Mean Activity Coefficients of NaCl in the NaCl–SrCl2–H2O Ternary

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

pubs.acs.org/jced

Mean Activity Coefficients of NaCl in the NaCl−SrCl2−H2O Ternary System at 308 K by EMF Method Zhou-Chi Wang,† Xiao-Ping Li,† Shi-Hua Sang,*,†,‡ and Xu-Chun Ma† †

College of Materials and Chemistry & Chemical Engineering, Chengdu University of Technology, Chengdu 610059, China Mineral Resources Chemistry Key Laboratory of Sichuan Higher Education Institutions, Chengdu 610059, China

Downloaded via IOWA STATE UNIV on January 16, 2019 at 12:04:04 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

‡

ABSTRACT: The mean activity coefficient of NaCl in NaCl− SrCl2−H2O was measured at 308 K by the electromotive force method. The total ion strength range of the mixed solution was 0.0100−1.0000 mol·kg−1, and the ion intensity fraction of yb of SrCl2, i.e., yb = (0.8, 0.6, 0.4, 0.2, 0). A liquid-free electrochemical cell (Na-ISE | NaCl(m1) SrCl2(m2)| Cl-ISE) was used to determine the electromotive force of a NaCl single salt and mixed solution. According to experimental data, the activity coefficient diagrams were drawn. The experimental results show that the measured activity coefficients are accurate and reliable, and the average activity coefficient of NaCl decreases with the increase of the ion strength of SrCl2. Using the measured average activity coefficient of NaCl, the parameters of the mixed ion action of the Pitzer equation θNa+·Sr2+ and φNa+·Cl−·Sr2+ are fitted. Furthermore, the Pitzer equation is used to calculate the average activity coefficents of SrCl2, the water activities aw, osmotic coefficients Φ, and Gibbs free energies GE of the mixed system.

1. INTRODUCTION Electrolyte solutions1−3 are widely found in marine, geotechnical, and other fields, as well as in the engineering of inorganic chemistry and hydrometallurgy, and in nature.4 As one of the important thermodynamic properties, the active coefficient has a mature theoretical basis for research. The Debye−Hü ckel theory represents a step of paramount importance within the general frame of electrolyte solutions. For a lower concentration of dilute solution (less than 0.01 mol/L), it provides a simple formula to calculate the mean activity coefficient in good agreement with experiments. The activity coefficient is accurate when calculating the solubility of inorganic matter in multiple groups of water solutions with high ionic strength.5−7 Activity factors can be measured based on the theory of available electrolyte solutions and correlation parameters of the osmosis coefficient, water activity, free energy, and so on. In recent years, the activity coefficient measurement methods can be roughly divided into two categories.8 Among them, the indirect isometric pressure method has a wide range of applications, flexibility, and a variety of advantages, despite it having a long measurement time and it being hard to determine a low concentration solution. The saturation vapor pressure method, with the advantage of being simple and fast, is used to determine the saturation vapor pressure when the gas and liquid phase are balanced under certain conditions, but the change of solvent vapor pressure is sensitive.9 For the above methods, existing experimental conditions cannot achieve the desired experimental results for most methods. Electromotive method force © XXXX American Chemical Society

(EMF), for its simpleness, convenience, and wide range of responses, is a kind of feasible measurement method. The ion selective electrode is a kind of important chemical sensor that measures the activity of specific ions in solution. So far, there are more than 30 ion selective electrodes.10−12 Although in the past few decades, there have been more studies of thermodynamic properties.13−16 In recent years, it has been reported that the method of calculating the activity coefficient using the Pitzer equation is constantly increasing at 298 K, but there are still more systems that have been reported less, especially at the 308 K temperature. The mean coefficients of the mixed solution system has been measured in our research, for example, the measurement of the mean activity coefficients of NaBr in the NaBr−SrBr2−H2O,17 NaCl in NaCl−SrCl2−H2O,18 and NaNO3 in NaNO3−Cd(NO3)2− H2O at 298 K19 and the mean activity coefficients of KCl in KCl−K2B4O7−H2O at 308 K.20 Although the study of the thermodynamic properties of the mixed electrolyte solution has become gradually mature in the past 10 years, most of the existing systems are at room temperature, while those at 308 K are scarcely reported. For example, common strontium containing systems are known. Sichuan underground brines are known to contain abundant strontium elements, due to the low global content of strontium, are of great help to the comprehensive development Received: June 28, 2018 Accepted: December 10, 2018

