Thermodynamic Properties and Solubility of Sodium and Potassium

Article pubs.acs.org/jced

Thermodynamic Properties and Solubility of Sodium and Potassium Chloride in Ethane-1,2-diol/Water Mixed Solvent Systems to High Temperatures Essmaiil Djamali,*,† Mason B. Tomson,‡ and Walter G. Chapman† †

Department of Chemical and Biomolecular Engineering, Rice University, MS-362, 6100 S. Main St., Houston, Texas 77005, United States Department of Civil and Environmental Engineering, Rice University, MS-519, 6100 S. Main St., Houston, Texas 77005, United States

‡

S Supporting Information *

ABSTRACT: Solid sodium chloride solubility is measured at temperatures from 297 to 467 K at pressure of 6.45 MPa in ethane-1,2-diol/water mixed solvent systems and at a concentration of cosolvent up to 75% w/w. The corresponding solubility is also predicted from an extension of the unified theory of electrolytes to mixed solvents (J. Phys. Chem. B 2012, 116, 9033−9042) for sodium and potassium chloride up to 473.15 K and over the whole composition range of the cosolvent. A comparison of the predicted solubility with the corresponding experimental values from this study and the available literature data indicates good agreement in all cases to well within the uncertainties of the experimental data. Also, for the saturated solution of sodium and potassium chloride in ethane-1,2-diol/ water mixed solvent systems, the stoichiometric activity coefficient values are estimated up to 473.15 K. These stoichiometric activity coefficients, over the complete range of mole fraction of the cosolvent, are then extended to all concentrations (0 ≤ m ≤ msat), and the results are compared with the available data in the literature.

1. INTRODUCTION There is a fundamental need for thermodynamic properties of electrolytes in mixed solvent systems; such properties are generally not available at temperatures above 298.15 K. These thermodynamic properties have significant economic value in many industrial processes such as oil/gas and mineral. The unified theory of electrolytes1,2 for the prediction of the standard state thermodynamic properties of aqueous electrolyte solutions at high temperatures and pressures was recently extended to include mixed solvent systems.3 For the prediction of the thermodynamic properties of electrolytes above 298.15 K, the unified theory requires two temperature and pressure independent model constants (CH and CS) for each electrolyte. Previously, it was proposed3 that, for aqueous/organic mixed solvent systems, these model constants (CH and CS) are also independent of the cosolvent; the hypothesis was then tested against the solubility data for sodium and potassium chloride in aqueous/methanol and aqueous/ethanol mixed solvent systems over a wide range of temperatures and mole fraction of the cosolvents.3 The extension of the unified model to include aqueous/organic mixed solvent systems required no additional model constants to account for the medium effect. Furthermore, the model constants for most solutes of interest are available1,2 and/or can be estimated from low temperature (T < 373.15 K) data in aqueous solutions. This is particularly important due to the lack of available experimental data in mixed solvent systems above 298.15 K. In this manuscript we report the experimental solubility data for NaCl(cr) in aqueous/ethane-1,2-diol (MEG) up to a © XXXX American Chemical Society

0.75 weight fraction (w/w) of MEG, temperatures up to 467.15 K, and pressure 6.45 MPa. The solubility data from this study up to 467.15 K and the other available solubility data at lower temperatures (T ≤ 348.15 K) from literature are then used to examine the validity of the assumption regarding the solvent independency of the unified model constants (CH and CS) for NaCl in aqueous/MEG mixed solvent systems. Furthermore, the thermodynamic properties for potassium chloride in MEG/ water mixed solvent systems over the complete range of mole fraction of MEG were predicted up to 473.15 K and compared with the available corresponding literature data. Values for the activity coefficients of the saturated solution of sodium chloride and potassium chloride in MEG/water mixed solvent systems were also calculated up to a temperature of 473.15 K.

