 1.0, 2.0, 4.0 and 5.5 mol.kg-1 NU of the sucrose in the molality range of NaCl from 0.5 to 6.0 mol.kg-1 are shown MA in Table 2 and represented in Figure 1. It is noted that this behavior of decrease of aw as a function of the molality is the same that observed for the other D aqueous mixed electrolytes. PT E INSERT TABLE 2 INSERT FIGURE 1 We have determined the values of the ECA parameters of the system NaCl- CE sucrose-H2O and we suggest =0.001302 (mol.kg-1)-2, and =-0.000309 AC (mol.kg-1)-3. The standard deviation for the fit is aw=0.0005. The water activities aw calculated by employing the assigned values of and are in good agreement (0.05 percent error on the average) with experimental values (Fig. 2). The predictions of water activity of the studied system mixtures, LS II and Lin et al. (with C12=0.0018), and experimental isopiestic data [19] are compared with our results. The thermodynamic properties of NaCl(aq) were calculated from our previous data [16], and those for sucrose(aq) from data of ACCEPTED MANUSCRIPT 11 Robinson and Stokes [30]. The comparison of the experimental aw(exp) with those calculated aw(cal) with the ECA rule (Eq. 3) are very close to those evaluated by the two models in the whole molality range (Fig. 2), with average difference less than 0.003. INSERT FIGURE 2 PT The osmotic coefficients of the studied system are calculated from the RI experimental aw(exp). The calculated values at different molalities are listed in Table 2. The uncertainty on the osmotic coefficients depend of the uncertainty SC of the water activity and is estimated to be u()=0.006 however the standard NU deviation obtained from PSC model is 0.001. 4-2. Activity coefficient MA In order to determine the all unknown model parameters of Eq.6, for watersucrose-sodium chloride, the general least-squares method was used. Our D experimental previous data [16], with the Hamer and Wu data [31] relative to PT E the osmotic coefficients and ionic mean activity coefficients of single electrolyte system of NaCl-water, were used for adjustment of model CE parameters BMX , W1, MX , U 1, MX and V1, MX . Table 3 lists these parameters AC estimated with the root mean square deviation σ and σ for each type of data. The calculated parameters in this study are compared to those adjusted by Hu and Guo [21], and to those of Clegg et al. [27] estimated from experimental data of Tang et al. [32]. As expected, a good agreement is observed between our calculated values and experimental data of literature [16, 31]. The parameters w12 and u12 of Eq.9 are evaluated from experimental data of Robinson et al. [30], relative to the and of water-sucrose at 298.15 K. ACCEPTED MANUSCRIPT 12 Table 3 shows the calculated parameters with the root mean square deviation (RMSD) of and for each type of data. The parameters calculated in the present work are compared to those adjusted by Hu and Guo [21]. It appears from this table that the present work shows a good correlation of and . PT The parameters W2, MX , U 2, MX , V2,MX , Y10, 2, MX and Y11, 2, MX are required to calculate the thermodynamic properties of the system water-sucrose-NaCl at 298.15. RI These mixing model parameters are obtained by simultaneous correlation of SC experimental data of osmotic coefficient data and mean activity coefficient of NaCl in water-sucrose-NaCl mixtures at 298.15. The measured data of osmotic NU coefficient in this work and those obtained by Robinson et al.[19] from MA isopiestic vapor pressure method for the considered system are used. The data of mean activity coefficient for this system are reported by Wang et al.[20] from emf measurements in the molality range 0.006-2.0 mol.kg-1. The PT E D estimated values of these parameters are given in Table 3 with the corresponding standard deviations of the fit. The total root-mean squareddeviation (SD) between the experimental and calculated is 0.001. The activity CE coefficients of NaCl and sucrose in the ternary mixture are listed in Table 4. AC The variation of natural logarithm of mean activity coefficient for NaCl and sucrose versus square root of molality of NaCl at different fixed molalities of sucrose of 0.0, 0.5, 1.0, 2.0, 4.0 and 5.5 mol.kg-1 are shown in Figures 3 and 4, respectively. INSERT TABLE 3 INSERT TABLE 4 INSERT FIGURE 3 INSERT FIGURE 4 ACCEPTED MANUSCRIPT 13 The comparison of our mean activity coefficients of NaCl with those of the literature shows a good agreement (Fig. 5). The average difference between our results and those given by Robinson et al. [19] is only ±0.005, for those given by Wang et al. [20] is ±0.003 and for those given by Hu and Guo [21] is ±0.003. PT INSERT FIGURE 5 RI The results presented in this work allow us to deduce the aspect of different SC interactions which can occur between sodium chloride and sucrose in the ternary solution of sodium chloride-sucrose-water by interpreting the activity NU coefficient of component in the solution. The effect of the addition of different amounts of sucrose on the activity coefficient of NaCl at 298.15 K is observed MA and exhibit significant deviation at different molalities of NaCl. The contribution of sucrose to the behavior of NaCl depends on the concentration D of sodium chloride. Figure 3 shows that as the proportion of sucrose is fixed, PT E the activity coefficients of NaCl, first decreases, passes through a minimum for molalities between 1.0 and 2.3 mol.kg-1 and then increases with increasing CE molality of NaCl. But, it increases with increasing the sucrose content in the mixture when the molality of the electrolyte is fixed and lower to the 3.5 AC mol.kg-1. This trend is inversed for the molalities superior to