A

DOI: 10.1021/acs.jced.8b00491 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

a = 2 and b = 1.2. β(0), β(1), and CØ depend on temperature and electrolyte, which are in accord with the formula described by Greenberg and Møller.21

and utilization of resources. So far, the mean activity coefficient for strontium-containing systems at 308 K NaCl−SrCl2−H2O has not been reported in the literature. We measured the total ion intensity of NaCl in the mixed system SrCl2 ranging from 0.0100 to 1.0000 mol·kg−1 at 308 K, and the Pitzer mixed ion interaction parameters were fitted. Then, we calculated the permeability coefficients, water activities, and excess Gibbs free energies in the ternary system NaCl−SrCl2−H2O at 308 K.

i e 2 zy zz A = (2πN0ρ) jj z (2) k 4πεkT { In eq 2, N0 is the Avogadro constant, ρ is the solvent density, e is the electronic charges, and ε is the permittivity.

2. EXPERIMENTAL SECTION 2.1. Chemical Reagents and Measuring Instrument. Sodium chloride (NaCl; purity ⩾ 99.8%) and strontium chloride (SrCl2·6H2O; purity ⩾ 99.8%) were made by Chinese Medicine Group Chemical Reagent Co., Ltd. (listed in Table 1). Sodium chloride (NaCl) was heated to 378.15 K in an oven

reagent level

molar fraction purity

purification method

NaCl SrCl2·6H2O

excellent grade analytical purity

≥99.8% ≥99.8%

oven heating no

+ a6T 2 + a 7 /(680 − T ) + a8/(T − 227)

a JB-1 blender PCl −1−01 ion selective electrode 217−01 reference electrode 6801−01 sodium ion selective electrode Bilon-HW-05

Na‐ISE|NaCl (m 0)|Cl‐ISE

(a)

Na‐ISE|NaCl (m1), SrCl 2 (m2)|Cl‐ISE

(b)

where m0 is the molarity of NaCl in the battery solution. m1 and m2 are the molar concentrations, of NaCl and SrCl2 in the mixture, respectively. The above cells are without liquid junction. Electrodes need to be excited before measurement and we washed them to a blank potential. The entire system was maintained constant at 308 K until the electrode potential was balanced, and the potential changed by less than 0.1 mV per 30 min. In cell a, we set the molar concentration in the range of 0.003−1.000 mol·kg−1 from low to high to obtain the standard electromotive force E0±NaCl and the electrode influence slope κ±NaCl. Then, cell b measures NaCl in the mixed solution in the order of yb (yb = 3m2/I) = (0.8, 0.6, 0.4, 0.2, 0) and with I (I = m1 + 3m2) in the range of 0.0100− 1.0000 mol·kg−1

Table 2. Main Instruments AL104 electronic balance Pxsj-216 ion meter

(3)

In eq 3, a1, a2, a3, a4, a5, a6, a7, and a8 are determined parameters. 2.4. The Cell Arrangements. The cell arrangements are as follows:

for several hours, and the weight remained constant. It was put into the dryer for use. The experimental solvent is deionized water with a conductivity of 10−5 S·cm−1. Table 2 lists the major instruments and equipment required for the experiment.

instrument name

3/2

P(T ) = a1 + a2T + a3/T + a4 ln T + a5/(T − 263)

Table 1. Sample Description Table chemical name

1/2 j j

Ø

source U.S. Mettler-Toledo Group Shanghai Leici Precision Scientific Instrument Co., Ltd.

