Isopiestic Measurements of Osmotic and Activity ... - ACS Publications

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

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Isopiestic Measurements of Osmotic and Activity Coefficients of NiCl2−NH4Cl−H2O Systems at 308.15 K Xin Yi, Jiugang Hu,* Weili Zhang, Xueying Zhang, Min Sun, and Shijun Liu* School of Chemistry and Chemical Engineering, Central South University, Changsha 410083, People’s Republic of China Hunan Provincial Key Laboratory of Efficient and Clean Utilization of Manganese Resources, Central South University, Changsha, Hunan 410083, China

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S Supporting Information *

ABSTRACT: In this work, the osmotic coefficients and water activities of NiCl2−NH4Cl−H2O ternary system and its two subsystems were obtained by isopiestic measurements at 308.15 K. The mean ion activity coefficients of NiCl2−H2O and NH4Cl−H2O systems with different molalities at 308.15 K were calculated by the Pitzer ion interaction model. Meanwhile, the self-consistency of experimental data was validated by Gibbs−Duhem equation, showing the calculated results have a good self-consistency between Pitzer ion interaction model and Gibbs−Duhem equation in the whole experimental molality range for NH4Cl−H2O system. Whereas for the NiCl2−H2O system, the Pitzer equation has its limitation of the molality range. Similarly, the osmotic coefficients of NiCl2−NH4Cl−H2O ternary system with different ionic strength can be obtained. Furthermore, the relative deviation between the experimental and calculated results indicated that the mixing parameters of Pitzer equation can be ignored in estimating the osmotic coefficients at the ionic strength of less than 2.5 mol·kg−1, whereas it cannot be omitted at the higher ionic strength.

1. INTRODUCTION

The thermodynamic properties like osmotic and activity coefficients of NiCl2 and NH4Cl solutions are widely used and offer the theoretical guidance in hydrometallurgy.8,9 Hence, it have been attracted much attention in recent years. For instance, Rard obtained the osmotic coefficients and water activities of NiCl2 solution with a wide molality range by isopiestic measurement at 298.15 K.10 Stokes concluded the osmotic and activity coefficients of many bivalent metal halides at 298.15 K, where the reported molality range for NiCl2 solution is from 0.522−5.8 mol·kg−1.11 For NH4Cl aqueous solution, Pearce reported the vapor pressure for NH4Cl solution from 0.1−7.38 mol·kg−1 at 298.15 K and then calculated the mean ion activity coefficients based on the obtained vaper pressure data.12 Wishaw obtained the osmotic coefficients of NH4Cl aqueous solution from dilute to near saturated and calculated the activity coefficients of corresponding molalities at 298.15 K.13 In the practical industrial process, accurate data of osmotic and activity coefficients are always required over a wide temperature range. However, owing to the time-consuming experimental methods, the existing studies of NiCl2−H2O and NH4Cl−H2O systems besides 298.15 K are seldom. For instance, Holmes obtained the osmotic coefficients of NiCl2−H2O system at 382.96 and 413.36 K by isopiestic measurements.14 Yi calculated the osmotic and

In hydrometallurgy, chloride media are widely used because of the unique coordination characteristics. Winand summarized the importance and convenience of chloride hydrometallurgy.1 Dutrizac reported the leaching technology for the sulfide minerals in chloride media including Cu, Fe, Pb, Zn.2 Leclerc and coauthors studied the hydrometallurgical recovery of zinc from electric arc furnace dust in the chloride solutions, showing the improved extraction efficiency of zinc.3 Moreover, the aqueous solution containing ammonium and chloride is a more efficient media for selective recovery of valuable metals. For instance, Oishi studied the recovery of high purity copper from PCBs (printed circuit boards) using ammoniacal chloride solutions, showing the excellent leaching efficiency of copper in this system.4 Serruya investigated the silver electrocrystallization from aqueous leaching solution containing ammonia and chloride and disclosed the effect of solution composition on silver deposition.5 Trejo reported the electrodeposition of gold in the ammoniacal chloride medium.6 These researches indicated the ammoniacal chloride solution is very useful in hydrometallurgy. NiCl2 and NH4Cl are important and familiar compositions in chloride hydrometallurgy for nickel and other valuable metals. Wu studied the electrodeposition of bright nickel from ammonia solution with chloride and disclosed the deposition behaviors of nickel with the change of solution concentration.7 Therefore, the NiCl2−NH4Cl−H2O system is important in hydrometallurgy and need to be further studied. © XXXX American Chemical Society