this value, it decreases with the increase of the sucrose content in the mixture. Similar trends of the activity coefficient have been noticed for other studies [20]. The comparison of the order of the curves of of NaCl versus mNaCl at different fixed sucrose molalities shows that the curves are arranged in the following order for the molalities lower to the noted value of 3.5 mol.kg-1 of sodium chloride (the first region) in the following order : ACCEPTED MANUSCRIPT 14 (m=(5.5)> (m=4.0)> (m=2.0)> (m=1.0)> (m=0.5)> (m=0.0), but beyond this molality (the second region), the order is reversed and becomes (m=0.0)> (m=0.5)> (m=1.0)> (m=2.0)> (m=4.0)> (m=(5.5). This can be explained by the nature of the interactions that predominate in each domain of sodium chloride molalities. These two different behaviors can be PT attributed to the fact that the nature of interactions between NaCl and sucrose RI in the first region is very different to that observed in the second region for SC concentrated solutions. In the first region, the increase in the activity coefficient of NaCl may be due to NU the effect of sucrose molecules on the structure of the water around dissociated NaCl. The competition in terms of hydration between sucrose molecules and MA ions of NaCl becomes important, hence the modification of the structure of the water and causes a decrease in the hydration of salt ions in the presence of D sucrose molecules. On the other hand, the association of sodium ions by PT E sucrose molecules is less important in this case. The decrease in the degree of hydration of ions is also reported by other studies on the physico-chemical CE properties of electrolytes in the presence of sugars [33-34], which also show that the addition of sucrose decreases the number of water molecules weakly AC related in the first sphere of hydration of the sodium and chloride ions [35]. This consequence of dehydration, in the first and second spheres of hydration, allows the ions sodium and chloride to interact and form aggregates, thus this changes the properties of the solution such, the viscosity and dielectric relaxation [36], the decrease in the permittivity, the increase of mobility of the ions and the conductivity of the mixture [33]. This process leads to a decrease the interaction in the solution and, therefore, an increase of the coefficient of ACCEPTED MANUSCRIPT 15 activity of NaCl. These effects have a positive contribution to sucrose molecules that can form stable H bonds with water [37], giving rise to the phenomenon of salting out. But above 3.0 mol.kg-1 NaCl (with high molalities of NaCl and sucrose), the behavior of activity coefficient of NaCl in this concentrated region is PT significantly different from that observed in the first region. The decrease in RI the activity coefficient of NaCl with sucrose as a function of sodium chloride SC concentration when the amount of two components increases is due to other nature of interaction [38]. In the presence of high concentrations of sucrose, the NU interaction becomes more important and the activity coefficient is decreased when the concentration of NaCl increases and approaches saturation. This MA behavior is due to the effect of sucrose molecules on the structure of the water around NaCl (Fig.3) which compete with the hydrated ions until to promote the D formation of new species resulting either from the association of salt ions PT E forming ion pairs [39], and also from the decrease in hydration with the concentration [40]. These observations can be attributed to the fact that the CE interactions between NaCl and sucrose product the phenomenon of salting in. In Figure 4, the activity coefficients of sucrose in the mixture NaCl-sucrose- AC water increase with the increase of its molality in the order: (m=(5.5)> (m=4.0)> (m=2.0)> (m=1.0)> (m=0.5)> (m=0.0). We note also, that this activity coefficient varies slightly versus the molality of NaCl and has the same trend in these solutions. The behavior of the sucrose activity coefficient in aqueous solutions when the concentration of NaCl increases is not affected by the presence of the solute NaCl, and the ions Na and Cl- have no influence on the molecules of the sucrose in solution. This is due to the ACCEPTED MANUSCRIPT 16 nature of the carbonic chain of sucrose molecules; therefore the sucrose activity coefficient in mixed aqueous solutions does not appear to be affected by association or aggregation between salt ions and sucrose. The interactions that exist in this region are compensated and the variation of the degree of hydration with concentration can be neglected. Thus, there is no net change in PT activity coefficients. RI These results show that these aqueous systems are largely dominated by the SC sucrose-water interaction, whereas the sodium and chloride ions act too weakly on the molecular groups of sucrose. The sucrose-water interactions are very NU weak, and do not disturb the structure of the sucrose. It can be concluded that only the hydrogen bond of the OH groups with hydrogen dominates in the MA system and concerns only the sucrose. 