Thermodynamic Study of the NaClâCuCl2âH2O Ternary System at

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Thermodynamic Study of the NaCl−CuCl2−H2O Ternary System at 298.15 K by the Electromotive Force Method Xu-Chun Ma,† Xiao-Ping Li,† Xiao-Feng He,† Shi-Hua Sang,*,†,‡ Ning-Fei Lei,‡ and Zhen Nie§ †

College of Materials and Chemistry & Chemical Engineering, Chengdu University of Technology, Chengdu 610059, P. R. China State Environmental Protection Key Laboratory of Synergetic Control and Joint Remediation for Soil & Water Pollution, Chengdu University of Technology, Chengdu 610059, P. R. China § Institute of Mineral Resources, CAGS, MNR Key Laboratory of Saline Lake Resources and Environments, Beijing 100037, China

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‡

ABSTRACT: In this work, we investigated some thermodynamic properties of the NaCl−CuCl2−H2O ternary system. We designed a cell without liquid junction as follows: Na-ISE | NaCl (m1), CuCl2 (m2) | Cl-ISE, which was used to study the mean activity coefficients of NaCl in the NaCl− CuCl2−H2O system at 298.15 K by the electromotive force method. In this system, the total ionic strength I ranges from 0.01 up to 1.00 mol·kg−1 for different ionic strength fractions yb of CuCl2, i.e., yb = (0.0, 0.2, 0.4, 0.6, 0.8). The results show that the Na-ISE and Cl-ISE have a good Nernst effect. The mean activity coefficients of NaCl in the ternary system were calculated using the Nernst equation. The Pitzer ion interaction parameters θNa,Cu and ψNa,Cu,Cl were fitted by Pitzer model with experimental results in this work. In addition, the osmotic coefficients, the solvent activities, and the excess Gibbs free energies of the ternary system were also calculated.

1. INTRODUCTION Thermodynamic properties of electrolyte solutions play a significant role in many fields, such as food processing, biology, atmospheric science, materials, physical chemistry, chemical industry involving electrolytes, and so on. These properties are also important for the operation and design of several chemical desalination processes.1 The investigation of thermodynamic properties, such as the activity coefficients of components, osmotic coefficients, and excess free energies of electrolyte solutions, provides fundamental thermodynamic data for many related scientific research areas. These data are indispensable for developing new thermodynamic models or testing new electrolyte solution theories.2−6 There are many ways to measure the thermodynamic properties of electrolyte solutions, such as the activity coefficients, the solvent activities, the Gibbs free energies, etc. At present, the methods for measuring the activity coefficients of components in electrolyte solutions mainly include the electromotive force method,7 the solubility method,8 the osmotic pressure method,9 the conductivity method,10 the isobaric method,11 etc. In recent years, with the increase of ion-selective electrode types and the continuous improvement of measuring technology, the electromotive force method has been favored by many scholars, because it has many advantages, such as simple device, convenient operation, short time consumption, etc. Therefore, it is widely used in the measurements of the thermodynamic properties of the mixed electrolyte solutions. With the development of electrolyte solution theory, many new models of electrolyte solutions have been put forward. © XXXX American Chemical Society

Because of the simple formulas, relatively few parameters, and high accuracy, the Pitzer model is widely used to calculate the mean activity coefficients of salts in mixed salt solution. Eva Rodil et al.12 used the electromotive force method to measure the mean activity coefficients of MgCl2 in the MgCl2− CaCl2−H2O and MgCl2−BaCl2−H2O solutions at 298.15 K. Flesia et al.13 determined the osmotic coefficients and activity coefficients of KCl in the NaCl−KCl−H2O solution at 318.15 K. Bagherinia et al.14 measured the mean activity coefficients of MgCl2 in the MgCl2−MgSO4−H2O solution at 298.15 K using the electromotive force method. Arvand et al.15 measured the mean activity coefficients of NiCl2 in the NiCl2−NiSO4−H2O solution using the electromotive force method. GhalamiChoobar et al.16 measured the mean activity coefficients of NaCl in the NaCl−NiCl2−H2O solution at 298.15 K by the electromotive force method. Our research group has carried out some studies on the mean activity coefficients of salts in mixed electrolyte solutions, such as the mean activity coefficients of NaCl in the NaCl− CdCl2−H2O17 and NaCl−SrCl2−H2O18 solutions at 298.15 K and the mean activity coefficients of NaBr in the NaBr− Na2B4O7−H2O19 and NaBr−SrBr2−H2O20 solutions at 298.15 K. Pitzer ion interaction parameters of the latter two ternary systems were fitted with the corresponding experimental activity coefficient data. Received: July 11, 2018 Accepted: December 7, 2018