2. EXPERIMENTAL SECTION 2.1. Materials. Distilled water (resistivity ≥18 MΩ cm) is used in all of the measurements. Reagent grade solid sodium chloride from Sigma-Aldrich (99.0%) and HPLC grade ethane1,2-diol (>99%) from Fisher Scientific were used as received. 2.2. Apparatus and Procedures. Solubility is measured with a flow-through apparatus (Figure 1). All measurements are based on sample mass, and concentrations are expressed in mole per kg of solvent. The details of experimental procedures are given elsewhere.3 However, only a summary of the procedures is Received: September 27, 2016 Accepted: March 13, 2017

A

DOI: 10.1021/acs.jced.6b00842 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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Figure 1. “Schematic diagram of apparatus: 1, syringe pump (3H2O); 2, syringe pump (NaCl solution); 3, valve; 4, Hastelloy C tubing; 5, preheating coil; 6, NaCl-packed column; 7, three-way valve; 8, oven; 9, cooling bath; 10, back pressure valve; 11, effluent collation vial.” Reprinted with permission from ref 3, Copyright 2012 American Chemical Society.

Figure 2. Values of ΔmB for sodium chloride () and potassium chloride (----) as a function of the mole fraction of MEG at 298.15 K.

outlined here. A sample cylinder, constructed from 316-stainless steel, is packed with reagent grade solid sodium chloride and placed in an oven. Additionally, all connections, valves, and tubings are constructed from Hastelloy C alloy. A saturated solution of aqueous sodium chloride, prepared at room temperature, is mixed with desired quantities of MEG and used as feed solution. The feed solution is pumped through a preheating coil into the sample cylinder by a high-pressure syringe pump (Teledyne ISCO) at a steady flow rate of 0.2 mL/min. To prevent the precipitation of sodium chloride as the solution temperature and the pressure decreased, a 3H2O solution is injected at the same flow rate at the exit of the sample cylinder using a second syringe pump (Teledyne ISCO). The dilution factor is determined from the radioactivity of the nonreactive tracer (3H2O) in the effluent by scintillation counting. A sufficient residence time is allowed to ensure that the dissolution experiment reached equilibrium. The effluent is collected at room temperature and 1 atm for ion concentration analysis. The inductively coupled plasma optical emission spectrometry (ICP-OES, PerkinElmer 4300DV) is used to measure the concentration of sodium ion in the effluents. The chloride ion concentration in the effluents was measured by Hg(NO3)2 titration. For most tests, the differences between Na+ ion and Cl− ion concentrations are less than 5%.

Figure 3. Comparison of experimental and predicted (eqs 10, 12) values for the solubility in MEG/water mixed solvent systems. (a) NaCl: ⧫, Pitzer et al.;28 ×, Djamali et al.;3 □, ■, Masoudi et al.;29 ▲, Baldwin et al.;30 ○, Kraus et al.;15 ●, Isbin and Kobe;31 △,◊, +, , This study. (b) KCl: ×, deLima and Pitzer;14 +, Kraus et al.;15 ○, △, ◊, □, ChiavoneFilho and Ramussen;16 , this study.

3. CALCULATIONS AND RESULTS The thermodynamic properties of a solution refers to the following reaction MX(cr) = MX(aq)

(1)

for which the standard state Gibbs free energies of solution, ΔsolG°(T,p), is Δsol G°(T , p) = G2◦(T , p , aq) − G°(T , p , cr)

In the present manuscript, the standard state Gibbs free energies of solution at temperature T and pressure p are calculated from the unified theory of electrolytes1,2 as follows:

(2)

where G2°(T,p,aq) is the standard state partial molar Gibbs free energy (the chemical potential) of the solute electrolyte, and G°(T,p,cr) is the molar Gibbs free energy of the solid. The thermodynamic functions of the solid salt are from the standard reference tables.4,5 For the ionic species the standard state adopted for the thermal properties of solutes (enthalpy, heat capacity, and volume) is infinite dilution and for the free energies and entropies, the hypothetically ideal one molal (mole of solute/kg of solvent) solution exhibiting infinitely diluted properties.6,7

Δsol G°(T , p) = Δsol G°(Tr , p) + Δsubl [G°(T , p) − F1(D)G°(Tr , p)] + Δsol G⊕(Tr , p)[F1(D) − 1] ⎛ RTdm° ⎞ ⎛ RT d m° ⎞ − CSΔT + υRT ln⎜ ⎟ − υRTr ln⎜ r r ⎟ ⎝ 1000p° ⎠ ⎝ 1000p° ⎠ (3)

where Tr is the reference temperature 298.15 K, d is the density of the solvent in g/cm3, dr is the density of the solvent at the reference temperature, υ is the stoichiometric B