3. RESULTS AND DISCUSSION 3.1. Experimental Determination Activity Coefficient of Pure NaCl. According to eq 3, the Pitzer single parameters Beijing Bi-Lang Co, Ltd.

2.3. Activity Coefficient Calculation. The Debye− Hückel equation can be derived from the corresponding theory. ln γ±NaCl = −AØZi2 I

Z is the number of charges, I is the ionic strength, and AØ is the constant related to the temperature. And then, the NaCl single salt activity coefficient could be calculated according to the Pitzer equation. ÄÅ ÉÑ Å ÑÑ I ij 2 yz ØÅ Å Å ln γ±NaCl = −A ÅÅ + jj zz ln(1 + b I )ÑÑÑÑ ÅÅÇ 1 + b I ÑÑÖ kb{ Ä Å l o ij a 2I yzz o (0) jij 2β (1) zyzÅÅÅÅ j j z β a I + mm 2 + 1 − 1 + − j z Å jj 2 zzÅÅ j o o 2 z{ o k k a I {ÅÅÇ n ÉÑ| ÑÑo o + 1.5m2C Ø exp( −a I )ÑÑÑÑ} ÑÑo o o (1) ÑÖ~ Ø In eq 1, A is Debye−Hückel coefficient for the osmotic coefficient; the value is related to temperature. I is the ionic strength, m is the molar mass concentration, and the constants

Figure 1. Plot of Ea vs 2ln a0±NaCl for calibration of sodium and chlorine selective electrode pair at 308 K.

β(0), β(1), and CØ of pure NaCl at 308 K are calculated as 0.08312, 0.28534, and 0.00041, respectively. Single salt activity coefficients are calculated according to eqs 1 and 2. The activity and activity coefficient of pure NaCl solution satisfy the relation. Ea = E 0 + κ ln a+a− = E 0 + 2κ ln a0 = E 0 + 2κ ln m0 γ0 ± NaCl B

(4) DOI: 10.1021/acs.jced.8b00491 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 3. Electromotive Force and Activity Coefficients of Pure Electrolyte NaCl and Uncertainties at Temperature T = 308 K and Pressure p = 94.77 KPaa γ±NaCl I/mol· kg−1

Eb/mV

2ln α0±NaCl

pitzer equation

regression

relative error (%)

0.0031 0.0049 0.0201 0.0502 0.0799 0.1000 0.1995 0.4985 0.5997 0.7000 0.9993

−172.3 −148 −79.3 −34.5 −10.5 0.8 34.7 79.3 89 96.6 115.5

−11.6933 −10.7944 −8.0955 −6.3831 −5.5261 −5.1134 −3.8493 −2.1594 −1.8120 −1.5188 −0.8303

0.941 0.926 0.869 0.819 0.790 0.775 0.732 0.681 0.674 0.668 0.661

0.956 0.950 0.846 0.789 0.780 0.771 0.733 0.681 0.680 0.673 0.673

−1.594 −2.553 2.666 3.661 1.256 0.558 −0.247 0.037 −0.915 −0.604 −1.880

Figure 2. Plot of ln γ±NaCl vs yb for different ionic strengths I of the NaCl−SrCl2−H2O ternary system at 308 K.

Table 5. Values of the Pitzer’s Pure-Electrolyte Parameters β0, β1, and Cφ for NaCl and SrCl2 at 308 K

a

I indicates the molalities of NaCl as single salts in water, and standard uncertainties are follows: u(I) = 0.0001 mol·kg −1 and u(T) = 0.1 K. The average uncertainties of the potential difference were calculated according to data scatter at 94.77 KPa and u(Eb) = 0.1 mV.