Received: May 14, 2018 Accepted: July 18, 2018

A

DOI: 10.1021/acs.jced.8b00400 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

mean ion activity coefficients of NiCl2−H2O system in the range of 298.15−363.15 K with the established thermodynamic model.15 Garnsey reported the osmotic coefficients of NH4Cl−H2O system at 273.15 K and obtained the related parameters.16 Therefore, the thermodynamic studies of the NiCl2−H2O and NH4Cl−H2O systems and their ternary system beyond 298.15 K are significant and necessary. In this work, the isopiestic measurements have been performed on the NiCl2−NH4Cl−H2O ternary system and its subsystems at 308.15 K to obtain the osmotic coefficients and water activity. The Pitzer ion interaction model was used to calculate the osmotic and mean ion activity coefficients of each system. Moreover, the self-consistency of the experimental data was validated by Gibbs−Duhem equation. Figure 1. Vertical view of the isopiestic chamber with sample cells. 1, NH4Cl−H2O; 2, NaCl-H2O; 3, NiCl2−H2O; 4, NaCl-H2O; 5, NiCl2−NH4Cl−H2O.

2. EXPERIMENTS 2.1. Chemicals. All chemicals used in the experiments were of the highest purity received from Alfa Aesar without further purification and are listed in Table 1. The water used was

Table 2. Comparison of the Osmotic Coefficients with Literature Values for KCl−H2O and NaOH−H2O System at 298.15 Ka

Table 1. Characteristics of Chemicals chemical name sodium hydroxide sodium chloride ammonia chloride nickel chloride hexahydrate potassium chloride silver nitrate

CAS number

source

initial mole fraction purity

1310-73-2 7647-14-5 12125-02-9 7797-20-0

Alfa Aesar Alfa Aesar Alfa Aesar Alfa Aesar

99% 99.99% 99.5% 99.99%

7447-40-7 7761-88-8

Alfa Aesar Alfa Aesar

99.99% 99.99%

system NaOH− H2O KCl−H2O

m/mol·kg−1

m/mol·kg−1 (NaCl)

ϕexp

ϕref19

σ (%)b

1.0038 2.0105 0.9956 2.0024

1.0124 2.0952 0.9983 1.9916

0.9589 1.0324 0.9011 0.9163

0.9551 1.0287 0.8980 0.9122

0.398 0.360 0.345 0.449

a NaCl aqueous solutions were used as reference solutions. bStandard uncertainties are u(T) = 0.05 K, u(m) = 0.0035 mol·kg−1 for NaCl solution; u(m) = 0.0026 mol·kg−1, and u(ϕ) = 0.0044 for NaOH solution; u(m) = 0.0038 mol·kg−1 and u(ϕ) = 0.0051 for KCl solution. cRelative deviation σ = (ϕexp − ϕref)/ϕref.

redistilled, deionized, and degassed. The stock solutions for NaCl, NH4Cl, and NiCl2 were prepared and their molalities were confirmed by AgCl precipitation method. The related data and uncertainties are listed in Supporting Information, Table S1.

accuracy and reliability of both apparatus and experiment method. 3.2. Isopiestic Measurements. The isopiestic measurements of NH4Cl−H2O, NiCl2−H2O, and NiCl2−NH4Cl− H2O systems with different molalities were performed at 308.15 K, The detailed data were listed in Table 3. For the molalities of each solution in isopiestic cup after equilibrium, it can be calculated by the following equation 1000ωWB mB = [(Wequ − ∑i Wi ω)MB] (1)

2.2. APPARATUS AND PROCEDURE The experimental apparatus containing thermostat bath, isopiestic chamber, powerplant, and vacuum system was elaborated according to the previous literature.17 Five silver isopiestic cups with small glass pearls were placed in the chamber. The NaCl, NH4Cl, NiCl2, and NiCl2 + NH4Cl aqueous solutions were respectively put into the corresponding sample cups where NaCl aqueous solution was used as the reference solution. The vertical view of the isopiestic chamber with solutions was shown in Figure 1. The isopiestic chamber was closed, air evacuated from it slowly to within 100 Pa of the reference solution’s water vapor pressure, and then the chamber was heated to 308.15 K at a uniform rate.18 After 168 h equilibrium, the isopiestic chamber was removed from the thermostat bath, each cup was weighed when approaches to the room temperature.