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Table 1. Experimental Solubility of Sodium Chloride in Ethane-1,2-diol/Water Mixed Solvent Systems at the Pressure p = 6.45 MPaa,b T/K g

298.15 298.15g 378.15g 466.15g 298.15 298.15 297.15 357.15 404.15 466.15 298.15 352.15 396.15 465.15 298.15 297.15 355.15 407.15 467.15

wc

x2d

mNa+e

mCl−e

mNaCle,f

ur(m)

0.0000 0.0000 0.0000 0.0000 0.2498 0.2498 0.2498 0.2498 0.2498 0.2498 0.4990 0.4990 0.4990 0.4990 0.7440 0.7440 0.7441 0.7441 0.7441

0.0000 0.0000 0.0000 0.0000 0.0880 0.0880 0.0880 0.0880 0.0880 0.0880 0.2241 0.2241 0.2241 0.2241 0.4573 0.4573 0.4575 0.4575 0.4575

6.1067 6.3342 6.5519 7.7481 4.4234 4.5742 4.5690 4.7211 5.3767 6.0935 3.1196 3.3682 3.7000 4.1861 2.0165 2.0238 2.1439 2.2232 2.3454

6.0089 5.9593 6.5738 7.5394 4.3951 4.4052 4.3884 4.5214 5.0696 5.6319 3.0203 3.2779 3.5429 3.9442 1.9639 1.9670 1.9943 2.1524 2.2846

6.0576 6.1439 6.5629 7.6431 4.4092 4.4889 4.4778 4.6202 5.2209 5.8581 3.0695 3.3228 3.6206 4.0633 1.9900 1.9952 2.0677 2.1875 2.3148

0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.03 0.03 0.05 0.02 0.02 0.05 0.05 0.05

Figure 5. Comparison of the experimental and predicted solubility (eqs 10 and 12) of sodium chloride in MEG/water mixed solvent systems at 298.15 K (○) and 467.15 K (□) as a function of mole fraction of the cosolvent. ---, Kraus et al.;15 ○, □, , this study.

⎡ ⎤ ⎡ ⎤ 1 1 F1(D) = ⎢1 − ⎥ / ⎢1 − ⎥ D(T , p) ⎦ ⎣ D(Tr , p) ⎦ ⎣

The values for the standard state Gibbs free energy of sublimation, ΔsublG°(T,p), are calculated from the Gibbs free energies of formation from the standard reference tables:5,4

a

Standard uncertainties for temperature and pressure are u(T) = 0.1 K and u(p) = 0.05 MPa, respectively. bFor the reaction NaCl(cr) = Na+(mix. solvt.) + Cl−(mix. solvt.). cWeight fraction of ethane-1,2-diol. d Mole fraction of ethane-1,2-diol. emol/kg of solvent. fmNaCl = (mNamCl−)1/2. gDjamali et al.3

Δsubl G°(T , p) = Δf G°(M+X−, g, T , p) − Δf G°(MX, cr, T , p) (5)

and the adjusted Gibbs free energy, ΔsolG⊕(Tr,p), of the solute electrolyte at the reference temperature 298.15 K is

Table 2. Unified Theory Constants1,3,a electrolyte

solvent

NaCl NaCl NaCl KCl KCl KCl

water water

a

water water

cosolvent ethane-1,2-diol ethane-1,2-diol ethane-1,2-diol ethane-1,2-diol

−1

−CS (J mol

70.52 70.52 90.20 40.88 40.88 40.88

−1

K )

(4)

Δsol G⊕(Tr , p) = Δsol G°(Tr , p) − C H + CSTr ⎛ RT d m° ⎞ − υRTr ln⎜ r r ⎟ ⎝ 1000p° ⎠

−1

CH (kJ mol ) 66.720 66.720 66.720 152.726 152.726 152.726

(6)

where m° is equal to 1 mol/kg and p° is equal to 0.1 MPa. The last two terms in the right-hand side of eq 3 are the standard state conversion terms for the hypothetically ideal 0.1 MPa gaseous ions being hydrated to the hypothetically ideal 1 m aqueous solution.1,8,9 Further

Equation 3.