In Figure 1, we take the potential difference E0 as the ordinate and ln α±NaCl as the abscissa and list the measured potential difference E0 and the calculated value of the activity coefficient in Table 3. The result shows that the average deviation of the

electrolyte

β(0)

β(1)

Cφ

ref

NaCl SrCl2

0.08312 1.34453

0.28534 1.75698

0.00041 −0.03310

21 22

calculated value of the activity coefficient from the regression value is 0.38%. It indicated that the experimental results are reliable, and the electrodes used in the experiments have a

Table 4. Mean Activity Coefficients of NaCl in NaCl + SrCl2 + H2O Ternary System and Uncertainties at Temperature T = 308 K and Pressure P = 94.77 KPaa I/mol·kg−1

yb

m1/mol·kg−1

m2/mol·kg−1

Eb/mV

γ±NaCl

I/mol·kg−1

yb

m1/mol·kg−1

m2/mol·kg−1

0.0101 0.0099 0.0100 0.0099 0.0098 0.0500 0.0499 0.0500 0.0500 0.0498 0.1001 0.0998 0.1001 0.1000 0.0999 0.2000 0.2000 0.1997 0.1998 0.2002 0.2997 0.2999 0.2998 0.2996 0.3000 0.4995 0.4998 0.4998 0.5000 0.4998 0.5993

0 0.2021 0.4021 0.6033 0.8080 0 0.1998 0.3981 0.6015 0.8002 0 0.1994 0.3987 0.6002 0.7997 0 0.2001 0.4002 0.6002 0.8005 0 0.2000 0.4001 0.6001 0.7998 0 0.2003 0.3999 0.6004 0.7995 0

0.0101 0.0079 0.0060 0.0039 0.0019 0.0500 0.0399 0.0301 0.0199 0.0100 0.1001 0.0799 0.0602 0.0400 0.0200 0.2000 0.1600 0.1198 0.0799 0.0399 0.2997 0.2399 0.1799 0.1198 0.0600 0.4995 0.3998 0.2999 0.1998 0.1002 0.5993

0.0000 0.0007 0.0013 0.0020 0.0026 0.0000 0.0033 0.0066 0.0100 0.0133 0.0000 0.0066 0.0133 0.0200 0.0266 0.0000 0.0133 0.0266 0.0400 0.0534 0.0000 0.0200 0.0400 0.0599 0.0800 0.0000 0.0334 0.0666 0.1001 0.1332 0.0000

−107.9 −119.4 −131.5 −147.2 −170.9 −27.5 −36.9 −49.0 −63.8 −85.6 6.6 −3.3 −15.2 −30.0 −51.0 40.0 30.8 19.3 4.9 −16.3 58.3 50.0 38.5 24.4 3.3 82.5 74.0 62.6 48.9 27.6 90.2

0.9847 0.9337 0.8807 0.8449 0.8214 0.9032 0.8778 0.8334 0.8076 0.7912 0.8596 0.8270 0.7892 0.7621 0.7578 0.8085 0.7865 0.7596 0.7377 0.7295 0.7621 0.7535 0.7270 0.7107 0.7035 0.7221 0.7115 0.6873 0.6766 0.6674 0.6961

0.5996 0.5993 0.5997 0.6000 0.6995 0.6985 0.6994 0.6994 0.6994 0.7996 0.7980 0.7993 0.7988 0.7985 0.8990 0.8965 0.8994 0.8998 0.8996 0.9997 0.9995 0.9993 0.9992 0.9998

0.1999 0.4001 0.6000 0.7997 0 0.2001 0.4001 0.6000 0.7999 0 0.1997 0.4002 0.6002 0.8009 0 0.1999 0.4001 0.6000 0.8000 0 0.1999 0.4001 0.6001 0.8000

0.4798 0.3596 0.2399 0.1202 0.6995 0.5587 0.4195 0.2798 0.1399 0.7996 0.6386 0.4795 0.3193 0.1590 0.8990 0.7173 0.5396 0.3599 0.1800 0.9997 0.7996 0.5995 0.3996 0.1999

