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10.1016@j.molliq.2019.03.156(1)

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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
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ACCEPTED MANUSCRIPT
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1
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Determination of Water Activity, Osmotic Coefficients, Activity
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Coefficients, solubility and Excess Gibbs Free Energies of
Messnaoui1
Brahim
Abdelfetah
4
5
Mounir2,
Dinane3,4*,
Abderrahim
Samaouali
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Abderrahim , Bahija Mounir
1
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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
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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),
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5
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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: dinaneab@yahoo.fr
Tel.: 212 64 27 21 99
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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
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coefficients. The experimental results are compared with the predictions of the
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extended composed additivity (ECA) rule, the Lin et al. equation, and Lietzke
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and Stoughton (LS II) models. The obtained results were interpreted by using
Pitzer-Simonson-Clegg model. The four mixture parameters are determined
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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
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transfer of sodium chloride are also calculated for this system.
Key words
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water activity; osmotic coefficient; activity coefficient; excess Gibbs energy;
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NaCl-sucrose-H2O; solubility; Pitzer-Simonson-Clegg model.
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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
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cloud formation and climate system regulation.
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plays an important role in the environmental domain, for example air quality,
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The physicochemical properties of these solutions has been performed by
several methods such as the emf techniques [1-3], isopiestic vapour pressure
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[4-7], and vapour pressure lowering [8-10].
We have developed in our previous studies the hygrometric method [11] which
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it is very adequate to determine directly the water activity of aqueous
electrolyte solutions, such as binary aqueous electrolytes [12, 13], and mixed
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electrolytes [14-18]. In this study, we develop the application of this method to
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the aqueous mixture of an electrolyte and non-electrolyte in order to determine
the physicochemical properties of the system NaCl-sucrose-H2O. This system
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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
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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
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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
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phase diagram of water-sucrose-NaCl system by DSC measurements.
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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
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and 5.5 mol.kg-1 in the molality range of NaCl from 0.5 to 6.0 mol.kg-1 at
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constant temperature of 298.15 K. From these measurements, the osmotic
coefficients were deduced. Our results are compared with the values obtained
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by other methods. The solute activity coefficients, excess Gibbs energy, Gibbs
energy of transfer of sodium chloride, and NaCl solubility in water-sucrose
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system are calculated by using the Pitzer-Simonson-Clegg model [25-27] with
21].
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our new ionic Pitzer parameters and are compared with data of literature [19-
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2. Experimental section:
The apparatus used for the hygrometric method is the same to the one
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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
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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
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determined. Thus, we calculate the growth ratio K (K=D(aw(ref))/D(aw)) of the
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drop which change its diameter by evaporation or condensation. The variation
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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
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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.
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The solutions were prepared from the anhydrous materials from Panreac,
Merck and Fluka (Table 1) with deionized distilled water (conductivity < 5.10-6
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S·cm-1). We checked the prepared molalities by measuring the refractive index
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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
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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
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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
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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
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Recently, Lin et al. [23] presented a very simple empirical equation for
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ternary systems. This proposed equation has the form:
(1)
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a w  1  (a w1  1)  (a w2  1)  C12 m1m2
where mi represents the molality of species i in a multicomponent solution, C12
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adjustable coefficient obtained from ternary mixture. The aw1 and aw2 are the
water activities of aqueous binary solutions of electrolyte 1 and non electrolyte
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2, respectively.
3-2. The ECA rule
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A simple mixing equation named ECA “Extended Composed Additivity”
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rule, proposed by Dinane [14] predicts the water activity in mixed electrolyte
solutions. We have applied the proposed equation for the aqueous mixture of
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an electrolyte and non electrolyte in the case of the studied system water (1)-
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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
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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
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water activity aw. The quantity on the left was plotted against the total molality
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to obtain a linear plot with intercept  and slope .
3-3. The LS model
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The LS II equation given by Lietzke and Stoughton [28,29] for the
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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
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system water (1)-sucrose (2)-sodium chloride (MX) by:
( MXmMX  m2 )   MXmMXMX  m22 ,
(4)
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where MX represent the number of ions when the molecule of considered
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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
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molality of the mixture. m2 is the molality of non electrolyte and 2 its osmotic
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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
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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:

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
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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
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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
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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 ,
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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)
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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
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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)
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gy 
The differentiation of equations (6) and (7) permits to obtain the corresponding
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expressions of activity and ionic mean coefficients of different components in
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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


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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
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

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)
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3
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ln  2  
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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



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 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
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

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:
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 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
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4-1. Water activity and osmotic coefficient
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 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
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of the sucrose in the molality range of NaCl from 0.5 to 6.0 mol.kg-1 are shown
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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
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aqueous mixed electrolytes.
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INSERT TABLE 2
INSERT FIGURE 1
We have determined the values of the ECA parameters of the system NaCl-
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sucrose-H2O and we suggest =0.001302 (mol.kg-1)-2, and =-0.000309
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(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
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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
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The osmotic coefficients of the studied system are calculated from the
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experimental aw(exp). The calculated values at different molalities are listed in
Table 2. The uncertainty on the osmotic coefficients depend of the uncertainty
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of the water activity and is estimated to be u()=0.006 however the standard
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deviation obtained from PSC model is 0.001.
4-2. Activity coefficient
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In order to determine the all unknown model parameters of Eq.6, for watersucrose-sodium chloride, the general least-squares method was used. Our
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experimental previous data [16], with the Hamer and Wu data [31] relative to
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the osmotic coefficients and ionic mean activity coefficients of single
electrolyte system of NaCl-water, were used for adjustment of model
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parameters BMX , W1, MX , U 1, MX and V1, MX . Table 3 lists these parameters
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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.
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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 .
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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.
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These mixing model parameters are obtained by simultaneous correlation of
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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
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coefficient in this work and those obtained by Robinson et al.[19] from
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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
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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
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coefficients of NaCl and sucrose in the ternary mixture are listed in Table 4.
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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
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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.
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INSERT FIGURE 5
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The results presented in this work allow us to deduce the aspect of different
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interactions which can occur between sodium chloride and sucrose in the
ternary solution of sodium chloride-sucrose-water by interpreting the activity
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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
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and exhibit significant deviation at different molalities of NaCl. The
contribution of sucrose to the behavior of NaCl depends on the concentration
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of sodium chloride. Figure 3 shows that as the proportion of sucrose is fixed,
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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 :
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  (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 i1
(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   2mN g EN  6mE 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
RTs  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
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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
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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].
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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.
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(a)
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39
(b)
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(c)
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PT
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(d)
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(e)
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PT
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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.
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
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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.
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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.
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•, 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].
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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; ,
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AC
CE
PT
E
D
MA
NU
SC
RI
PT
Graphical Abstract

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47
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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
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