Δsol G◦(Tr , p) = Δsol G◦(Tr , pr ) +

number of ions in the solute, R is the ideal gas constant, and F1(D) is a function of dielectric constant, D(T,p), of the solvent

∫p

p

Δsol V °(Tr , p′) dp′

r

(7)

Figure 4. Comparison of experimental and predicted solubility in pure MEG. (a) NaCl: △, Kraus et al. (99.97% MEG);15 □, Isbin and Kobe;31 ○, Baldwin et al.;30 , this study. (b) KCl: □ Kraus et al. (99.97% MEG);15 ×, Isbin and Kobe;31 ○, Chiavone-Filho and Ramussen;16 , this study. C



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Figure 6. Standard state Gibbs free energy of transfer of sodium chloride (a) and potassium chloride (b) from water to MEG/water mixed solvents at 298.15 K: ◊, Ceccattini et al.;32 □, Li et al.;33 , Emelin et al.;34 ○, this study.

Figure 7. Stoichiometric activity coefficients at solid saturation for sodium chloride (a) and potassium chloride (b) in MEG/water as a function of temperature and weight fraction of MEG.

principle, be calculated from the values for the corresponding asat(T,p) from the following equation,

and Δsol V °(Tr , p) = V 2◦(Tr , p) − V °(Tr , p)

(8)

msat (T , p) = [asat(T , p)/γsat(T , p ; msat )]

where pr is the reference pressure 0.1 MPa, values for ΔsolG°(Tr,pr) are from NBS tables,5 V°2 is the standard state partial molar volume,10 and V° is the molar volume of the solid calculated from available density at 298.15 K,11 assuming the pressure effect on the molar volume of the solid is negligible. At the equilibrium of a solid with its saturated solution, for a given temperature T and pressure p, the activity of the solid saturated solution, asat(T,p), is directly related to the standard state Gibbs free energy of the solution of the electrolyte, ΔsolG°(T,p), according to the following thermodynamic cycle

provided that the related value for the stoichiometric activity coefficient of the solid saturated solution, γsat(T,p,msat), is given. In case where there is some ion association, eq 10 is refined mobs(T , p) =

asat(T , p) γsat(T , p ; msat )

× [1 + asat(T , p) × γsat(T , p ; msat )/kd(T , p)]

(11)

where the last term on the right-hand side accounts for the contribution due to ion association. In eq 11, the activity coefficient of the ion pair is assumed to be equal to one at all temperatures and pressures. The values for the equilibrium constant for the dissociation of the ion pair, kd, of sodium chloride in MEG/water mixed solvent solutions are from the literature.12 At 473.15 K, the highest temperature of this study, the contribution to observed solubility from ion association is less than 4%, well within uncertainty of the experimental data. Unless otherwise stated, the solubility in mixed solvent system in this study is calculated from eq 10. Values for the activity coefficients of a solute electrolyte in a mixed solvent systems, γssat, are usually not available at temperatures greater than 298.15 K. In the present study, the

from which asat(T , p) = a°(T , p) exp( −Δsol G°(T , p)/νRT )

(10)

(9)

where a°(T,p) = m° is the standard state activity equal to 1 mol/kg at all temperatures T and pressures p. The values for solubility (mol of solute/kg of solvent) of the solid saturated solution of the electrolyte, msat(T,p), can now, in D



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Figure 8. Comparison of the calculated and experimental stoichiometric activity coefficients of sodium chloride at 298.15 K and all concentrations (0 ≤ m ≤ msat) for different weight fractions (w/w) of MEG (a−d): ○, Ceccattini et al.;32 □, Li et al.;33 ●, , this study.

values for γssat(T,p;mssat), where mssat is the solubility in the mixed solvent system, are estimated from the activity coefficient of the electrolyte in aqueous solution, γwsat(T,p;m), at the same T, p, and mssat:3 ln γ±s = ln γ±w + AφZ+Z −f γ (1 − g γ ) + ΔmB × m