0.0400 0.0799 0.1199 0.1599 0.0000 0.0466 0.0933 0.1399 0.1865 0.0000 0.0531 0.1066 0.1598 0.2132 0.0000 0.0597 0.1200 0.1800 0.2399 0.0000 0.0666 0.1333 0.1999 0.2666

Eb/mV

γ±NaCl

80.5 69.4 55.3 34.5 95.5 85.8 74.2 59.8 38.6 100.9 90.5 78.9 64.8 43.1 105.5 95.2 83.7 69.9 48.5 109.1 99.3 87.4 73.5 51.9

0.6703 0.6518 0.6363 0.6337 0.6591 0.6361 0.6116 0.5939 0.5878 0.6385 0.6083 0.5848 0.5717 0.5619 0.6194 0.5918 0.5690 0.5586 0.5509 0.5963 0.5736 0.5491 0.5386 0.5287

I indicates the total ionic strength for the NaCl−SrCl2−H2O ternary system and m1 and m2 are the molalities of NaCl and SrCl2 in the mixture, respectively. Standard uncertainties u are as follows: u(I) = 0.0001 mol·kg −1, u(m1) = 0.0001 mol·kg −1, u(m2) = 0.0001 mol·kg −1 , u(T) = 0.1 K. The average uncertainties of emf were calculated according to data scatter: u(Eb) = 0.1 mV, u(γ±NaCl) = 0.04. a

C

DOI: 10.1021/acs.jced.8b00491 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 7. Mean Activity Coefficients γ±SrCl2, γ±NaCl, the Osmotic Coefficients Φ, Solvent Activities aw, and Excess Gibbs Free Energies GE at T = 308 K

Table 6. Values of the Pitzer Mixing Interaction Parameters θNa+·Sr2+, φNa+·Cl−·Sr2+ for the NaCl + SrCl2 + H2O Ternary System at 308 K I/mol·kg−1

θNa+·Sr2+

φNa+·Cl−·Sr2+

R2

ref

0.0100−1.0000

−0.2276

0.1124

0.9839

this work

good Nernst linear response while their standard electromotive force E0±NaCl = 136.51 mV and electrode influence slope κ±NaCl = 26.487. 3.2. Experimental Mean Activity Coefficients of NaCl in the Mixed System. According to cell b, the electromotive force of NaCl in the NaCl−SrCl2−H2O mixed solution system was experimentally determined. The total ionic strength of the mixed solution ranges from 0.010 to 1.000 mol·kg−1. Our experiment sets SrCl2 ion intensity fraction yb = 3m2/(m1 + 3m2) = 0.8, 0.6, 0.4, 0.2, 0. The concentration approaches saturation from low to high. The NaCl activity coefficient in the mixed solution of NaCl and SrCl2 has the following relationship: E b = E 0 + κ ln α Na+·αCl− = E 0 + κ ln m1(m1 + 2m2)γ±2NaCl

(5)

According to eq 1, the average activity coefficients of NaCl in the mixed solution is calculated: ln γ±NaCl =

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

(6)

According to eq 6 and parameters listed above, the results are presented in Table 4. The relationship diagram between the logarithm of mean activity coefficients ln γ(±NaCl) of NaCl in the system and the SrCl2 ion intensity fraction yb is shown in Figure 2. From Figure 2, when ion intensity I is constant, mean activity coefficients lnγ±NaCl decreases with increasing of the ionic strength fraction yb, and the trend is expected to gradually decrease. When I is less than 1.0000, mean activity coefficients lnγ±NaCl decreases as the ionic strength fraction yb increases. It is shown that in the ternary system NaCl−SrCl2−H2O, the greater the concentration of the solution is, the smaller is the mean activity coefficient of NaCl. 3.3. Mixed Ion Parameter Calculation. According to the experimental results, using the reordered Pitzer electrolyte thermodynamic formulas, a relatively simple calculation formula, namely, the HW formula, was obtained. For the mixed solution system, the average activity coefficient γ±NaCl, γ±SrCl2, and the permeability coefficients Φ are obtained through a series of derivation transformation simplifications to obtain the following formula: (0) (0) ln γ±NaCl = 2(m1 + m2)βNaCl + m2βSrCl + 2(m1 + m2) 2

g (2

(1) I )βNaCl

(1) + m2g (2 I )βSrCl

2

+

(1.5m12

+

2 Ø CSrCl + m2θ + m2E θ 2 2(m1m2 + 2m22)