where mB is the molality of the corresponding electrolyte solution; MB represents the molar mass of the electrolyte; WB is the mass and ω is for the mass fraction of the stock solution; Wequ represents the mass of solution after equilibrium. 3.3. Osmotic and Mean Ion Activity Coefficients of NiCl2−H2O and NH4Cl−H2O Systems. After isopiestic measurement, the following eq 2 can be used to calculate the osmotic coefficients φ=

3. RESULTS AND DISCUSSION 3.1. Method Verification. To verify the reliability and accuracy of the experiment method, the osmotic coefficients of KCl−H2O and NaOH−H2O with different molalities have been measured. As shown in Table 2, the osmotic coefficients of the two systems agree well with the literature values and the maximum deviation is less than 0.45%, showing the good

ν*m*ϕ* ∑i νimi

(2)

where ϕ and ϕ* are the osmotic coefficients of the experimental and reference solutions; vi is the total ion number of the experimental solution while v* is for reference; m and m* represent the molality of the experimental and reference solutions after equilibrium, respectively. Meanwhile, the water activity can be calculated as the following equation: B



Article a,b

Table 3. Isopiestic Measurements Data of NH4Cl−H2O, NiCl2−H2O, and NiCl2−NH4Cl−H2O systems at 308.15 K set

cups

Wstock/g

Wwater/g

Wequ/g

m/mol·kg−1

1

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1

0.09659 0.07806 0.02445 0.08574 0.09333/0.06091c 0.14396 0.13317 0.04932 0.12234 0.27051/0.18287 0.32067 0.27061 0.10640 0.28786 0.37941/0.11894 0.34360 0.27601 0.30543 0.27564 0.56608/0.40143 0.51359 0.40470 0.29706 0.39301 0.74482/0.24368 0.66380 0.51090 0.48383 0.52015 1.095331/0.35934 0.69863 0.56116 0.52112 0.55791 1.11012/0.73724 0.87416 0.67499 0.59172 0.67210 1.47981/0.47804 0.92361 0.70218 0.69433 0.71843 1.49362/0.98993 1.09470 0.84256 0.83261 0.84632 1.86411/0.61187 1.17152 0.89662 0.86247 0.90486 2.22442/0.72458 1.33622d 1.13909 1.00593 1.12583 2.22441/0.72463 0.13128d

1.28700 1.31098 1.37099 1.31209 3.95431 1.25367 1.39500 1.34992 1.27211 3.64892 1.06464 1.11982 1.29425 1.11385 3.59801 1.06517 1.12840 1.09467 1.15070 3.25711 0.88587 0.99038 1.08919 0.99553 3.26783 0.75057 0.89235 0.94271 0.92330 2.90004 0.68915 0.85830 0.87672 0.84805 2.59613 0.52951 0.72522 0.82101 0.76171 2.54751 0.47395 0.68110 0.70969 0.69639 2.13841 0.30425 0.55791 0.60695 0.59322 2.16909 0.32586 0.60312 0.65964 0.59448 1.81094 0 0.38304 0.48613 0.37867 1.81090 0.47824

1.17926 1.14727 1.17284 1.21827 3.71958 1.22327 1.34752 1.15636 1.23152 3.76141 1.25301 1.28984 1.19324 1.36257 3.79287 1.27914 1.26146 1.26149 1.26438 3.89566 1.30334 1.28380 1.18152 1.24552 3.85480 1.37712 1.33197 1.41420 1.35608 4.06609 1.33615 1.36069 1.29469 1.35197 4.21957 1.36035 1.34833 1.38806 1.34169 4.32998 1.33242 1.31056 1.39205 1.34069 4.44337 1.32587 1.34224 1.39273 1.34885 4.36362 1.40394 1.41284 1.43195 1.42544 4.49762 1.33071 1.52274 1.46727 1.50481 4.49761 0.56853

0.2736 0.2677 0.0453 0.2726 0.0541/0.0543 0.3956 0.3916 0.0933 0.3936 0.1601/0.1648 0.8823 0.8532 0.1976 0.8595 0.2235/0.1066 0.9281 0.89166 0.5611 0.8913 0.3336/0.3605 1.3940 1.3151 0.5842 1.3163 0.4465/0.2226 1.7340 1.6271 0.8173 1.6270 0.6401/0.3200 1.8958 1.7621 0.9799 1.7620 0.6346/0.6421 2.3852 2.1871 1.0457 2.1886 0.8429/0.4107 2.5992 2.3619 1.2523 2.3623 0.8377/0.8462 3.1797 2.8343 1.5510 2.8328 1.0784/0.5395 3.2201 2.8707 1.5650 2.8715 1.2823/0.6365 4.0155 3.4884 1.8328 3.4890 1.2823/0.6365 4.3161