4-5. Excess Gibbs energy and Gibbs energy of transfer D From obtained activity coefficients data, we have determined the excess PT E Gibbs energy of ternary system water-sucrose-sodium chloride using the following expression: CE g ex xi ln i x1 ln 1 x2 ln 2 2 xI ln , RT i1 (12) AC g ex is excess Gibbs energy per mole of particles. The excess Gibbs energy Gex for any amount of material is G ex ni g ex . The results obtained for Gex are i listed in Table 4. The standard free energy of transfer presents an important parameter because it takes into account of the interactions of ion present in the mixed aqueous solution with solvent molecules. ACCEPTED MANUSCRIPT 17 The Gibbs energy of transfer of sodium chloride GtrNaCl from water (W) to sucrose-water (W+S) mixtures is calculated using the expression [39]: f , GtrNaCl W W S RT ln NaCl 0 f NaCl (13) where υ is the number of ions into which the electrolyte dissociates, f NaCl and PT 0 f NaCl are the mole fraction activity coefficients of NaCl in ternary system RI NaCl-sucrose-H2O and binary system NaCl-H2O, respectively. Using the SC model, the calculated result of the transfer Gibbs energies of sodium chloride from water to water+sucrose mixtures are plotted in Figure 6 as a function of NU salt molality and at different molality of sucrose. It can be seen from this figure MA that for the molality of NaCl inferior to 6.0 mol.kg-1, the transfer Gibbs energies for NaCl increase positively by increasing the sucrose molality. Thus the interaction between the sucrose and sodium chloride becomes increasingly PT E D unfavorable by increasing the sucrose concentration [40]. Also, the positive increasing profiles of the transfer Gibbs energies against composition of salt show increased destabilization and decreased hydration in the mixture. The CE same trends were occurred for the transfer of some electrolytes from water to AC aqueous mixtures of other solvents [42-45]. This phenomenon can also be explained to the stronger interactions between sucrose and water. To illustrate the different electrolyte-sucrose interactions in water, on can derive the free energy parameters of pair interaction gEN (E and N are assigned, respectively, to electrolyte and non-electrolyte) between the electrolyte and sucrose in water [41, 46]. These quantities characterize the mean comportment of all the pair interactions between sucrose and different ions of given salt. ACCEPTED MANUSCRIPT 18 By applying McMillan–Mayer’s theory of solutions, the transfer Gibbs energies of transfer for NaCl from water to water+sucrose mixtures at constant temperature and pressure can be expressed as: GtrNaCl W W S 2mN g EN 6mE mN g EEN 3 2 mN2 g ENN , (14) PT where mN and mE are the molality of nonelectrolyte (sucrose) and electrolyte (NaCl), respectively. g EN , g EEN and g ENN are the pair interaction and the triplet RI interaction parameters. The data of transfer Gibbs energy of NaCl from water SC to mixture water+sucrose were used for optimization of g EN , g EEN and g ENN . At low concentrations of electrolyte and nonelectrolyte species, all triplet NU interaction terms can be neglected and the salting coefficient s can be MA determined from the pair interaction parameter g EN by using the following equation [47]: (15) D RTs 2 g EN , PT E The salting constant s is used to express the effects of salting-in and saltingout. Table 5 shows the values of pair interaction parameters, triplet interaction CE parameters and salting constant. For comparison, the interaction parameters and the salting constant values available or calculated from data in literature AC are also listed in this table. It can be seen that our estimated value of salting constant s for sodium chloride in presence of sucrose is positive and is in close agreement with that reported by Wang et al.[20] and Robinson et al.[19]. The positive value of the interaction parameter g EN , representing the interaction of the pair NaCl-sucrose, indicates a repulsive interaction between ions and sucrose. It can be explained by the fact that the sucrose is salted-out ACCEPTED MANUSCRIPT 19 by adding NaCl. These results are qualitatively in agreement with those reported in literature [48]. The interactions of salt with sucrose appear to be induced by the average number of sucrose molecules in OH group, which remain one of the most important factors in this mixture. At high molalities of both components (NaCl and sucrose) the phenomenon of salting-in occurs for PT the studied system [19]. The salting constants of the NaCl-sucrose-water RI calculated from Eq.(15) is 0.1148 kg.mol-1 ( Table 5). Thus, this positive value SC corresponds also to extensive to the salting-out of sucrose by NaCl. INSERT TABLE 5 NU 4-6. Solubility prediction The Sodium Chloride dissolution in aqueous solutions is given as: MA k sp mNa Na mCl Cl m 2 2 NaCl , (16) D NaCl is the ionic mean activity coefficient of NaCl, mNaCl is its molality PT E and ksp its solubility product set to value of 38.19 reported by Pitzer et al. [49]. The calculated and experimental solubility values of sodium chloride in CE water-sucrose system at 298.15 K are shown at different sucrose molality in Table 6. The predicted solubilities in this work are compared to those AC calculated by Hu and Guo [21] with a good concordance for all the studied molalities of sucrose. The relative error is estimated to be less than 0.46%, while it is 0.61% for the values given by Hu and Guo [21]. The effect of NaCl on the solubility of sucrose in water has reported in literature [50]. The results obtained in this work show that NaCl increase the solubility of sucrose in water. Our results confirm that the interactions between NaCl and sucrose in dilute aqueous solutions are different from those in concentrated solutions. ACCEPTED MANUSCRIPT 20 INSERT TABLE 6 5. Conclusions We have measured the thermo-physical properties as the water activity and osmotic coefficients for the ternary system NaCl-sucrose-H2O by hygrometric method at 298.15 K. The obtained results are compared with experimental data PT from isopiestic method and those calculated by three thermodynamic models RI (Lin et al, LSII and ECA) with a good agreement. Furthermore, the osmotic SC coefficients of