+ 4m1m2 +

Ø 2m22)C NaCl

+ (1.5m1m2 + m22)φ + F

yb

I/mol· kg−1

γ±SrCl2

γ±NaCl

Φ

aw

GE × 104/kJ· mol−1

0 0 0 0 0 0 0 0 0 0 0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8

0.0101 0.0500 0.1001 0.2000 0.2997 0.4995 0.5993 0.6995 0.7996 0.8990 0.9997 0.0099 0.0499 0.0998 0.2000 0.2999 0.4998 0.5996 0.6985 0.7980 0.8965 0.9995 0.0100 0.0500 0.1001 0.1997 0.2998 0.4998 0.5993 0.6994 0.7993 0.8994 0.9993 0.0099 0.0500 0.1000 0.1998 0.2996 0.5000 0.5997 0.6994 0.7988 0.8998 0.9992 0.0098 0.0498 0.0999 0.2002 0.3000 0.4998 0.6000 0.6994 0.7985 0.8996 0.9998

0.7331 0.6867 0.6366 0.6070 0.6092 0.6524 0.6865 0.7280 0.7765 0.8320 0.8963 0.7362 0.6919 0.6440 0.6176 0.6227 0.6718 0.7090 0.7531 0.8047 0.8633 0.9331 0.8167 0.6964 0.6508 0.6280 0.6361 0.6911 0.7314 0.7794 0.8348 0.8982 0.9699 0.8190 0.7010 0.6575 0.6381 0.6493 0.7108 0.7543 0.8055 0.8641 0.9316 1.0066 0.8214 0.7052 0.6638 0.6480 0.6625 0.7302 0.7774 0.8318 0.8937 0.9647 1.0437

0.9546 0.9013 0.8576 0.8064 0.7642 0.7242 0.6982 0.6565 0.6372 0.6187 0.5932 0.9321 0.9795 0.8252 0.7881 0.7514 0.7102 0.6740 0.6320 0.6055 0.5935 0.5748 0.8798 0.8315 0.7913 0.7621 0.7202 0.6812 0.6553 0.6134 0.5863 0.5675 0.5482 0.8465 0.8096 0.7642 0.7395 0.7215 0.6742 0.6374 0.5955 0.5731 0.5573 0.5371 0.8298 0.7931 0.7542 0.7223 0.7067 0.6653 0.6313 0.5843 0.5647 0.5475 0.5299

0.9675 0.9430 0.9321 0.9240 0.9219 0.9239 0.9264 0.9295 0.9330 0.9368 0.9410 0.9646 0.9398 0.9309 0.9283 0.9325 0.9483 0.9582 0.9690 0.9806 0.9928 1.0062 0.9606 0.9357 0.9290 0.9326 0.9436 0.9741 0.9917 1.0105 1.0302 1.0509 1.0723 0.9559 0.9303 0.9263 0.9371 0.9559 1.0028 1.0285 1.0554 1.0833 1.1124 1.1420 0.9497 0.9233 0.9224 0.9420 0.9703 1.0360 1.0713 1.1072 1.1442 1.1820 1.2205

0.9996 0.9983 0.9966 0.9934 0.9901 0.9835 0.9802 0.9768 0.9735 0.9701 0.9667 0.9997 0.9985 0.9970 0.9940 0.9910 0.9847 0.9815 0.9783 0.9749 0.9715 0.9679 0.9997 0.9987 0.9973 0.9946 0.9919 0.9861 0.9830 0.9798 0.9765 0.9731 0.9696 0.9998 0.9988 0.9977 0.9953 0.9928 0.9874 0.9846 0.9816 0.9784 0.9751 0.9716 0.9998 0.9990 0.9980 0.9959 0.9937 0.9889 0.9862 0.9834 0.9805 0.9773 0.9740