2

3

4

5

6

7

8

9

10

11

12

13

C



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Table 3. continued set

14

15

16

cups

Wstock/g

Wwater/g

Wequ/g

m/mol·kg−1

2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

1.08472 1.05745 1.10234 2.40381/1.58346 0.26059d 1.09273 0.99309 1.11143 2.51771/0.83008 0.32302d 1.28305 1.10646 1.29113 3.33371/1.09478 0.35133d 1.33661 1.14571 1.32898 2.96292/1.92648

0.33567 0.47204 0.31214 0.96818 1.14487 0.30162 0.42202 0.30606 1.15541 1.10298 0.12059 0.28794 0.18001 0.69852 1.04694 0.12426 0.24766 0 0.26501

1.37737 1.48495 1.39978 4.64451 1.35332 1.36363 1.36898 1.38509 4.42248 1.47368 1.43249 1.42387 1.44157 5.11671 1.44325 1.37891 1.44452 1.37714 5.15057

3.7122 1.9214 3.7121 1.4063/1.4115 4.4585 3.7919 1.9665 3.7955 1.5528/0.7651 5.2481 4.3519 2.1453 4.3517 1.8046/0.9031 6.0151 4.8102 2.2024 4.9484 1.6074/1.5925

a Notation: Cup number 1, NH4Cl−H2O; 2, NaCl−H2O; 3, NiCl2−H2O; 4, NaCl−H2O; 5, NiCl2−NH4Cl−H2O; Wstock, mass of stock solutions; Wwater, mass of water; Wequ, mass of solutions after equilibrium; m, molalities of solutions after equilibrium. bStandard uncertainties are u(T) = 0.05 K, u(Wwater) = 0.00230 g, u(Wequ) = 0.00161 g, u(Wstock) = 0.00143 g, and u(m) = 0.0032 mol·kg−1 for NH4Cl solution; u(Wstock) = 0.00299 g and u(m) = 0.0041 mol·kg−1 for NaCl solution; u(Wstock) = 0.00347 g and u(m) = 0.0045 mol·kg−1 for NiCl2 solution. cA/B represents the corresponding physical quantities for NiCl2/NH4Cl. dNH4Cl in solid phase were used in the corresponding sets.

−νmMW ϕ 1000

ln aW =

ϕ−1=

(3)

+ 0.28590 exp( −2m1/2)) + 0.00037m2

where aW is the water activity of the experimental solution, v represents the ion number, and MW is the molar mass of water. In the isopiestic measurement, NaCl−H2O system was used as reference, for the osmotic coefficients of NaCl solution at 308.15 K, it can be calculated with the osmotic coefficient equation of Pitzer. The equation can be expressed as ϕ − 1 = | z Mz X | f ϕ +

f

ϕ

=

(0) (1) ϕ BMX = βMX + βMX exp( −αI1/2)

I=

1 2

(4)

−AϕI1/2 (1 + bI1/2)

∑ mizi2 i

(5)

Therefore, the osmotic coefficients of NiCl2−H2O and NH4Cl−H2O systems at different molalities were calculated with eq 2 and listed in Table 4. Fitting the experimental data in Table 4 with the osmotic coefficient function of Pitzer, the related parameters can be obtained, as shown in Table 5. Figure 2 shows the comparison of the experimental and calculated osmotic coefficients of the two systems. For NiCl2−H2O system, the osmotic coefficient has a tiny deduction before 0.1 mol·kg−1, and then grows steadily as the molality increases at 308.15 K. It can be explained that in the very dilute molality range the solution can be treated as the ideal solution and the osmotic coefficients decrease as the molality increases. After the molality reaches a proper value, the practical solution diverges from the ideal solution and the osmotic coefficients raise with the increase of the molality. Whereas for NH4Cl−H2O system, the value of osmotic coefficient decreases sharply from dilute to near 1 mol· kg−1 and then raises smoothly in the follow-up experimental molality range. For both of the two systems, the maximum relative deviation is within 0.5%, indicating the osmotic coefficient function of Pitzer can well describe the experimental data of both NiCl2−H2O and NH4Cl−H2O systems. Mean ion activity is an important thermodynamic property which shows the deviation between the real electrolyte solution and ideal solution. The mean ion activity coefficient of Pitzer expressed as the following equations