cosolvent, are estimated from the available experimental activity coefficients of NaCl in aqueous/MEG mixed solvent systems at 298.15 K (see Figure 2). Figure 3a summarizes a comparison of the calculated solubility (eqs 10 and 12) of sodium chloride in MEG/water mixed solvent systems up to 473 K at steam saturation pressure, psat, and the entire concentration range of the cosolvent with the corresponding literature data and the experimental values from this study at 6.45 MPa (Table 1). The estimated uncertainties, disregarding the pressure corrections from 6.45 MPa to psat, in the values of the solubility at the highest experimental temperature, 467 K, is less than 2%, well within the uncertainties of the solubility data. In Figure 3b a similar comparison is made between calculated values for the solubility of potassium chloride in MEG/water mixed solvent systems at psat and over the entire range of the mole fraction of MEG with the available corresponding experimental values.14−16 A comparison indicates good agreement in all cases to well within the combined uncertainties of the experimental data and uncertainties arising from errors in estimated activity coefficients and dielectric constants of mixed solvents at higher temperatures. The required values for the activity coefficient of KCl(aq) in eq 12 are from Pabalan and Pitzer.17 The values for the unified model constants, CH and CS, for NaCl and KCl are listed in Table 2.

(12)

with fγ =

I1/2 + (2/1.2)ln(1 + 1.2I1/2) 1 + 1.2I1/2

(13)

and g γ = [(d s/d w )(Dw /Ds)3 ]1/2

(14)

where I is the ionic strength, 1/2∑imiZ2i , Z is the ionic charge, Aφ is the limiting slope for the osmotic function (pure water)13 and the superscript s and w refer to mixed solvent and pure water, respectively. The second term in the right-hand side of eq 12 corrects for the differences in the long-range interionic forces between the ions in MEG/water and in pure water as solvent, and ΔmB is the difference in short-range interactions in pure water and in mixed solvent; the value of ΔmB is fixed from experimental data using eq 12. In eq 12, it is assumed that ΔmB is independent of temperature and its values, as a function of mole fraction of the E



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Figure 9. Comparison of the calculated and experimental stoichiometric activity coefficients of potassium chloride at 298.15 K and all concentrations (0 ≤ m ≤ msat) for different weight fractions (w/w) of MEG (a−d): □, ○, Manzoni et al.37

the literature (Supporting Information (SI)).18−26 Akerlof26 reported values for dielectric constant of MEG/water mixed solvents from 293.15 to 333.15 K and at mole fractions up to 1 of the cosolvent. Values for dielectric constants of MEG/water mixed solvents up to 473 K were estimated from the Akerlof correlation3,26 (see SI): log D = a + b(T − 293.15)

(15)

For temperatures above 473 K, the dielectric constant for aqueous/organic mixed solvent can be estimated from the more comprehensive model recently presented by Maribo-Mogensen et al.27 The solubility of sodium and potassium chloride in pure MEG up to 323.15 and 348.15 K, respectively, is also available in the literature.15,30,31,16 These values were extended to 473 K using the unified model and plotted in Figure 4. A comparison of the calculated solubility for sodium chloride from the unified model with the corresponding experimental values at 467.15 and 298.15 K over the entire range of concentration of MEG/water mixed solvent system is summarized in Figure 5. The values for the Gibbs free energies of transfer, ΔtG°, of sodium and potassium chloride from pure water (as solvent) to MEG/water mixed solvents at the reference temperature 298.15 K over the entire range of mole fraction of MEG are

Figure 10. Effective electrostatic radius, RB (Å), for NaCl and KCl in aqueous/organic mixed solvent systems as a function of mole fraction of the cosolvent.

The required auxiliary data for the density and the dielectric constant of MEG/water mixed solvents (see eq 3) are available in F



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Table 3. Unified Theory Equations for the Thermodynamic Properties of Electrolytesa Δsol G°(T , p) = Δsol G°(Tr , p) + Δsubl [G°(T , p) − F1(D)G°(Tr , p)] + Δsol G⊕(Tr , p)[F1(D) − 1] − CSΔT + Δss[G°(T , p) − G°(Tr , p)]

(18a)

⊕

Δsol G (Tr , p) = Δsol G°(Tr , p) − C H + CSTr − ΔssG°(Tr , p)

⎤ ⎡ ⎤ ⎡ 1 1 F1(D) = ⎢1 − ⎥ ⎥/⎢1 − D(T , p) ⎦ ⎣ D(Tr , p) ⎦ ⎣

⎛ RTd°m° ⎞ ΔssG°(T , p) = υRT ln⎜ ⎟ ⎝ 1000p° ⎠

(18b)

(18c)

(18d)