−0.0004 −0.0036 −0.0094 −0.0233 −0.0390 −0.0725 −0.0897 −0.1070 −0.1243 −0.1414 −0.1585 −0.0004 −0.0036 −0.0091 −0.0225 −0.0370 −0.0669 −0.0815 −0.0956 −0.1091 −0.1218 −0.1343 −0.0004 −0.0035 −0.0089 −0.0215 −0.0350 −0.0616 −0.0738 −0.0853 −0.0957 −0.1049 −0.1128 −0.0004 −0.0035 −0.0087 −0.0206 −0.0331 −0.0565 −0.0667 −0.0757 −0.0832 −0.0894 −0.0939 −0.0003 −0.0034 −0.0084 −0.0198 −0.0312 −0.0516 −0.0600 −0.0667 −0.0718 −0.0753 −0.0768

(7) D

DOI: 10.1021/acs.jced.8b00491 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data 3 ln γ±SrCl

2

Article

ji 2 zyzz Ø = 4(m1 + 2m2)jjjjm1C NaCl + zz φ j z 2m2CSrCl 2{ k (0) (0) + 4m1βNaCl + (2m1 + 8m2)βSrCl

+

time, the excess Gibbs free energies GE decreases. As for the permeability coefficients Φ, when the ionic strength fraction yb is constant, the value first increases and then decreases. For the SrCl2 mean coefficient, the numerical value shows the trend of increasing first and then decreasing.

2

2 (1) + 4m1g (2 I )βNaCl Ø 2(m1 + 2m2)2 CSrCl 2

4. CONCLUSION The Na-ISE and Cl-ISE selective electrodes were used to determine the thermodynamic properties of NaCl using the electromotive force method at 308 K. The electrode constants E0±NaCl and electrode response slope κ±NaCl are obtained from the single salt electromotive force plots, and the average activity coefficient of NaCl in the NaCl−SrCl2−H2O system can be measureed using the EMF method. The results show that the electrode has a good Nernst effect, and the data obtained are relatively reliable. The Pitzer ion mixing parameters θNa+·Sr2+ and φNa+·Cl−·Sr2+ were fitted by linear regression using the experimental data in this work. At the same time, the average activity coefficients of SrCl2, permeability coefficients Φ, water activities aw, and excess Gibbs free energies GE were calculated using the fitting parameters. The final research shows that the Pitzer model can be used to describe the system, and the results can be used as a reference for thermodynamic data.

(1) + (2m1 + 8m2)g (2 I )βSrCl + 2m1θ 2

+ 2m1Eθ + (6m1m2 + m12)φ + 6F

l o 2 ln(1 + 1.2 I ) | o I F = − Aφ m + } o 1 + 1.2 I o o o 1.2 n ~

(8)

(1) (1) )/I + (m1 + 2m2)g ′(2 I )(m1βNaCl + m2βSrCl 2

+ 2m1m2Eθ′

(9)

where I is the total ionic strength and β(0), β(1), and CØ are the Pitzer equation single-salt parameters. The physical parameters of the SrCl2 are obtained from Steiger’s22 study and are listed in Table 5 with the known parameters. Using the above formula and known data, the mixed parameters θNa+·Sr2+ and φNa+·Cl−·Sr2+ were fitted by a linear regression method. The results are listed in Table 6. 3.4. Calculation of Related Parameters. Gibbs free energy (GE) and solvent activity (aw) can be calculated by the following formula:

■

Corresponding Author

*Tel.:13032845233. E-mail: [email protected], [email protected].