NaCl-sucrose-H2O were fitted by PSC equation for mixtures to obtain the four parameters. Comparing the recalculated osmotic coefficients NU and the experimental ones, we note that the relative deviation is acceptable in the ionic strength range of less than 2.5 mol·kg−1, while it becomes larger if the MA ionic strength increases. Therefore, mixing parameters can be ignored when we calculate the osmotic coefficients at low ionic strengths, whereas they cannot D be omitted at high ionic strengths. PT E The activity coefficients of NaCl and sucrose in the NaCl-sucrose-water are also calculated using the PSC model using our obtained interaction parameters. CE The results indicate that the presence of the long chain of carbon and OH groups of sucrose affect the activity coefficient of NaCl(aq) in the mixture. AC This thermodynamic behavior can be explained by the destructuring effects of sucrose on the water structure around the ions of electrolyte. These results can be also justified by an increase of the activity coefficient of NaCl, which is not accompanied by any increase in the hydrated radii of sucrose molecules. It is also noted that the behavior of activity coefficient of sucrose vary slightly versus the concentration of NaCl. ACCEPTED MANUSCRIPT 21 The Gibbs excess energy Gex of ternary system water-sucrose-sodium chloride and the standard free energy of transfer GtrNaCl of sodium chloride from water to sucrose-water mixtures are also determined from the obtained results of osmotic and activity coefficients. It has been shown that the standard free PT energy of transfer GtrNaCl increases linearly with increasing mole fraction of sucrose. The experimental results are discussed in terms of solute-solvent and RI solute-solute interactions in water-sucrose-NaCl systems. SC The predicted solubilities are also evaluated and compared to those given in literature with a good concordance for all the studied molalities of sucrose with NU a relative error less than 0.46%. The solubility of sucrose in water increases MA with NaCl. Our results confirm that the interactions between NaCl and sucrose AC CE PT E D in dilute aqueous solutions are different from those in concentrated solutions. ACCEPTED MANUSCRIPT 22 List of symbols a Activity Ax Debye–Hückel parameter BMX Salt parameter D Droplet diameter Excess Gibbs energy per mole of particles g EN Pair interaction for transfer Gibbs energy g EEN and g ENN Triplet interaction parameters for transfer Gibbs energy Gex PT gex RI Total excess Gibbs energy GtrNaCl SC Gibbs energy of transfer of sodium chloride K Ratio of droplets ks Solubility product Molality, mol.kg-1 H2O NU m n mole number Gas constant, J mol-1 K-1 SDY Standard deviation of Y= 1 N Y N i exp Yi cal 2 i D MA R T Absolute temperature, K mole fraction u(p) PT E x CE w12 and u12 uncertainty of parameter p Neutral –Neutral Model parameters W j , MX , U j , MX and V j , MX Short-range parameters between molecule j and salt MX Short-range ternary parameters molecule-molecule-Salt MX AC Y10, 2, MX and Y11, 2, MX Greek letters Constant s Salting constant ρ Closest approach distance , ECA parameters Osmotic coefficient Activity coefficient ACCEPTED MANUSCRIPT 23 aw Uncertainty of measured water activity Uncertainty of measured osmotic coefficient calc Calculated exp Experimental E Electrolyte (NaCl) ref Reference Indicate solution N Nonelectrolyte (Sucrose) Pitzer-Simonson-Clegg PSC Pitzer-Debye-Hückel SC PDH Excess CE PT E D MA Ex NU Superscripts AC RI i, 1, 2 PT Subscripts ACCEPTED MANUSCRIPT 24 REFERENCES [1] H.N. Harned, B.B. Owen, The physical Chemistry of Electrolyte Solutions, Reinhold Publishing Corporation, New York. 1958. [2] M.F. Zhou, S.H. Sang, J.J. Zhang, J.X. Hu, S.Y. Zhong, Studies on Mean Activity Coefficients of NaBr in NaBr–SrBr2–H2O Ternary System at 298.15 K by EMF Method, J. Chem. Eng. Data 59 (2014) 3779-3784. PT https://doi.org/10.1021/je500655k [3] H. Ashassi-Sorkhabi, A. Kazempour, Application of Pitzer and six local RI composition models to correlate the mean ionic activity coefficients of SC aqueous 1-butyl-3-methylimidazolium bromide ionic liquid solutions obtained by EMF measurements, J. Chem. Thermodyn. 110 (2017) 71-78. NU https://doi.org/10.1016/j.jct.2017.02.015 [4] R.A. Robinson, R. H. Stokes, Electrolyte Solutions, Butterworth Scientific Publications, London. 1955. MA [5] J.A. Rard, R.F. Platford, Experimental Methods: Isopiestic. In Activity Coefficients in Electrolyte Solutions, 2nd ed. Pitzer, K. S., Ed.; CRC Press, Boca Raton, FL, 1991, pp 209−277. D [6] T. Ivanović, D.Ž. Popović, J.A. Rard, S.R. Grujić, Z.P. Miladinović, J. PT E Miladinović, Isopiestic determination of the osmotic and activity coefficients of at T = 298.15 K, J. the {yMg(NO3)2 + (1 − y)MgSO4}(aq) Chem. Thermodyn.113 (2017) system 91-103. CE https://doi.org/10.1016/j.jct.2017.05.006 [7] M.T. Zafarani-Moattar, H. Shekaari, E. Mazaher, Isopiestic determination AC of water activity and vapour pressure for ternary (ionic liquid, 1-hexyl-4methyl pyridinium bromide + D-fructose or sucrose + water) systems and corresponding binary ionic liquid solutions at 298.15 K J. Chem. Thermodyn. 116 (2018) 42–49. https://doi.org/10.1016/j.jct.2017.08.023 [8] N.A. Gokcen, Report of Investigations, U. S. Dept. of the Interior, Bureau of Mines, 1979. [9] S. El Golli, G. Arnaud, J. Bricard, C. Treiner, Evaporation of volatile solvent from saline multi-component droplets carried in a stream of air, ACCEPTED MANUSCRIPT 25 J. Aerosol Sci. 8 (1977) 39-54. https://doi.org/10.1016/0021- 8502(77)90061-1 [10] M. Michielsen, G. Y. Loix, J. Gilbert,; P. J. Cleas, Masse spécifique et tension de vapeur de systèmes constitues d’électrolyte et d’eau à toutes compositions, J. Chim. Phys. 79 (1982) 247-252. https://doi.org/10.1051/jcp/1982790247 [11] M. El Guendouzi, A. Dinane, Determination of water activities, osmotic Chem. Thermodyn. 