A

DOI: 10.1021/acs.jced.8b00598 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

readings were taken during the test. The chloride ion selective electrode was soaked in 10−3 mol·L−1 NaCl solution, activated for 2 h, and washed with deionized water to a blank potential; the second salt bridge of the 217-01 reference electrode was filled with saturated lithium acetate solution, and the second salt bridge of the 6802-01 reference electrode was filled with saturated potassium nitrate solution. 2.3. Experimental Procedure. Two cells without using liquid-junction are used to measure the activity coefficients of salts in aqueous solutions. One of the cells contains NaCl− H2O solution, and the other contains NaCl−CuCl2−H2O solution. The two cells21 are designed as follows: (a) Na-ISE | NaCl (m0) | Cl-ISE (b) Na-ISE | NaCl (m1), CuCl2 (m2) | Cl-ISE where m0 is the molality (mol·kg−1) of NaCl as single salt in pure water; m1 and m2 are the molalities of NaCl and CuCl2 in the mixed salt solution, respectively. The specific operation process is as follows: (1) Preparation of single salt solution and determination of the electromotive force of cell (a): According to the range of the determined ionic strength I (0.001−1 mol·kg−1), weigh the corresponding mass of reagent in the sequence from small to large and then dissolve it in 50 g of high-purity water in a beaker and place the beaker on the stirrer until the reagent is completely dissolved. Next, put the beaker into the constant temperature circulating water bath and measure the electromotive force value of the cell assembled with this solution and an ion electrode. Finally, read the electromotive force every 5 min until the difference between the two readings is equal to 0.1 mV and the system can be considered in equilibrium. When a group of tests finishes, the ion electrode needs to be cleaned with high-purity water and then a filter paper will be used to dry the water on the electrode. (2) Preparation of NaCl−CuCl2−H2O solution and determination of the electromotive force of cell (b): In this mixed salt solution, the total ionic strength is I = m1 + 3m2 and the ionic strength fraction of CuCl2 is yb = 3m2/(m1 + 3m2). When I is constant, let yb = 0.0, 0.2, 0.4, 0.6, and 0.8, and then, measure the five points in ascending order. The measurement process was the same as that of the cell filled with single salt solution.

Although experimental thermodynamic properties of mixed electrolyte solutions have been reported extensively, the thermodynamic properties of mixed salt solutions containing heavy metal(s), e.g., copper, are still rare. The investigation of the thermodynamic properties of heavy metals is vital in the process of mining and the process of treating wastewater; both anthropogenic activities and natural processes make the heavy metals in soil and ores get mobilized into groundwater and surface water. Plenty of people have been threatened by heavy metal contaminations in natural water. Therefore, it is very necessary to study the thermodynamic properties of heavy metal solutions. In this work, the mean activity coefficients of NaCl in the NaCl−CuCl2−H2O solution at 298.15 K were measured by the electromotive force method, then they were used to fit the mixed ion interaction parameters in the Pitzer model, and finally the solvent activities aw, the osmotic coefficients Φ, and the excess Gibbs free energies GE were calculated.

2. EXPERIMENT 2.1. Chemical Reagents. The water used in experiments was deionized water obtained by second reverse osmosis, with conductivity 0.998) is from Chengdu Kelong Chemicals Co, Ltd., and the A.R. grade CuCl2·2H2O (mass fraction >0.99) is from Chengdu Kelong Chemicals Co, Ltd. NaCl was placed in an oven at 120 °C for 2 h and then placed in a desiccator before experiment. The mass fraction purities of chemical reagents were listed in Table 1. Table 1. Sample Description Table initial mole fraction chemical name purity

purification method

final mole fraction purity

NaCla

0.998

oven heating

0.999

CuCl2·2H2Oa

0.99

none

analysis method potential difference method potential difference method

The source of chemicals: NaCl and CuCl2·2H2O, Chengdu Kelong Chemicals Co, Ltd. a

2.2. Measuring Instruments. The main instruments were listed in Table 2. Before the experiment, we need to pretreat Table 2. Main Instruments instrument AL104 electronic balance Bilon-HW-05 Pxsj-216 ion meter JB-1 stirrer 6801-01 sodium ion selective electrode PCl-1-01 ion selective electrode 217-01 reference electrode 6802-01 reference electrode

3. RESULTS AND DISCUSSION 3.1. Performance of the Electrode. For cell (a), the mean activity coefficient γ0±NaCl of NaCl has the following relationship with Ea (electromotive force of cell (a))

source America Mettler-Toledo Group Beijing Bi-Lang Co., Ltd. Shanghai Leici Precision Scientific Instrument Co., Ltd. Shanghai Leici Precision Scientific Instrument Co., Ltd. Shanghai Leici Precision Scientific Instrument Co., Ltd. Shanghai Leici Precision Scientific Instrument Co., Ltd. Shanghai Leici Precision Scientific Instrument Co., Ltd. Shanghai Leici Precision Scientific Instrument Co., Ltd.