⊕

S2°(T , p) = − [Δsol G (Tr , p) − Δsubl G°(Tr , p)]F2(D) + CS +

∑ υiSi°(g , T ) + ΔssS°(T , p)

(19a)

i

⎤⎛ ∂D ⎞ ⎡ D(T , p) ⎤⎡ 1 r ⎥⎜ ⎟ F2(D) = ⎢ ⎥⎢ 2 ⎝ ⎣ D(Tr , p) − 1 ⎦⎣ D(Tr , p) ⎦ ∂T ⎠ p

(19b)

⎡ ⎤ ⎛ ∂ ln d° ⎞ ⎟ + 1⎥ ΔssS°(T , p) = − υR ⎢ln(RTd°) + T ⎜ ⎝ ⎠ ⎢⎣ ∂T p ⎦⎥

(19c)

⊕

V 2°(T , p) = [F3(D) − F3(Dr ) × F1(D)][Δsol G (Tr , p) − Δsubl G⊕(Tr , p)] + V 2°(Tr , p) × F1(D) + ΔssV °(T , p) − ΔssV °(Tr , p) × F1(D) ⎡ ⎤⎛ ∂D ⎞ 1 ⎥⎜ ⎟ F3(D) = ⎢ ⎣ (1 − Dr )D2 ⎦⎝ ∂p ⎠T

(20b)

⎛ ∂ ln d° ⎞ ΔssV °(T , p) = υRT ⎜ ⎟ ⎝ ∂p ⎠T

(20c)

(20a)

C p°,2(T , p) = − T[Δsol G⊕(Tr , p) − Δsubl G°(Tr , p)]F4(D) +

∑ υiCp°,i(g , T ) + ΔssCp◦(T , p)

(21a)

i 2⎤ ⎡ ⎤⎡⎛ ∂ 2D ⎞ 1 2 ⎛ ∂D ⎞ ⎥⎢ F4(D) = ⎢ − ⎜ ⎟ ⎥ 2 ⎢⎜ 2⎟ D ⎝ ∂T ⎠ p⎥⎦ ⎣ (1 − Dr )D ⎦⎣⎝ ∂T ⎠ p

⎡ ⎛ ∂α° ⎞ ⎤ ⎟ ⎥ ΔssC °p(T , p) = − υR ⎢1 − 2Tα° − T 2⎜ ⎝ ∂T ⎠ p⎥⎦ ⎢⎣ ⎛ ∂ ln d° ⎞ ⎟ α° = − ⎜ ⎝ ∂T ⎠ p

(21b)

(21c)

(21d)

Definition of symbols: D is the bulk dielectric constant of the solvent; CS and CH solute specific model constants; υ, stoichiometric number of ions in the solute; m° is equal to 1 mol/kg; d° is the density of the pure solvent in g/cm3; p° is equal to 0.1 MPa; α° is the coefficient of thermal expansion of solvent, S°i (g) and C°p,i(g) are the molar entropies and molar heat capacities of the gaseous ions; ΔssX°,X° = G°, S°, C°, V° are the standard state correction terms. a

agreement between the values for activity coefficients of sodium chloride from this study calculated from eq 12 and the corresponding values reported by Li et al.33 and Ceccattini et al.32 up to 60% weight fraction of MEG/water. At 0.8 (w/w) of MEG/water, the values for activity coefficients of sodium chloride from this study at 298.15 K disagree with the corresponding values reported by Ceccatti et al.32 However, a similar comparison of the activity coefficients of potassium chloride from this study at 298.15 K with those reported by Manzoni al.37 indicates good agreement at all weight fraction of MEG/water (Figure 9). The effective electrostatic radius, RB,1,3 for NaCl in the MEG/water mixed solvent systems as a function of mole fraction of the cosolvent, x2, is compared with the corresponding value in methanol/water mixed solvent systems in Figure 10. In both cosolvents, the effective electrostatic radius for NaCl changes

summarized in Figure 6. A comparison of the values of the Gibbs free energies of transfer of NaCl and KCl at 298.15 K from this study with the available corresponding values from the literature indicates a good agreement to well within combined uncertainties (Figure 6). The stoichiometric activity coefficients of sodium and potassium chloride in MEG/water mixed solvent systems at the solid-saturated solution, γssat(T,p;msat), up to 473.15 K and as a function of mole fraction of MEG calculated from eq 12 are summarized in Figure 7. From the modified Meissner model,3,35,36 the values for γssat(T,p;msat) can be extended to all concentrations. The stoichiometric activity coefficients of sodium and potassium chloride in MEG/water mixed solvent systems at 298.15 K and at all concentrations (0 ≤ m ≤ msat) from this study are compared with the available literature data in Figures 8 and 9, respectively. The comparison indicates a good G