ϕ 2mνMνXBMX φ ν + 2m2(νMνX )3/2 C MX ν

−0.39849m1/2 + m(0.08021 (1 + 1.2m1/2)

(4-1)

(4-2)

(4-3)

where ϕ is osmotic coefficient, z represents the number of charges, and v is the ion number; M and X are cation and anion respectively; α is a universal parameter with the value 2.0 kg1/2·mol1/2; b has the value 1.2 kg1/2·mol1/2; Aϕ is Debye− Hückel parameter for osmotic coefficient and can be obtained (1) ϕ from the literature;20 β(0) MX, βMX, and CMX are three defined parameters of the osmotic coefficient equation of Pitzer.21 On the basis of the three defined parameters of NaCl solution at 308.15 K in literature,22 the osmotic coefficients of Pitzer for NaCl solution at 308.15 K can be expressed as

ln γ±MX = |z Mz X|f γ +

γ γ 2mνMνXBMX + 2m2(νMνX)3/2 CMX ν

(6) D



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Table 4. Experimental Osmotic Coefficients (ϕ) and Water Activities (aW) of NiCl2−H2O and NH4Cl−H2O systems at 308.15 Ka NiCl2−H2O system m/mol·kg

−1

0.0453 0.0933 0.1976 0.5611 0.5842 0.8713 0.9799 1.0457 1.2523 1.5510 1.5650 1.8328 1.9214 1.9665 2.1453 2.2024

ϕ

b

0.8563 0.8445 0.8522 0.9412 0.9480 1.0360 1.0750 1.0973 1.1687 1.2738 1.2787 1.3734 1.4046 1.4204 1.4829 1.5027

γ BMX

NH4Cl−H2O system aw

c

0.9979 0.9957 0.9910 0.9716 0.9704 0.9524 0.9447 0.9398 0.9241 0.8988 0.8976 0.8729 0.8644 0.8600 0.8422 0.8363

−1

ϕ

aw

0.9154 0.9115 0.9056 0.9038 0.9054 0.9099 0.9102 0.9188 0.9196 0.9272 0.9298 0.9404 0.9441 0.9452 0.9496 0.9613

0.9910 0.9870 0.9716 0.9704 0.9558 0.9447 0.9398 0.9241 0.9175 0.8992 0.8977 0.8728 0.8634 0.8592 0.8358 0.8119

m/mol·kg 0.2736 0.3956 0.8823 0.9281 1.3940 1.7340 1.8958 2.3852 2.5992 3.1797 3.2201 4.0155 4.3161 4.4582 5.2481 6.0151

γ CMX =

Standard uncertainties are u(T) = 0.05 K, u(m) = 0.0045 mol·kg−1, u(ϕ) = 0.0081, and u(aw) = 0.0093 for NiCl2 solution, u(m) = 0.0032 mol·kg−1, u(ϕ) = 0.0075, and u(aw) = 0.0082 for NH4Cl solution. b Osmotic coefficients were calculated by eq 2. cWater activity were calculated by eq 3.

Table 5. Parameters of Equation 4 for NiCl2−H2O System and NH4Cl−H2O System at 308.15 Ka β(0)

β(1)

Cϕ

R2

D

NiCl2−H2O NH4Cl−H2O

0.3761 0.0481

1.2923 0.2952

−0.0134 −0.0026

0.9906 0.9869

0.0182 0.0207

a R is the correlation coefficient in equation fitting, D is the standard deviation between the experiment osmotic coefficients and the calculated values through eq 4.

ÅÄÅ ÑÉ ÅÅ 2 ln(1 + bI1/2) ÑÑÑÑ I1/2 Å f = −AϕÅÅ + ÑÑ ÅÅÅ (1 + bI1/2) ÑÑÑ b Ç Ö

+

(1) 2βMX

[1 − (1 + αI1/2 −

α 2I )exp(− αI1/2)] 2

α 2I

ϕ 3CMX 2

(6-2)