Ea = E 0 + κ ln a+a− = E 0 + 2κ ln a0 = E 0 + 2κ ln m0γ0 ± NaCl

(1)

where k = RT/F is the electrode response slope. R, F, and T respectively represent the gas constant, Faraday constant, and absolute temperature, and E0 stands for the standard electromotive force of cell (a). The γ0±NaCl values were obtained from Hamer and Wu.22 The electromotive force of the cell is given in Table 3. On the basis of the measured molality and the electromotive force of the cell, the linear Nernst response curve of the sodium ion and chloride ion selective electrodes was plotted, as shown in Figure 1.

the electrode. The sodium ion selective electrode was soaked and activated in 10−3 mol·L−1 NaCl solution for 2 h and washed with deionized water to a blank potential. Static B



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Table 3. Electromotive Force of the Cell and Activity Coefficients of NaCl in Its Standard Solution at 298.15 K and 94.77 kPa m0a/mol·kg−1

γ0±NaCl22

2 ln a±NaCl

Eab/mV

0.0012 0.0050 0.0106 0.0199 0.0500 0.1002 0.2000 0.3000 0.4001 0.5001 0.6001 0.6998 0.8006 0.8999 0.9981

0.9750 0.9280 0.9030 0.8720 0.8220 0.7790 0.7340 0.7090 0.6930 0.6810 0.6730 0.6670 0.6620 0.6590 0.6570

−13.5647 −10.7478 −9.2982 −8.1067 −6.3851 −5.1012 −3.8378 −3.0956 −2.5654 −2.1543 −1.8135 −1.5238 −1.2697 −1.0449 −0.8439

−201.8 −136.7 −100.8 −69.9 −26.0 7.1 39.7 58.6 72.9 84.7 92.7 100.1 106.9 112.7 117.9

ln γ±NaCl =

(E b − E 0 ) 1 − ln[m1(m1 + 2m2)] 2κ 2

(3)

where m1 and m2 are the molalities of NaCl and CuCl2 in the mixed salt solution, respectively. The mean activity coefficients γ±NaCl of NaCl can be calculated through eq 3, and the results are listed in Table 4. The relationship between the mean activity coefficients ln γ±NaCl in the mixed salt solution and the ionic strength fraction yb is shown in Figure 2. 3.3. Pitzer Equation. According to the Pitzer model, the ionic activity coefficients of the ternary system NaCl−CuCl2− H2O can be calculated as follows (eqs 4−21) (γ±NaCl)2 = γNa+ γCl−

(4)

{γ±CuCl }3 = (γCu2+)(γCl−)2

(5)

2

ln γNa+ = F ′ + mCl (2B Na,Cl + ZC Na,Cl) + mCu(2ΦCu,Na + mCl ψNa,Cu,Cl) + mCumCl CCu,Cl

a

m0 indicates the molality of NaCl in pure water at 94.77 kPa. The standard uncertainties u (0.68 level of confidence) are as follows: u(m0) = 0.0001 mol·kg−1, u(T) = 0.1 K. bThe average uncertainties of the potential difference were calculated according to data scatter at 94.77 kPa: u(Ea) = 0.1 mV.

+ mNa mCl C Na,Cl

(6)

ln γCl− = F ′ + mNa (2B Na,Cl + ZC Na,Cl) + mCu(2BCu,Cl + ZCCu,Cl) + mNa mCuψNa,Cu,Cl + mNa mCl C Na,Cl + mCumCl CCu,Cl

(7)

ln γCu2+ = 4F ′ + mCl (2BCu,Cl + ZCCu,Cl) + 2mNa mCl C Na,Cl + 2mCumCl CCu,Cl + mNa (2ΦCu,Na + mCl ψNa,Cu,Cl)

ÄÅ ÑÉÑ Å I1/2 ij 2 yz ΦÅ 1/2 Ñ ÑÑ j z F ′ = −A ÅÅÅÅ + ln(1 + bI ) ÑÑ j z ÅÅÅ (1 + bI1/2) ÑÑÑ b k { Ç Ö ′ ′ + mNa mCl B Na,Cl + mCumCl BCu,Cl + mNa mCu Φ′Cu,Na

Figure 1. Response curve of Ea vs 2 ln a±NaCl at 298.15 K.