32 https://doi.org/10.1006/jcht.1999.0574 (2000) 297-313. RI J. PT and activity coefficients in aqueous solutions using the hygrometric method, SC [12] M. El Guendouzi,; A. Dinane, A. Mounir, Water activities, osmotic and activity coefficients in aqueous chloride solutions at T = 298.15 K by the NU hygrometric method, J. Chem. Thermodyn. 33 (2001) 1059-1072. https://doi.org/10.1006/jcht.2000.0815 [13] M. El Guendouzi, A. Mounir, A. Dinane, Water activity, osmotic and MA activity coefficients of aqueous solutions of Li2SO4, Na2SO4, K2SO4, (NH4)2SO4, MgSO4, MnSO4, NiSO4, CuSO4, and ZnSO4 at T=298.15 K, D J. Chem. Thermodyn. 35 (2003) 209-220. https://doi.org/10.1016/S00219614(02)00315-4 PT E [14] A. Dinane, M. El Guendouzi, A. Mounir, Hygrometric study of thermodynamic properties of NaCl-KCl-H2O at 298.15 K. J. Chem. Thermodyn. 34 (2002) 1-19. https://doi.org/10.1006/jcht.2001.0845 CE [15] A. Dinane, A. Mounir, Water activities, osmotic and activity coefficients in aqueous mixtures of sodium and magnesium chlorides at 298.15 K by the AC hygrometric method, Fluid Phase Equilib. 206 (2003)13-25. https://doi.org/10.1016/S0378-3812(02)00300-X [16] A. Mounir, M. El Guendouzi, A. Dinane, Hygrometric Determination of Water Activities, Osmotic and Activity Coefficients, and Excess Gibbs Energy of the System MgSO4–K2SO4–H2O, J. Solution Chem. 31 (2002) 793-799. https://doi.org/10.1023/A:1021341226708 [17] A. Mounir, M. El Guendouzi, A. Dinane, Thermodynamic properties of {(NH4)2SO4(aq) + Li2SO4(aq)}and {(NH4)2SO4(aq) + Na2SO4(aq)} at ACCEPTED MANUSCRIPT 26 temperature of 298.15 K, J. Chem. Thermodyn. 34 (2002) 1329-1339. https://doi.org/10.1006/jcht.2002.0984 [18] A. Mounir, A. Dinane, H. kHajmi, B. Mounir, A. Tounsi Thermodynamic Properties of Aqueous-Mixed Electrolyte Solutions of {y Na2SO4 + (1 – y) K2SO4}(aq), J. Chem. Eng. Data, 63 (2018) 3545–3550. https://doi.org/10.1021/acs.jced.8b00418 [19] R.A. Robinson, R.H. Stokes, and K.N. Marsh, Activity coefficients in the PT ternary system: water + sucrose + sodium chloride, J. Chem. Thermodyn. 2 (1970) 745-750. https://doi.org/10.1016/0021-9614(70)90050-9 RI [20] J.J. Wang, W.B. Liu, J. Fan; and J. Lu, Mean Activity Coefficients of Soc. Faraday Trans., SC NaCl in Glucose-Water and Sucrose-Water Mixtures at 298.15 K. J. Chem. 90 (21) (1994) 43281-3285. NU https://doi.org/10.1039/FT9949003281 [21] Y. Hu and T. Guo, Thermodynamics of electrolytes in aqueous systems containing both ionic and nonionic solutes. Application of the Pitzer– MA Simonson–Clegg equations to activity coefficients and solubilities of 1 : 1 electrolytes in four ternary systems at 298.15 K electrolyte–non-electrolyte– H2O, Chem. Phys., 1 (1999) 3303-3308. https://doi.org/10.1039/A900232D D [22] J.F. Comesaňa, A. Correa and A.M. Sereno, Water activity at 35 °C in PT E sugar + water and sugar + sodium chloride + water systems, International Journal of Food Science and Technology, 36 (2001) 655–661. https://doi.org/10.1046/j.1365-2621.2001.00501.x CE [23] D.Q. Lin, Z.Q. Zhu, L.H. Mei, L.R. Yang, Isopiestic Determination of the Water Activities of Poly(ethyleneglicol) + Salt + Water Systems at 25 °C. J. AC Chem. Eng. Data 41 (1996) 1040-1042. https://doi.org/ 10.1021/je960065a [24] E.Yu. Shalaev, F. Franks, Equilibrium phase diagram of the watersucrose-NaCl system, Thermochimica Acta https://doi.org/10.1016/0040-6031(94)02180-V 255 (1995) 49-61. ACCEPTED MANUSCRIPT 27 [25] K.S. Pitzer, J. M. Simonson, Thermodynamics of Multicomponent, Miscible, Ionic Systems: Theory and Equations, J. Phys. Chem. 90 (1986) 3005-3009. https://doi.org/10.1021/j100404a042 [26] S.L. Clegg, K.S. Pitzer, Thermodynamics of multicomponent, miscible, ionic solutions: generalized equations for symmetrical electrolytes J. Phys. Chem. 96 (1992) 3513–3520. https://doi.org/ 10.1021/j100187a061 [27] S.L. Clegg, K.S. Pitzer, P. Brimblecombe, Thermodynamics of miscible, ionic solutions. 2. Mixtures including PT multicomponent, https://doi.org/doi: 10.1021/j100202a074 RI unsymmetrical electrolytes. J. Phys. Chem. 96, 9470–9479 (1992). SC [28] M.H. Lietzke, R.W. Stoughton, Simple empirical equation for the prediction of the activity coefficients value of each component in aqueous NU electrolyte mixtures containing a common ion. J. Solution Chem. 1 (1972) 299-308. https://doi.org/10.1007/BF00715989 [29] M.H. Lietzke, R.W. Stoughton, A simple method for predicting the electrolyte. MA osmotic coefficient of aqueous solutions containing more than one J. Inorg. Nucl. Chem. 36 (1974) 1315-1317. D https://doi.org/10.1016/0022-1902(74)80070-9 [30] R.A. Robinson, R.H. Stokes, Activity coefficients in aqueous solutions of PT E sucrose, mannitol and their mixtures at 25°, J. Phys. Chem. 65 ( 1961) 1954–1958. https://doi.org/10.1021/j100828a010 [31] W.J. Hamer and Y.C. Wu, Osmotic Coefficients and Mean Activity CE Coefficients of Uni-univalent Electrolytes in Water at 25°C, J. Phys. Chem. Ref. Data, 1(1972) 1047- 1099. https://doi.org/10.1063/1.3253108 AC [32] I.N. Tang, H.R. Munkelwitz, N. Wang, Water Activity Measurements with Single Suspended droplets: The NaCI-H2O and KCI-H2O Systems, J. Colloid Interface Sci., 114 (1986) 409-415. https://doi.org/10.1016/00219797(86)90426-1 [33] A.C.F. Ribeiro, M. A. Esteso, V.M.M. Lobo, A.J.M. Valente, S.M.N. Simões, A.J.F.N. Sobral, H.D. Burrows, Interactions of copper (II) chloride with sucrose, glucose, and fructose in aqueous solutions, J. Mol. Structure, 826 (2007) 