(6-3)

where β(0), β(1), and C(ϕ) are the three calculated parameters for the osmotic coefficient equation of Pitzer listed in Table 5. The mean ion activities of NiCl2−H2O and NH4Cl−H2O systems at 308.15 K can be obtained through eq 4 and the related parameters. Owing to the lack of the literature data at higher temperature, the values of mean ion activity for the two systems at 298.15 K were selected as comparison11,13 and plotted in Figure 3. For NiCl2−H2O system, similar to the osmotic coefficients, the comparison between the values at 298.15 and 308.15 K indicates that the mean ion activity coefficients of NiCl2 solutions have a negative growth as the temperature raises and is consistent with the previous work.15 The values at both two temperatures show a downward trend from very dilute to near 0.5 mol·kg−1 and then raise rapidly with the increase of the molality due to the increased interionic interaction. Whereas for NH4Cl−H2O system, the values at 298.15 K are smaller than the ones at 308.15 K, indicating the mean ion activity coefficients have a growth trend with the temperature increases. Meanwhile, the mean ion activity coefficients decrease sharply before the molality reaches about 3 mol·kg−1 and then nearly invariant even the solution approaches to the higher molalities. As shown in Figure 3, for both NiCl2−H2O and NH4Cl−H2O systems, the variation tendency of mean ion activity coefficients for the calculated data obtained by the experiment has a good consistency with the reference data, indicating the calculated results are reliable. 3.4. Self-Consistency Validation of the Experimental Data. The Pitzer ion interaction model is widely used in studying the electrolyte solutions in an appropriate molality range. To justify the reliability of the data processing, Gibbs− Duhem equation was used to compare with the Pitzer equation. For NiCl2−H2O system, the Gibbs−Duhem equation can be expressed as

a

system

=

(0) 2βMX

γ

(6-1)

x d ln γx ,1 + (1 − x)d ln γx ,2 = 0

(7)

Figure 2. Osmotic coefficients for the (a) NiCl2−H2O system and (b) NH4Cl−H2O system at 308.15 K. E



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Figure 3. Mean ion activity coefficients for the (a) NiCl2−H2O system and (b) NH4Cl−H2O system at 308.15 K.

Figure 4. Verification of self-consistency for the (a) NiCl2−H2O system and (b) NH4Cl−H2O system. Line I for Gibbs−Duhem equation, line II for ion interaction model of Pitzer.

where x is the mole fraction of NiCl2; γx,1 represents the activity coefficient of NiCl2 at corresponding mole fraction and γx,2 is that for water. Some related transformation equations are as follow x=

νmMW (1000 + νmMW )

d ln γx,1 =

(7-2)

γx,2 = aW (1 + 0.001νmMW )

(7-3)

(8)

For the expression for γx,1 and x based on the ion interaction model of Pitzer, it can be derived as follow defined as line II in Figure 4

(7-1)

γx ,1 = γm ,1(1 + 0.001νmMW )

19.3012 − 18.9023x − 0.3989 x

d ln γx,1 =

10.5216 + 62.7652x − 0.2187 x

(9)

Similarly, the two lines for NH4Cl−H2O system can be expressed as eq 10 defined as line I for Gibbs−Duhem equation and eq 11 for the ion interaction model of Pitzer defined as line II, respectively. The related authentication data were listed in Supporting Information, Table S3

where MW represents the molar mass of water; m is the molality of NiCl2−H2O system; γm,1 represents the activity coefficient of NiCl2 at corresponding molarlity. The authentication data of Gibbs−Duhem equation can be calculated and listed in Supporting Information, Table S2. Therefore, the representation for the activity coefficient of NiCl2 at corresponding molar fraction (γx,1) and the molar fraction of NiCl2 (x) based on Gibbs−Duhem equation can be expressed as the following equation defined as line I in Figure 4

d ln γx,1 =

2.5200 − 0.2370x − 0.1496 x

(10)

d ln γx,1 =

0.5293 + 2.0073x − 0.1148 x

(11)

Figure 4 represents the verification of self-consistency of the two systems. For NiCl2−H2O system, there is a certain amount F



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where Bϕca and Cϕca are the parameters of each single electrolyte in the mixture system; whereas θcc′, θaa′, ψcc′a, and ψaa′c represent separately the mixing parameters of Pitzer model for the mixtures, which can be obtained by fitting the experimental data. For NiCl2−NH4Cl−H2O system, the osmotic coefficient equation of Pitzer is Ä ij 2 yzÅÅÅÅ −AϕI 3/2 zzÅÅ (ϕ − 1) = jjjj + 2 ∑ ∑ mcma zzÅÅ 1/2 Å ∑ m i c a i k {ÅÅÇ (1 + bI ) É Ñ ij ϕ (∑ mz) ϕ yzzÑÑÑÑ jjjBca + C zzÑÑ 1/2 ca z j Ñ ( z z ) (13) c a k {ÑÑÖ By substituting the fitted parameters of NiCl2 and NH4Cl at 308.15 K into eq 13, the equation can be simplified as Ä ij 2 yzÅÅÅÅ −0.39894I 3/2 j z Å (ϕ − 1) = jjj zzzÅÅÅ 1/2 ∑ m i k i {ÅÅÅÇ (1 + bI )