The experimental standard electromotive force E0 and the electrode response slope κ can be obtained from Figure 1. It shows that E0 is 137.73 mV, the electrode response slope κ is 25.237 mV, and the coefficient of fitting (R2) is 0.9997. Apparently, the Na-ISE and Cl-ISE electrode pairs have a good Nernst response, so the experimental results obtained should be reliable and can be used to determine the electromotive force of the cell containing the mixed salt solution. 3.2. Measurement Results of the Mean Activity NaCl in Mixed Salt Solutions. According to the standard electromotive force E0 and the electrode response slope κ, combined with the experimental electromotive force of the cell filled with mixed electrolyte solution, the mean activity of NaCl can be calculated by the Nernst equation. The Nernst equation of cell (b) had the following relations

(9) (0) (1) Φ BCA = βCA + βCA exp( −αI1/2)

l [1 − (1 + αI1/2) exp( −αI1/2)] | o o o (0) (1)o BCA = βCA + βCA m } 2 o2 o o o αI n ~

CCA =

m21/2(m1 + 2m2)

Φ CCA

(2 |ZCZA|1/2 )

(12)

ÑÉÑ | ÅÄÅ l i Ñ Å α 2I y o 2ÅÅÅÅ1 − jjj1 + αI1/2 + 2 zzz exp(−αI1/2)ÑÑÑÑ o o o o ÑÑÖ o ÅÅÇ o { k (1)o βCA m − } 2 o o α I o o o o o o n ~ ′ = BCA I

3/2 2

(10)

(11)

E b = E 0 + κ ln m1(m1 + 2m2)γ±NaCl 2 pot + KNa,Cu γ±CuCl

(8)

(2)

where γ±NaCl and γ±CuCl2 are the mean activity coefficients of NaCl and CuCl2 in cell (b), respectively; m1 and m2 are the molalities of NaCl and CuCl2 in the mixed salt solution, respectively. Kpot Na,Cu is the selective coefficient of Na-ISE for Cu. In cell (b), Kpot Na,Cu is very small so that we can ignore the interfering effect of Cu2+ and then eq 2 can be simplified as C

−1/2

(13)

which is α = 2.0 mol ·kg , b = 1.2 mol ·kg , and AΦ = 0.391475 mol1/2·kg−1/2. β(0), β(1), and CΦ are Pitzer parameters of the electrolyte as shown in Table 5, the Pitzer mixed ion interaction parameters at 298.15 K are listed in Table 6, and Z is given by Z = mNa + 2mCu + mCl; mNa = m1; mCu = m2; mCl = m1 + 2m2. In the symbols of BCA, CCA, BCA, and BΦ CA, C represents the cation Na+ or Cu2+ and A represents the anion 1/2

1/2

−1/2



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Table 4. Mean Activity Coefficients of NaCl in the NaCl−CuCl2−H2O Ternary System and Uncertainty at 298.15 K and 94.77 kPa I = 0.01

I = 0.05

I = 0.1

I = 0.2

I = 0.3

I = 0.4

I = 0.5

I = 0.6

I = 0.7

I = 0.8

I = 0.9

I=1

Ia/mol·kg−1

yb

m1a/mol·kg−1

m2a/mol·kg−1

Ebb/mV

γ±NaClb

0.0100 0.0101 0.0100 0.0099 0.0100 0.0500 0.0499 0.0499 0.0499 0.0500 0.1000 0.1001 0.0998 0.0999 0.1003 0.1998 0.1999 0.2000 0.2001 0.2000 0.2999 0.3001 0.3000 0.3002 0.2999 0.4000 0.4000 0.4001 0.4000 0.4001 0.5001 0.5001 0.5001 0.5001 0.5000 0.6001 0.6001 0.5997 0.5999 0.5993 0.7000 0.7002 0.6998 0.6998 0.7001 0.7991 0.7996 0.7999 0.7992 0.7995 0.9001 0.8999 0.8994 0.8997 0.8994 0.9998 1.0001 1.0000