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smoothly with x2; however, in the limit as x2 approaches 1, a sudden decrease in the magnitude of RB in methanol/water mixed solvent system is detected. This sudden decrease in the value of RB for sodium chloride, for the process of transfer from methanol/water mixed solvents to pure methanol as the solvent, was interpreted3 as an indication that water molecules preferentially hydrate the ions in the case of methanol as the cosolvent; this is in agreement with simulation results reported by Chialvo and Cummings38 and Hawlicka and Swiatla-Wojcik.39 However, in the region of low concentration of water in MEG/water mixed solvent systems, the unified model predicts that the ions are preferentially solvated by MEG (Figure 10). From Figure 10, in the low water concentration region, a similar conclusion can also be reached regarding the preferential solvation of KCl in MEG/water mixed solvent systems. Conversely, in the case of potassium chloride in ethanol/water mixed solvent systems, the ions are preferentially hydrated even in the region of low concentration of water, similar to NaCl in methanol/water mixed solvent systems. A detailed investigation of the molecular structure of mixed solvent electrolyte systems is the subject of our future study. This analysis is needed for a better understanding of the molecular mechanism of the salt effect.

“from which” Δsol G°(T , p) = Δsubl G°(T , p) + Δsolv G°(T , p)

(16)

“The values for ΔsublG°(T,p) are calculated from the Gibbs free energies of formation from standard reference tables16,17:” Δsubl G°(T , p) = Δf G°[M+X−(g, T , p)] − Δf G°[MX(cr, T , p)]

(17)

“The values for ΔsolvG°(T,p) are calculated from the unified theory of electrolytes,1 which is summarized in Table 3. In the unified theory of electrolytes,1 the standard state Gibbs free energies of solvation are calculated from the electrostatic and nonelectrostatic contribution to the solvation process.”

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.6b00842. Density and dielectric constant for MEG/H2O mixed solvent systems (PDF)

4. CONCLUSION The solubility was predicted a priori for sodium and potassium chloride in ethane-1,2-diol/water mixed solvent systems up to 473.15 K from an extension of the unified theory of electrolytes1,2 to include mixed solvent systems.3 When these predicted solubility values are compared with the corresponding experimental data from this study and those from the available literature, we find good agreement over the complete range of temperatures and compositions. The uncertainties in the predicted solubility values arise mainly from the propagated errors in the estimated dielectric constants and densities of the mixed solvents at higher temperatures. These uncertainties in the predicted solubility values are well within the corresponding experimental uncertainties. The estimated values are reported for the stoichiometric activity coefficients of saturated solution of sodium and potassium chloride in MEG/water mixed solvent systems up to 473.15 K. These activity coefficients, over the complete range of mole fraction of cosolvents, can be extended to all concentrations (0 ≤ m ≤ msat) (eq 12). We also find good agreement in the comparison of the activity coefficients from this study with the available literature data (mainly at 298.15 K) in MEG/water mixed solvent systems. Furthermore, no additional parameters were required to account for the effect of medium in the application of the unified theory of electrolytes to NaCl and KCl in MEG/water mixed solvent systems.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Essmaiil Djamali: 0000-0003-0616-5722 Funding

The authors acknowledge RPSEA/DOE 10121-4204-01 for their financial support. Notes

The authors declare no competing financial interest.

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REFERENCES

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APPENDIX The material in this section is reprinted with permission from ref 3 (Copyright 2012, American Chemical Society), with references that match the current paper. The table shows different material pertaining to this work. “The standard state Gibbs free energy of the solution, ΔsolG°(T,p), of an electrolyte at any temperature and pressure is associated with the standard state Gibbs free energy of solvation, ΔsolvG°(T,p), and the standard state Gibbs free energy of sublimation, ΔsublG°(T,p), at the same T and p according to the following thermodynamic cycle:” H



Article

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Thermodynamic Properties and Solubility of Sodium and Potassium

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