113–119, https://doi.org/10.1016/j.molstruc.2006.04.035 [34] V. Martorana, L. Fata, D. Bulone, P.L. San Biagio, Potential of mean ACCEPTED MANUSCRIPT 28 force between two ions in a sucrose rich aqueous solution Chem. Phys. Lett. 329 (2000) 221-227. https://doi.org/10.1016/S0009-2614(00)01028-9 [35] G.W. Neilson, J. E. Enderby, The Coordination of Metal Aquaions, Adv. Inorg. Chem. 34 (1989) 195-218. https://doi.org/10.1016/S08988838(08)60017-3 [36] T. Matsuoka, T. Okada, K. Murai, S. Koda, H. Nomura , Dynamics and hydration of trehalose and maltose in concentrated solutions, Journal of PT Molecular Liquids 98–99 (2002) 319-329. https://doi.org/10.1016/S0167- RI 7322(01)00337-3 [37] S.L. Lee, P.G. Debenedetti, J.R. Errington, A computational study of SC hydration, solution structure, and dynamics in dilute carbohydrate solutions, J. Chem. Phys. 122 (2005) 204511. http://dx.doi.org/10.1063/1.1917745 NU [38] Jean M. Stokes, and R.H. Stokes, The Conductances of Some Simple Electrolytes in Aqueous Sucrose Solutions at 25°.J. Phys. Chem. 60 (1956) MA 217-220. https://doi.org/10.1021/j150536a018 [39] T. Arakawa, S.N. Timasheff, The stabilization of proteins by osmolytes, Biophys. J. 47 (1985) 411. https://doi.org/10.1016/S0006-3495(85)83932-1 D [40] Ana C.F. Ribeiro, Miguel A. Esteso, Victor M. M. Lobo, Artur J. M. PT E Valente, Susana M. N. Simões, Abilio J. F. N. Sobral, and Hugh D. Burrows, Diffusion Coefficients of Copper Chloride in Aqueous Solutions at 298.15 K and 310.15 K, J. Chem. Eng. Data, 50 (2005) 1986-1990. CE https://doi.org/10.1021/je050220y [41] D.H. Dagade, K.J. Patil, Thermodynamic studies for aqueous solutions AC involving 18-crown-6 and alkali bromides at 298.15 K, Fluid Phase Equilib. 231 (2005) 44–52. https://doi.org/10.1016/j.fluid.2004.12.011 [42] J.J. Wang, W.B. Lui, T.Ch. Bai and J.S. Lu, Standard Gibbs Energies of Transfer of some Electrolytes from Water to Aqueous Sucrose Solutions at 298.15 K, J. Chem. Soc. Faradays Trans., 89 (1993) 1741-1744. https://doi.org/10.1039/FT9938901741 [43] H. Talukdar, S. Rudra and K.K. Kundu, Single-ion transfer energetics of some ions using tetraphenylarsonium tetraphenylborate reference electrolyte ACCEPTED MANUSCRIPT 29 assumption in aqueous mixtures of urea and glycerol. Can. J. Chem., 67 (1989) 321-329. https://doi.org/10.1139/v89-053 [44] J.P. Chatterjee and I.N. Basumallick, Thermodynamics of transfer of electrolytes and ions from water to aqueous solutions of polyhydroxy compounds, J. Chem. Soc. Faraday Trans., 86 (1990) 3107. https://doi.org/10.1039/FT9908603107 [45] J.J. Wang, L. Zeng ‘, W.B Liu and J. Lu, A thermodynamic study of the PT ternary system water + glucose + electrolyte at 298.15 K, Thermochimica Acta, 224 (1993) 261-269. https://doi.org/10.1016/0040-6031(93)80176-B RI [46] G. Perron, D. Joly, J.E. Desnoyers, L. Avedikian and J.P. Morel, SC Thermodynamics of the salting effect; free energies, enthalpies, entropies, heat capacities, and volumes of the ternary systems electrolyte–alcohol– NU water at 25 °C. Can. J. Chem., 56 (1978) 552. https://doi.org/10.1139/v78089 [47] J.P. Morel, C. Lhermet, N.M. Desrosiers, Interactions between cations and MA sugars. Part 4. Free energy of interaction of the calcium ion with some aldopentoses and aldohexoses in water at 298.15 K, J. Chem. Sot. Faraday [48] D Trans. 184 (1988) 2567- 2571. https://doi.org/10.1039/F19888402567 F. Hernández-Luis, E. Amado-González, M.A. Esteso, Activity PT E coefficients of mixtures of threalose — NaCl and maltodextrins -NaCl AT 298.15K by EMF, Carbohydrate Research 338 (2003) 1415- 1424. https://doi.org/10.1016/S0008-6215(03)00177-0 CE [49] K.S. Pitzer, P. Christopher, R.H. Busey, Thermodynamic Properties of Aqueous Sodium Chloride", J. Phys. Chem. Ref. Data, 13 (1984) 1-102. AC https://doi.org/10.1063/1.555709 [50] F.H.C. Kelly, Phase equilibria in sugar solutions. I. Ternary systems of water-sucrose-inorganic salts, J. Appl. Chem., 4 (1954) 401-404. https://doi.org/10.1002/jctb.5010040801 ACCEPTED MANUSCRIPT 30 FIGURE CAPTIONS Fig.1. Water activity (aw) of NaCl-sucrose(aq) against molality of NaCl (mNaCl) at different constant molalities of sucrose (msucrose): , 0.5 mol.kg-1; , 1 mol.kg-1; , 2 mol.kg-1; , 4 mol.kg-1; , 5.5 mol.kg-1. PT Fig.2. Water activity (aw) of NaCl-sucrose(aq) against molality of NaCl (mNaCl) at different constant molalities of sucrose (msucrose): (a), 0.5 mol.kg-1; (b), 1 RI mol.kg-1; (c), 2 mol.kg-1; (d), 4 mol.kg-1; (e), 5.5 mol.kg-1; and compared to SC those calculated by different models. Fig.3. Natural logarithm of mean activity coefficient for NaCl (ln (NaCl)) NU versus square root of molality of NaCl (m1/2) at different constant molalities of sucrose (msucrose): , 0.0 mol.kg-1 [16]; , 0.5 mol.kg-1; , 1 mol.kg-1; , 2 MA mol.kg-1; , 4 mol.kg-1; , 5.5 mol.kg-1. Fig.4. Natural logarithm of activity coefficient for sucrose (ln (sucrose)) D versus square root of molality of NaCl (m1/2) at different constant molalities of PT E sucrose (msucrose): , 0.0 mol.kg-1 [29]; , 0.5 mol.kg-1; , 1 mol.kg-1; , 2 mol.kg-1; , 4 mol.kg-1; , 5.5 mol.kg-1. CE Fig.5. Deviations of the mean activity coefficients ( ) of NaCl (aq) against total molality of NaCl-sucrose-H2O (mtot). •, difference between our results AC and those given by Robinson et al. [19]; Δ, Wang et al. [20]; , Hu and Guo, [21]. Fig.6. Transfer Gibbs energy of NaCl ( GtrNaCl ) from water to water-sucrose mixtures as function of molality of sucrose (msucrose) at different constant molality of NaCl (mNaCl): , 0.5 mol.kg-1; , 1 mol.kg-1; , 2 mol.kg-1; , 4 mol.kg-1; , 5.5 mol.kg-1. ACCEPTED MANUSCRIPT 31 Legends of Tables: Table 1. Descriptions of the used Chemicals. PT Table 2. Water activities (aw) and