0.0000 0.2052 0.4095 0.6032 0.7955 0.0000 0.1975 0.3995 0.5999 0.8009 0.0000 0.2010 0.3987 0.5997 0.8000 0.0000 0.2000 0.4001 0.6001 0.8000 0.0000 0.1998 0.4004 0.5998 0.7998 0.0000 0.2002 0.4000 0.6001 0.8001 0.0000 0.2000 0.4004 0.6001 0.7999 0.0000 0.2000 0.4001 0.5999 0.8001 0.0000 0.2001 0.3999 0.6001 0.7999 0.0000 0.1998 0.3999 0.6001 0.8001 0.0000 0.2000 0.4000 0.6000 0.8000 0.0000 0.2002 0.3998

0.0100 0.0080 0.0059 0.0039 0.0021 0.0500 0.0400 0.0299 0.0200 0.0100 0.1000 0.0800 0.0600 0.0400 0.0201 0.1998 0.1599 0.1200 0.0800 0.0400 0.2999 0.2402 0.1799 0.1201 0.0601 0.4000 0.3199 0.2401 0.1600 0.0800 0.5001 0.4001 0.2999 0.2000 0.1000 0.6001 0.4801 0.3598 0.2400 0.1198 0.7000 0.5601 0.4199 0.2799 0.1401 0.7991 0.6399 0.4800 0.3195 0.1598 0.9001 0.7199 0.5396 0.3599 0.1799 0.9998 0.7999 0.6002

0.0000 0.0007 0.0014 0.0020 0.0027 0.0000 0.0033 0.0066 0.0100 0.0133 0.0000 0.0067 0.0133 0.0200 0.0267 0.0000 0.0133 0.0267 0.0400 0.0533 0.0000 0.0200 0.0400 0.0600 0.0800 0.0000 0.0267 0.0533 0.0800 0.1067 0.0000 0.0333 0.0668 0.1000 0.1333 0.0000 0.0400 0.0800 0.1200 0.1599 0.0000 0.0467 0.0933 0.1400 0.1867 0.0000 0.0533 0.1066 0.1599 0.2132 0.0000 0.0600 0.1199 0.1799 0.2398 0.0000 0.0667 0.1333

−102.0 −110.9 −122.8 −136.1 −155.4 −22.2 −31.8 −43.1 −57.2 −77.7 10.9 1.6 −9.8 −24.5 −45.3 44.5 34.2 23.2 8.4 −13.5 63.5 52.6 41.2 26.4 4.5 76.3 65.5 53.2 38.2 17.0 86.1 75.2 63.0 47.5 25.1 93.9 82.4 69.5 54 30.9 99.5 88.2 75.1 59.0 35.7 104.5 92.6 79.2 62.7 39.0 108.9 96.8 82.9 66.1 41.9 112.7 100.2 86.3

0.8665 0.8333 0.8052 0.7886 0.7719 0.8413 0.8050 0.7727 0.7452 0.7332 0.8107 0.7797 0.7463 0.7108 0.6931 0.7893 0.7444 0.7171 0.6814 0.6527 0.7661 0.7138 0.6831 0.6486 0.6212 0.7403 0.6918 0.6493 0.6152 0.5969 0.7190 0.6705 0.6311 0.5916 0.5607 0.6993 0.6444 0.5985 0.5608 0.5250 0.6698 0.6196 0.5730 0.5309 0.4940 0.6479 0.5918 0.5437 0.5004 0.4619 0.6276 0.5716 0.5203 0.4753 0.4348 0.6092 0.5502 0.5005

D



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Table 4. continued Ia/mol·kg−1

yb

m1a/mol·kg−1

m2a/mol·kg−1

0.9998 0.9999

0.6001 0.8000

0.3998 0.2000

0.2000 0.2666

Ebb/mV

γ±NaClb

69.1 44.6

0.4540 0.4126

a

I is the total ionic strength; m1 and m2 are the molalities of NaCl and CuCl2 in the mixed salt solution, respectively; Eb is the electromotive force of the cell (b); and γ±NaCl is the mean activity coefficients of NaCl in the mixed salt solution. The standard uncertainties u (0.68 level of confidence) are as follows: u(m1) = 0.0001 mol·kg−1, u(m2) = 0.0001 mol·kg−1, u(T) = 0.1 K. bThe average uncertainties of emf were calculated according to data scatter: u(Eb) = 0.1 mV, u(γ±NaCl) = 0.025.

Figure 2. ln γ±NaCl versus yb in different ionic strengths.