of deviation between the calculated data by the ion interaction model of Pitzer, the data obtained from Gibbs−Duhem equation before the additional fraction of NiCl2 reaches 0.023 and then have a good self-consistency at higher additional fraction in the experiment, reflecting that the ion interaction model of Pitzer has its limitation of molality range for the specific electrolyte solution. Whereas for the NH4Cl−H2O system, the calculated results for the two functions are in mutual corroboration with each other very well in the entire experimental mole fraction range, showing that the ion interaction of Pitzer can be used well to calculate the corresponding thermodynamic properties for the NH4Cl− H2O system. 3.5. Osmotic and Mean Ion Activity Coefficients of NiCl2−NH4Cl−H2O system. Similar with the two subsystems, the osmotic coefficients and water activities of NiCl2−NH4Cl− H2O ternary system with different ionic strength and mole ratio can be obtained and listed in Table 6. It can be found that Table 6. Experimental Osmotic Coefficients (ϕ) and Water Activities (aW) of NiCl2−NH4Cl−H2O System at 308.15 Ka m1/m2b

m1/mol·kg−1

m2/mol·kg−1

I/mol·kg−1

ϕc

awd

1:1 1:1 1:1 1:1 1:1 1:1 1:1 1:1 2:1 2:1 2:1 2:1 2:1 2:1 2:1 2:1

0.0541 0.1601 0.3336 0.6346 0.8377 1.0637 1.4063 1.6074 0.2235 0.4465 0.6401 0.8429 1.0784 1.2823 1.5228 1.8046

0.0543 0.1648 0.3605 0.6421 0.8462 1.0776 1.4115 1.5925 0.1066 0.2226 0.3200 0.4107 0.5395 0.6365 0.7651 0.9031

0.2166 0.6451 1.3613 2.5459 3.3593 4.2687 5.6304 6.4147 0.7771 1.5621 2.2402 2.9395 3.7747 4.4834 5.3336 6.3169

0.8729 0.8934 0.9282 0.9899 1.0422 1.1029 1.1888 1.2435 0.8684 0.9334 0.9799 1.0280 1.1081 1.1695 1.2384 1.3166

0.9957 0.9870 0.9716 0.9447 0.9241 0.8992 0.8600 0.8358 0.9863 0.9704 0.9558 0.9398 0.9175 0.8977 0.8728 0.8426

ϕ + m Ni2+mCl−(B NiCl + mCl−C NiCl 2) 2 φ + m NH+4 mCl−(B NH + mCl−C NH4Cl) 4Cl

+ m NH+4 m Ni2+(θ NH+4 Ni2+ + mCl−ψ NH+Ni2+Cl−)] 4

(13-1)

where mi = m Ni2+ + mCl− + m NH+4 1 2 2 2 (m Ni2+z Ni 2 + + m NH+z NH+ + mCl−z Cl−) 4 4 2 1 = (4m Ni2+ + m NH+4 + mCl−) 2

I=

−1

a

Standard uncertainties are u(T) = 0.05 K, u(m1) = 0.0045 mol·kg , u(m2) = 0.0032 mol·kg−1, u(ϕ) = 0.0087, and u(aw) = 0.0103. bm1/m2 represents the mole ratio of NiCl2 and NH4Cl, where m1 refers to the molality of NiCl2 and m2 is that of NH4Cl. cOsmotic coefficients were calculated by eq 2. dWater activity were calculated by eq 3.

+

∑ ∑ mama′(θaa′ + Iθaa′ + ∑ mcψaa′ c)]

c

a

< c′

< a′

(13-4)

ϕ B NH = 0.0481 + 0.2950 exp(− 2I1/2) 4Cl

(13-5)

C NiCl 2 = −0.0134

(13-6)