osmotic coefficients (of NaCl-sucroseH2O for 0.5, 1, 2, 4 and 5.5 mol.kg-1 of the sucrose (mSucrose) in the molality range of NaCl (mNaCl) from 0.5 to 6.0 mol.kg-1 at the temperature 298.15 K and P=0.1 MPa. Table 3. Model Parameters for system NaCl-H2O, sucrose-H2O and Mixing model parameters for system NaCl-sucrose-H2O at 298K and P=0.1 MPa. SC RI Table 4. Mean activity coefficients of NaCl ( NaCl), activity coefficients of sucrose ( sucrose) and excess Gibbs energy (Gex (J.mol-1)) of NaCl-sucrose(aq) at the temperature 298.15 K and P=0.1 MPa. NU Table 5. Interaction parameters of Gibbs energies of transfer of NaCl from water to mixture water+sucrose and salting constants ηs at 298.15 K. MA Table 6. Solubility of NaCl (in mol.kg-1) in the ternary system NaCl-sucrose- AC CE PT E D H2O at 298.15 K and P=0.1 MPa. ACCEPTED MANUSCRIPT 32 Table 1. Descriptions of the used Chemicals. Form Source Fraction Purity NaCl Anhydrous Fluka ≥ 0.995 LiCl Anhydrous Merck ≥ 0.999 Sucrose Anhydrous Panreac ≥ 0.990 AC CE PT E D MA NU SC RI PT Compound ACCEPTED MANUSCRIPT 33 Table 2. Water activities (aw) and osmotic coefficients () of NaCl-sucrose-H2O for 0.5, 1, 2, 4 and 5.5 rnol.kg-1 of the sucrose (mSucrose) in the molality range of NaCl (mNaCl) from 0.5 to 6.0 mol.kg-1 at the temperature 298.15 K and P=0.1 MPa. m Sucrose m NaCl aw m Sucrose m NaCl aw exp cal exp cal 0.976 4.00 0.50 0.891 1.279 1.277 0.972 4.00 1.00 0.876 1.230 1.228 0.940 0.976 0.985 0.984 4.00 1.50 0.860 1.198 1.196 2.00 0.922 1.000 1.002 4.00 2.00 0.844 1.177 1.174 0.50 2.50 0.904 1.023 1.024 4.00 2.50 0.828 1.161 1.160 0.50 3.00 0.884 1.049 1.050 4.00 3.00 0.813 1.152 1.151 0.50 3.50 0.865 1.078 1.078 4.00 3.50 0.797 1.146 1.146 0.50 4.00 0.844 1.108 1.108 4.00 4.00 0.781 1.145 1.145 0.50 4.50 0.823 1.140 1.140 4.00 4.50 0.764 1.147 1.147 0.748a 1.151 1.151 0.732a 1.156 1.158 0.715a 1.166 1.167 0.50 0.50 0.850 1.00 1.00 0.835 1.392 1.335 1.392 1.50 1.50 0.821 2.00 2.00 0.806 2.50 2.50 0.792 1.291 1.288 1.257 1.256 1.232 1.231 3.00 3.00 0.778 3.50 3.50 0.763 4.00 4.00 0.750a 1.211 1.212 1.199 1.197 1.185 1.186 1.179 1.179 1.171 1.174 1.170 1.172 1.171 1.173 0.9739 0.50 1.00 0.9570 0.50 1.50 0.50 0.50 0.50 5.50 0.779 1.207 1.207 4.00 5.00 5.50 0.50 6.00 0.756 1.242 1.243 4.00 6.00 1.00 0.50 0.50 0.9638 1.023 1.025 5.50 1.00 1.00 1.00 0.947 1.008 1.009 5.50 1.00 1.50 1.50 0.93 1.007 1.012 5.50 1.00 2.00 2.00 0.913 1.010 1.023 5.50 SC 1.173 4.00 NU 1.173 MA 0.801 2.50 2.50 0.895 1.026 1.038 5.50 1.00 3.00 3.00 0.876 1.050 1.058 5.50 1.00 3.50 3.50 0.857 1.071 1.080 5.50 1.00 4.00 4.00 0.837 1.097 1.105 5.50 1.00 4.50 1.00 5.00 1.00 1.129 1.131 5.50 5.00 0.794 1.164 1.160 5.50 5.50 5.50 0.772 1.197 1.189 5.50 1.00 6.00 6.00 0.748a 1.240 1.221 5.50 6.00 6.00 2.00 0.50 0.942 1.115 1.114 2.00 1.00 0.925 1.082 1.083 2.00 1.50 0.908 1.071 1.072 2.00 0.891 1.071 1.070 2.00 2.50 0.873 1.076 1.074 3.00 0.855 1.085 1.082 3.50 0.837 1.097 1.094 4.00 0.818 1.113 1.109 4.50 0.800 1.126 1.126 5.00 0.780 1.147 1.145 5.50 0.761a 1.167 1.167 6.00 0.741a 1.190 1.189 PT E 4.50 0.816 4.50 4.50 0.735a 5.00 5.00 0.721a 5.50 5.50 0.706a CE 1.00 D 5.00 RI 0.50 PT 0.979 0.50 AC 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 a The 0.691a 1.332 reference solution is Lithium Chloride, otherwise it is Sodium Chloride. In superscript, exp: from experimental data, cal: calculated by PSC model Standard uncertainty of molality is u(m) = 0.01 mol.kg-1, temperature is u(T) = 0.02 K, and pressure is u(P) = 102 Pa. The average uncertainty of water activity is u(aw) = 0.0015, and for the osmotic coefficient ϕ is u(ϕ) = 0.006. ACCEPTED MANUSCRIPT 34 Table 3: Model Parameters for system NaCl-H2O, sucrose-H2O and mixing model parameters for system NaCl-sucrose-H2O at 298K and P=0.1 MPa. NaCl-H2O This work Hu and Guo[21] Clegg et al.[25,26] Sucrose-H2O This work Hu and Guo[21] NaCl-Sucrose-H2O This work Hu and Guo[21] mmax(mol.kg-1) 6.00 6.00 BMX 10.2650 11.9825 16.2622 mmax (mol.kg-1) W1N 6.00 -11.0138 6.00 -5.8444 Na UNMX 60 11.776 3.39 U1MX -11.7970 -9.2361 -6.8641 U1N 1.7533 -0.2250 VNMX 3.29 -30.71 V1MX 4.1495 2.4578 1.0289 W1MX -9.3975 -8.3877 -7.4364 WNMX -26.08 -12.50 Y0MNMX 12.616 1.02 a SD*104 3.99 5.35 64.42 SD*102 1.2124 0.9130 Y1MNMX -353.42 -336.06 AC CE PT E D MA NU SC RI PT The number of data points (This work, Robinson et al. [19] data and Wang et al. [20] data) The SD values are standard deviation of the fit. SDγ*104 2.99 5.35 183.10 SDγ *102 2.0183 7.7966 SD*103 4.384 - ACCEPTED MANUSCRIPT 35 Table 4. Mean activity coefficients of NaCl ( NaCl), activity coefficients of sucrose ( ex excess Gibbs energy (G a b γSucrosea γSucroseb γSucrosec 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00 NaCl 0.696 0.670 0.668 0.678 0.695 0.719 0.749 0.783 0.823 0.867 0.917 0.971 1.144 1.188 1.229 1.264 1.292 1.310 1.318 1.315 1.302 1.278 1.245 1.204 1.156 1.200 1.241 1.277 1.306 1.327 1.338 1.340 1.330 1.311 1.282 1.245 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00 0.709 0.681 0.678 0.685 0.700 0.721 0.748 0.779 0.814 0.855 0.900 0.950 0.709 0.681 0.678 0.686 0.701 0.723 0.750 0.782 0.818 0.859 0.905 0.955 1.249 1.292 1.332 1.366 1.391 1.408 1.415 1.411 1.396 1.371 1.336 1.293 1.278 1.322 1.363 1.398 1.426 1.445 1.454 1.453 1.441 1.418 1.386 1.346 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00 0.731 0.701 0.694 0.699 0.710 0.726 0.747 0.773 0.802 0.836 0.875 0.917 1.487 1.525 1.561 1.590 1.612 1.625 1.627 1.619 1.601 1.572 1.534 1.487 Gex b - -589.50 -1440.35 -2278.46 -3046.77 -3715.64 -4266.44 -4686.33 -4965.96 -5098.39 -5078.39 -4902.07 -4566.60 -581.56 -1431.37 -2268.90 -3036.61 -3704.24 -4252.68 -4668.82 -4943.31 -5069.38 -5042.13 -4858.14 -4515.09 