Table 5. Single Salt Parameters of the Pitzer Model for the NaCl and CuCl2

Table 6. Mixed Salt Parameters of the Pitzer Model at 298.15 K

electrolyte

β(0)

β(1)

Cφ

ref

I/mol·kg−1

θNa,Cu

ψNa,Cu,Cl

R2

ref

NaCl CuCl2

0.07722 0.23052

0.25183 2.20897

0.00106 −0.01639

23 23

0.0050−1.0000

−0.5426

−0.9914

0.9877

this work

The osmotic coefficients, excess Gibbs free energy, and solvent activity of the system are calculated according to the following formula (eqs 22−24): ÄÅ Å Φ 3/2 y 1 zz zyzÅÅÅ jij − A I jij z zÅÅ2jj Φ = 1 + jj z j mNa + mCu + mCl zÅÅ j 1 + bI1/2 zz {ÅÇ k k { Φ Φ + mNamCl (B Na,Cl + ZC Na,Cl) + mCumCl (BCu,Cl + ZCCu,Cl) ÑÉÑ ÑÑ Ñ + mNamCu{ΦΦ Na,Cu + mCl ψNa,Cu,Cl}Ñ ÑÑ ÑÑÖ (22)

Cl−. ZC and ZA represent the charge numbers of the cation and anion, respectively, E E ′ ΦΦ Na,Cu = θ Na,Cu + θ Na,Cu + I θ Na,Cu

(14)

ΦNa,Cu = θ Na,Cu + E θ Na,Cu

(15)

É ÅÄ J(χNa,Na ) J(χCu,Cu ) ÑÑÑÑ ij Z NaZCu yzÅÅÅÅ ÑÑ j z =j − zÅÅJ(χNa,Cu ) − ÑÑ 2 2 ÑÑÖ k 4I {ÅÅÅÇ

Φ′Na,Cu = E θ′Na,Cu E

θ Na,Cu

(16)

G E = RT[2m1(1 − ⌀ + ln γ±NaCl)

Ä ij E θ Na,Cu yz i Z Z y ÅÅÅÅ Na Cu j z j z ′ zz + j z + ÅÅχ J ′(χ θ Na,Cu = −jjj ) j I zz jk 8I 2 z{ ÅÅÅÅ Na,Cu Na,Cu Ç k { É χNa,Na J ′(χNa,Na ) χCu,Cu J ′(χCu,Cu ) ÑÑÑÑ ÑÑ − − ÑÑ 2 2 ÑÑÖ (18) (17)

E

χNa,Cu = 6Z NaZCuAΦI1/2 J(χ ) = χ [4 + C1 χ

−c 2

2

aW

−1

exp( −C3 χ )]

(23)

(24)

The results of γ±CuCl2, Φ, aw, and G were listed in Table 7. Those data are shown in Table 7 and draw four groups of Figures 3−6. Figures 2 and 3 illustrate that the mean activity coefficients of NaCl and CuCl2 in the mixed electrolyte decrease with the increase of the total ionic strength I when the ionic strength fraction yb is constant. The reasons may be that the interaction between ions is stronger with the increase of I and the mutual attraction between ions plays a major role. As a result, the activities of ions decrease and the mean activity coefficients of NaCl and CuCl2 is reduced; when the total ionic strength I is constant, the mean activity coefficients NaCl of the mixed electrolyte solution decreases with the increase of the fraction E

(19) c4

ÉÑ ÄÅ ÑÑ ÅÅi 18.0513 y j z Å z(2m1 + 3m2)⌀ÑÑÑ = expÅÅjj− ÑÑÖ ÅÅÇk 1000 z{

+ 3m2(1 − ⌀ + ln γ±CuCl )]

(20)

J ′(χ ) = [4 + C1χ−c2 exp( −C3 χ c4)]−1 + [4 + C1χ−c2 exp( −C3 χ c4)]−2 × [C1χ exp(−C3 χ c4)(C2 χ−c2 − 1 + C3C4 χC4 − 1χ−C2)] (21)

where C1 = 4.581; C2 = 0.7237; C3 = 0.0120; C4 = 0.528. E



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Table 7. Mean Activity Coefficients ln γ±CuCl2, Osmotic Coefficients Φ, Solvent Activities aw, and Excess Gibbs Free Energies GE of the NaCl−CuCl2−H2O Solution at 298.15 K I = 0.01