C NH4Cl = −0.0026

(13-7)

system

θNH4+Ni2+

ψNH4+Ni2+Cl−

R2

D

NiCl2−NH4Cl−H2O

−0.0260

−0.0231

0.9824

0.0269

R is the correlation coefficient in equation fitting; D is the standard deviation between the experiment osmotic coefficients and the calculated values through eq 13. a

mixture system, due to the ionic interaction law, there are much more anions like Cl− around the cations, which means there is a week interaction force between Ni2+, NH4+, and Cl−. Consequently, to simplify the calculating process, the two mixing parameters of Pitzer can be ignored (θ = Ψ = 0) in the estimation of osmotic coefficients by the equation of Pitzer for the mixtures. As shown in Figure 5, comparing the results between the calculated data which considering mixing parameters (θ, Ψ ≠ 0) and experimental data for NiCl2−

a

c

ϕ B NiCl = 0.3761 + 1.2923 exp(− 2I1/2) 2

Table 7. Parameters of Pitzer for NiCl2−NH4Cl−H2O System at 308.15 Ka

ÄÅ Å i (∑ mz) ϕ yzz jij 1 zyzÅÅÅ ϕ zzÅÅ2If + 2 ∑ ∑ mcma jjjjBcaϕ + (ϕ − 1) = jjj Cca zz jj j ∑ mi zzÅÅÅ (zcza)1/2 zz{ c a k k i {ÅÇ

∑ ∑ mcmc′(θcc′ + Iθcc′+ ∑ maψcc′ a)

(13-3)

Therefore, the mixing parameters of Pitzer for NiCl2−NH4Cl− H2O ternary system can be fitted and listed in Table 7. In this

the osmotic coefficient raises with the increase of the ionic strength without an observed minimum value, which is mainly induced by the interaction between the three kinds of ions and the complex species. Meanwhile the value of osmotic coefficient for m1/m2 = 2:1 mixture (m1 represents NiCl2 and m2 is NH4Cl) increases more obviously than that of m1/m2 = 1:1 mixture, owing to the higher ionic strength of NiCl2 at the same molality. For the ternary electrolyte solutions, the osmotic coefficient of Pitzer can be expressed as

+

(13-2)

(12) G



Article

Figure 5. Relative deviation between experimental data and (a) calculated results considering mixing parameters (θ, Ψ ≠ 0), (b) calculated results ignoring mixing parameters (θ = Ψ = 0) for NiCl2−NH4Cl−H2O system at 308.15 K.

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NH4Cl−H2O system at 308.15 K, the maximum relative deviation is within 0.6% in the whole ionic strength range. Therefore, the osmotic coefficient equation of Pitzer for the mixtures can well describe the ternary electrolyte solutions. For the comparison between the calculated data, which ignored the mixing parameters and the experimental ones, the relative deviation is acceptable in the lower ionic strength range (less than 2.5 mol·kg−1) but raises a lot with the increase of the ionic strength. These results showed that the interaction force between Ni2+, NH4+, and Cl− raises with the increase of the ionic strength due to the greater ion number and short ionic distance in the solution, indicating the mixing parameters cannot be ignored at high ionic strength.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.8b00400.

■

Molalities of NiCl2, NH4Cl, and NaCl stock solutions; authentication data of Gibbs−Duhem equation for NiCl2−H2O and NH4Cl−H2O systems (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (J.H.). *E-mail: [email protected] (S.L.). ORCID

4. CONCLUSIONS The osmotic and water activity coefficients of NiCl2−NH4Cl− H2O ternary system and its two subsystems were obtained by isopiestic measurements at 308.15 K. By fitting the original data of NiCl2−H2O and NH4Cl−H2O systems by the osmotic coefficient equation of Pitzer, the related parameters of these two systems were obtained. Meanwhile, the mean ion activity coefficients of NiCl2−H2O and NH4Cl−H2O systems with different molalities at 308.15 K were calculated based on the equation of Pitzer and showed the similar trends with the reference data at 298.15 K. Moreover, Gibbs−Duhem equation was used to validate the reliability of Pitzer equation, showing that the ion interaction model of Pitzer has its limitation of molality range for NiCl2−H2O system. For the NH4Cl−H2O system, the calculated results have a good self-consistency between Pitzer equation and Gibbs−Duhem equation in the whole experimental molality range. Furthermore, the osmotic coefficients of NiCl2−NH4Cl−H2O ternary system were fitted by Pitzer equation for mixtures to obtain the two mixing parameters. Comparing the recalculated osmotic coefficients and the experimental ones, the relative deviation is acceptable in the ionic strength range of less than 2.5 mol·kg−1, whereas reaches excessive with the increase of ionic strength. Hence, the mixing parameters can be ignored in estimating the osmotic coefficients at low ionic strength whereas they cannot be omitted at high ionic strength.

Jiugang Hu: 0000-0002-5702-9547 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was financially supported by National Basic Research Program of China (2014CB643401), the National Natural Science Foundation of China (No.51134007), and the Hunan Provincial Science and Technology Plan Project of China (No. 2016TP1007).

■

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