1.273 1.349 1.393 1.402 1.374 1.309 -332.02 -1120.28 -1902.07 -2621.85 -3250.98 -3771.40 -4170.51 -4438.97 -4569.67 -4557.08 -4396.91 -4085.84 -303.37 -1091.48 -1872.82 -2591.46 -3218.20 -3734.55 -4127.73 -4388.43 -4509.75 -4486.55 -4315.01 -3992.40 1.548 1.591 1.630 1.663 1.687 1.702 1.706 1.698 1.680 1.650 1.611 1.562 1.519 1.590 1.624 1.620 1.579 1.498 538.01 -143.81 -829.50 -1466.46 -2028.03 -2497.33 -2862.35 -3113.92 -3244.73 -3248.81 -3121.23 -2857.92 645.73 -34.71 -718.62 -1353.01 -1910.58 -2374.00 -2731.07 -2972.60 -3091.50 -3082.15 -2940.11 -2661.87 RI SC NU PT Gex a 0.758 0.725 0.715 0.714 0.719 0.728 0.741 0.758 0.778 0.801 0.828 0.859 0.765 0.730 0.719 0.717 0.722 0.731 0.744 0.761 0.781 0.805 0.832 0.863 2.083 2.105 2.125 2.140 2.148 2.148 2.139 2.119 2.090 2.051 2.002 1.944 2.202 2.238 2.268 2.291 2.303 2.304 2.293 2.270 2.235 2.188 2.130 2.063 2.170 2.221 2.231 2.195 2.111 1.993 3665.13 3126.76 2571.50 2046.43 1574.44 1169.88 843.23 602.93 456.15 409.20 467.71 636.71 4019.31 3498.16 2955.58 2439.90 1975.32 1577.21 1256.79 1022.95 883.05 843.38 909.38 1085.77 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00 0.765 0.731 0.719 0.716 0.718 0.723 0.732 0.743 0.758 0.775 0.796 0.820 0.781 0.743 0.728 0.722 0.722 0.726 0.734 0.744 0.758 0.775 0.795 0.819 2.654 2.656 2.658 2.655 2.648 2.633 2.609 2.577 2.535 2.485 2.425 2.357 2.797 2.823 2.842 2.852 2.851 2.838 2.811 2.773 2.721 2.658 2.583 2.499 - 7185.38 6699.72 6192.90 5708.31 5266.10 4878.68 4555.18 4303.22 4129.52 4040.29 4041.25 4137.78 7742.11 7298.05 6820.97 6356.52 5927.09 5546.92 5226.61 4974.82 4799.01 4705.83 4701.27 4790.74 MA 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00 PT E 0.731 0.701 0.695 0.700 0.711 0.729 0.751 0.777 0.807 0.842 0.881 0.924 CE AC 5.50 5.50 5.50 5.50 5.50 5.50 5.50 5.50 5.50 5.50 5.50 5.50 and D mNaCl sucrose) of NaCl-sucrose(aq) at the temperature 298.15 K and P=0.1 MPa. NaCl 0.696 0.669 0.668 0.677 0.695 0.718 0.747 0.781 0.820 0.864 0.913 0.968 sucorse 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 a (J.mol-1)) This work, breference [21], c reference [19]. ACCEPTED MANUSCRIPT 36 Table 5 : Interaction parameters of Gibbs energies of transfer of NaCl from water to mixture water+sucrose and salting constants ηs at 298.15 K. gEN/J.kg.mol-2 71.15 75.25 72.00 65.75 gEEN/J.kg.mol-3 -3.579 -3.739 --- gENN/J.kg.mol-3 -0.7491 -0.8317 --- AC CE PT E D MA NU SC RI PT This work Hu et al.[21] Wang[20] RSM[19,20] ηs 0.1148 0.1214 0.1160 0.1000 ACCEPTED MANUSCRIPT 37 Table 6. Solubility of NaCl (in mol.kg-1) in the ternary system NaCl- sucrose- H2O at 298.15 K and P=0.1 MPa. 0.0000 0.5800 1.1036 1.9932 2.3400 3.0800 4.0620 5.1286 5.4749 6.7300 this work expa RAD% This work RAD% Ref. [21] 6.1601 6.2441 6.3216 6.4572 6.5114 6.6297 6.7924 6.9770 7.0387 7.2695 6.1470 6.2300 6.3050 6.4530 6.5400 6.7900 6.7820 6.9910 7.0460 7.3500 0.21 0.23 0.26 0.07 -0.44 -2.36 0.15 0.20 0.10 1.10 0.0000 -0.1605 -0.2379 -0.5269 -1.0550 -2.9308 -0.2802 -0.3147 -0.0852 -0.4762 PT msucorse AC CE PT E D MA NU SC RI The experimental values were taken from ref. [21]. ACCEPTED MANUSCRIPT SC RI PT 38 Fig.1. Water activity (aw) of NaCl-sucrose(aq) against molality of NaCl (mNaCl) NU at different constant molalities of sucrose (msucrose): , 0.5 mol.kg-1; , 1.0 AC CE PT E D MA mol.kg-1; , 2.0 mol.kg-1; , 4.0 mol.kg-1; , 5.5 mol.kg-1. ACCEPTED MANUSCRIPT AC CE PT E D MA NU SC (a) RI PT 39 (b) ACCEPTED MANUSCRIPT AC CE PT E D MA NU SC (c) RI PT 40 (d) ACCEPTED MANUSCRIPT SC (e) RI PT 41 Fig.2. Water activity (aw) of NaCl-sucrose(aq) against molality of NaCl (mNaCl) NU at different constant molalities of sucrose (msucrose): (a), 0.5 mol.kg-1; (b), 1.0 mol.kg-1; (c), 2.0 mol.kg-1; (d), 4.0 mol.kg-1; (e), 5.5 mol.kg-1; and compared to AC CE PT E D MA those calculated by different models. ACCEPTED MANUSCRIPT SC RI PT 42 Fig.3. Natural logarithm of mean activity coefficient for NaCl (ln (NaCl)) NU versus square root of molality of NaCl (m1/2) at different constant molalities of sucrose (msucrose): , 0.0 mol.kg-1 [16]; , 0.5 mol.kg-1; , 1.0 mol.kg-1; , 2.0 AC CE PT E D MA mol.kg-1; , 4.0 mol.kg-1; , 5.5 mol.kg-1. ACCEPTED MANUSCRIPT RI PT 43 SC Fig.4. Natural logarithm of activity coefficient for sucrose (ln (sucrose)) versus square root of molality of NaCl (m1/2) at different constant molalities of NU sucrose (msucrose): , 0.0 mol.kg-1 [29]; , 0.5 mol.kg-1; , 1.0 mol.kg-1; , 2.0 AC CE PT E D MA mol.kg-1; , 4.0 mol.kg-1; , 5.5 mol.kg-1. ACCEPTED MANUSCRIPT PT 44 •, difference SC total molality of NaCl-sucrose-H2O (mtot). RI Fig.5. Deviations of the mean activity coefficients ( ) of NaCl (aq) against between our results and those given by Robinson et al. [19]; Δ, Wang et al. [20]; , Hu and Guo, AC CE PT E D MA NU [21]. ACCEPTED MANUSCRIPT RI PT 45 SC Fig.6. Transfer Gibbs energy of NaCl ( GtrNaCl ) from water to water-sucrose mixtures as function of molality of sucrose (msucrose) at different constant AC CE PT E D MA 4.0 mol.kg-1; , 6.0 mol.kg-1. NU molality of NaCl (mNaCl): , 0.5 mol.kg-1; , 1.0 mol.kg-1; , 2.0 mol.kg-1; , ACCEPTED MANUSCRIPT 46 AC CE PT E D MA NU SC RI PT Graphical Abstract ACCEPTED MANUSCRIPT AC CE PT E D MA NU SC RI PT 47 ACCEPTED MANUSCRIPT 48 Highlights • Measurements of relative humidities of NaCl-sucrose-water by hygrometric method • he determined water activities and osmotic coefficients are compared to PT tree models • RI alculation of NaCl and sucrose activity coefficients in ternary system by SC PSC model • NU etermination of Gibbs excess energy Gex and the standard free energy of MA transfer GtrNaCl • AC CE PT E in literature D he solubilities of the system are evaluated and compared to those given