I = 0.05

I = 0.1

I = 0.2

I = 0.3

I = 0.4

I = 0.5

I = 0.6

I = 0.7

I = 0.8

I = 0.9

I = 1.0

I/mol·kg−1

yb

γ±CuCl2

Φ

aw

GE/kJ·mol−1

0.0100 0.0101 0.0100 0.0099 0.0100 0.0500 0.0499 0.0499 0.0499 0.0500 0.1000 0.1001 0.0998 0.0999 0.1003 0.1998 0.1999 0.2000 0.2001 0.2000 0.2999 0.3001 0.3000 0.3002 0.2999 0.4000 0.4000 0.4001 0.4000 0.4001 0.5001 0.5001 0.5001 0.5001 0.5000 0.6001 0.6001 0.5997 0.5999 0.5993 0.7001 0.7002 0.6998 0.6998 0.7001 0.7991 0.7996 0.7999 0.7992 0.7995 0.9001 0.8999 0.8994 0.8997 0.8994 0.9998 1.0001 1.0000 0.9998 0.9999

0.0000 0.2052 0.4095 0.6032 0.7955 0.0000 0.1975 0.3995 0.5999 0.8009 0.0000 0.2010 0.3987 0.5997 0.8000 0.0000 0.2000 0.4001 0.6001 0.8000 0.0000 0.1998 0.4004 0.5998 0.7998 0.0000 0.2002 0.4000 0.6001 0.8001 0.0000 0.2000 0.4004 0.6001 0.7999 0.0000 0.2000 0.4001 0.5999 0.8001 0.0000 0.2001 0.3999 0.6001 0.7999 0.0000 0.1998 0.3999 0.6001 0.8001 0.0000 0.2000 0.4000 0.6000 0.8000 0.0000 0.2002 0.3998 0.6001 0.8000

0.7278 0.7290 0.7328 0.7352 0.7358 0.5399 0.5452 0.5501 0.5544 0.5581 0.4523 0.4586 0.4652 0.4709 0.4759 0.3671 0.3752 0.3831 0.3907 0.3984 0.3195 0.3285 0.3376 0.3466 0.3559 0.2872 0.2968 0.3067 0.3169 0.3272 0.2632 0.2732 0.2836 0.2945 0.3060 0.2446 0.2547 0.2656 0.2770 0.2894 0.2275 0.2398 0.2509 0.2628 0.2756 0.2178 0.2277 0.2388 0.2510 0.2643 0.2079 0.2177 0.2287 0.2410 0.2547 0.2001 0.2095 0.2203 0.2325 0.2463

0.9678 0.9639 0.9596 0.9546 0.9480 0.9428 0.9362 0.9287 0.9204 0.9104 0.9313 0.9221 0.9131 0.9036 0.8935 0.9220 0.9082 0.8959 0.8854 0.8773 0.9190 0.8994 0.8833 0.8719 0.8626 0.9185 0.8918 0.8714 0.8589 0.8487 0.9195 0.8845 0.8589 0.8450 0.8325 0.9214 0.8768 0.8454 0.8300 0.8156 0.9284 0.8686 0.8306 0.8135 0.7985 0.9270 0.8599 0.8144 0.7956 0.7795 0.9304 0.8501 0.7969 0.7758 0.7562 0.9342 0.8396 0.7777 0.7546 0.7308

0.9997 0.9997 0.9997 0.9998 0.9998 0.9983 0.9985 0.9987 0.9988 0.9990 0.9966 0.9970 0.9974 0.9977 0.9981 0.9934 0.9941 0.9948 0.9955 0.9962 0.9901 0.9913 0.9924 0.9934 0.9944 0.9868 0.9885 0.9900 0.9914 0.9927 0.9835 0.9857 0.9877 0.9894 0.9910 0.9802 0.9830 0.9855 0.9875 0.9895 0.9722 0.9804 0.9834 0.9857 0.9880 0.9736 0.9779 0.9814 0.9841 0.9866 0.9702 0.9754 0.9795 0.9825 0.9854 0.9668 0.9731 0.9778 0.9811 0.9843

−0.0004 −0.0004 −0.0005 −0.0005 −0.0006 −0.0035 −0.0041 −0.0047 −0.0051 −0.0060 −0.0092 −0.0110 −0.0124 −0.0136 −0.0188 −0.0234 −0.0287 −0.0328 −0.0358 −0.0436 −0.0400 −0.0504 −0.0580 −0.0629 −0.0709 −0.0580 −0.0752 −0.0872 −0.0942 −0.1057 −0.0770 −0.1029 −0.1203 −0.1296 −0.1408 −0.0967 −0.1334 −0.1569 −0.1685 −0.1840 −0.1170 −0.1667 −0.1975 −0.2113 −0.2312 −0.1375 −0.2023 −0.2419 −0.2576 −0.2781 −0.1586 −0.2412 −0.2900 −0.3084 −0.3289 −0.1797 −0.2829 −0.3426 −0.3628 −0.3839

F



Article

number of free water molecules decreases, and Φ and aw get smaller. As shown in Figure 6, when yb is fixed, GE gradually decreases as I increases.

4. CONCLUSIONS The thermodynamic properties of the NaCl−CuCl2−H2O ternary system at 298.15 K were determined by the electromotive force method. First, the standard electromotive force E0 and the electrode response slope k were obtained by measuring the electromotive force of the cell filled with single salt solution and demonstrated the electrode had a good Nernst effect. Then, the electromotive force of a cell filled with mixed salt was determined and we calculate the mean activity coefficients of NaCl with the Nernst equation. At last, the Pitzer ion interaction parameters θNa,Cu and ψNa,Cu,Cl were obtained by Matlab with the linear regression method. The osmotic coefficients Φ, solvent activities aw, and excess Gibbs free energies GE of the solution were calculated with these mixed salt parameters and

Figure 3. Mean activity coefficients ln γ±CuCl2 of CuCl2 against ionic strength I at different ionic strength fractions of CuCl2 in the NaCl− CuCl2−H2O system.

yb and the mean activity coefficients CuCl2 of the mixed electrolyte solution increases with the increase of the fraction yb. Figures 4 and 5 show that, when yb is constant, Φ and aw decrease with increasing I. Generally, as the solution concentration increases, the number of solvated ions increases, the

Figure 4. Osmotic coefficients Φ against ionic strength I at different ionic strength fractions of CuCl2 in the NaCl−CuCl2−H2O solution.

Figure 5. Solvent activities aw against ionic strength I at different ionic strength fractions of CuCl2 in the NaCl−CuCl2−H2O solution.

Figure 6. Excess Gibbs free energies GE against ionic strength I at different ionic strength fractions of CuCl2 in the NaCl−CuCl2−H2O solution. G



Article

(NiCl2+NiSO4+H2O) system by potentiometric method at T = 298.15 K. J. Chem. Thermodyn. 2009, 41, 916−922. (16) Ghalami-Choobar, B. Thermodynamic study of the ternary mixed electrolyte (NaCl + NiCl2 + H2O) system: Application of Pitzer model with higher-order electrostatic effects. J. Chem. Thermodyn. 2011, 43, 901−907. (17) Wang, D.; Yang, Y. Y.; Zhang, X. P. Mean activity coefficients of NaCl-CdCl2-H2O ternary system at 298.15 K by potential difference method. J. Chem. Eng. Data 2016, 61, 3027−3033. (18) Zhou, M. F.; Sang, S. H.; Liu, Q. Z. Mean activity coefficients of NaCl in NaCl+SrCl2+H2O ternary system at 298.15 K determined by potential difference. J. Chem. Eng. Data 2015, 60, 3209−3214. (19) Zhang, J. J.; Sang, S. H. Studies on mean activity coefficients of NaBr in NaBr-Na2B4O7-H2O system at 298.15 K by potential difference measurements. J. Sichuan. Univ. (Eng. Sci. Ed.) 2012, 44, 240−243. (20) Zhou, M. F.; Sang, S. H.; Zhang, J. J. Studies on mean activity coefficients of NaBr in NaBr-SrBr2-H2O ternary system at 298.15 K by potential difference method. J. Chem. Eng. Data 2014, 59, 3779− 3784. (21) Xie, S. L. Analytical techniques of ion-selective electrode; Chemical Industry Press: Beijing, 1985; 32−57. (22) Hamer, W. J.; Wu, Y. C. Osmotic coefficients and mean activity coefficients of Uni-univalent electrolytes in water at 298.15 K. J. Phys. Chem. Ref. Data 1972, 1, 1047−1100. (23) Kim, H. T.; William, J.; Frederick, J. Evaluation of Pitzer ion interaction parameters of aqueous electrolytes at 25°C. 1. Single salt parameters. J. Chem. Eng. Data 1988, 33 (2), 177−184.

the Pitzer model. The thermodynamic calculation of the ternary system indicates that the Pitzer model can describe the properties of the electrolyte solution well and provides effective thermodynamic fundamental data for future research applications.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +86 13032845233. Fax: +86 28 84079074. E-mail: [email protected], [email protected]. ORCID

Shi-Hua Sang: 0000-0002-5948-3882 Funding

This project was supported by the National Natural Science Foundation of China (41873071, 41473061) and Scientific Research and Innovation Team in Universities of Sichuan Provincial Department of Education (15TD0009). Notes

The authors declare no competing financial interest.

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REFERENCES

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