GE = RT[ν1m1(1 − Φ + ln γ1) + ν2m2(1 − Φ + ln γ2)]

ÅÄÅ ÑÉ ÅÅ mi ÑÑÑÑ Å ÑÑ a w = expÅÅ−Φ·M w ·∑ ÅÅ 1000 ÑÑÑ ÅÇ i Ö ÄÅ ÅÅ Å (0) (0) Φ = ÅÅÅÅm1(m1 + 2m2)βNaCl + m2(m1 + 2m2)βSrCl 2 ÅÅ ÅÇ

ORCID

(10)

Shi-Hua Sang: 0000-0002-5948-3882 Funding (11)

This work was supported by the National Natural Science Foundation of China (41873071) and scientific research and innovation team in Universities of Sichuan Provincial Department of Education (15TD0009). Notes

The authors declare no competing financial interest.

(1) + m1(m1 + 2m2) exp( −2 I )βNaCl + m1(m1 + 2m2)

exp( − 2

(1) I )βSrCl 2

2

+ m1(m1 + 2m2)

■

Ø C NaCl

2 + Ø 2m2(m1 + 2m2)2 CSrCl 2 EE

′ 2I ) θNa,Sr 1.5

/(m1 + 1.5m2) + 1

REFERENCES

(1) Pitzer, K. S.; Mayorga, G. Thermodynamics of electrolytes. II. Activity and osmotic coefficients for strong electrolytes with one or both ions univalent. J. Phys. Chem. 1973, 77, 2300−2308. (2) Pitzer, K. S.; Mayorga, G. Thermodynamics of electrolytes. III. Activity and osmotic coefficients for 2−2 electrolytes. J. Solution Chem. 1974, 3, 539−546. (3) Pitzer, K. S.; Kim, J. J. Thermodynamics of electrolytes. IV. Activity and osmotic coefficients for mixed electrolytes. J. Am. Chem. Soc. 1974, 96, 5701−5707. (4) Zhang, L. Z. Determination of Activity Coefficients for Mixed Electrolyte Aqueous Soultions using A Flow Method. J. Nanjing. Chem. College 1994, 16 (4), 65−68. (5) Moggia, E.; Bianco, B. Mean Activity Coefficient of Electrolyte Solutions. J. Phys. Chem. B 2007, 111, 3183−3191. (6) Roy, R.; Roy, L.; Gregory, D.; Van Landuyt, A.; Pierrot, D.; Millero, F. Activity Coefficients of (Hydrogen Chloride+Europium Chloride) (aq) Using Harned’s Rule and the Pitzer Formalism. J. Chem. Eng. Data 2001, 46, 551−556. (7) Pitzer, K. S. Thermodynamics of electrolytes. I. Theoretical basis and general equations. J. Phys. Chem. 1973, 77, 268−277. (8) Qu, S. S. Isobarometric Study of Permeability and Activity Coefficient of Na2SO4-H2O Systems [D]; Hunan University, 2016.

ÉÑ ÑÑ Ñ + 2m1m2(m1 + 2m2)φ − AφI /(1 + 1.2 I )ÑÑÑÑ ÑÑ ÑÖ + 2m1m2( E θNa,Sr2 + θ +

AUTHOR INFORMATION

(12)

In eqs 10 and 12, m1 and m2 are the total number of anions (Cl−) and cations (Na+, Sr+ total) generated by one molecule of NaCl and SrCl2, respectively. Mw is the molar mass of water, and mi is the molar mass of the solute. EθNa,Sr2 and EθNa,Sr ′ 2 are functions of the number of charges carried by the ions and the total ionic strength I, which are calculated from empirical formulas that consider the electrostatically asymmetric mixing effect. The results in Table 7 show that when the mass molar fraction yb is constant, the corresponding water activities aw decreases with increasing ionic strength I, and at the same E

DOI: 10.1021/acs.jced.8b00491 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

(9) Chen, H. H. Exploration of a New Method for Measuring Activity Coefficient of Chlorine Water Solution [D]; Central South University, 2014. (10) Haghtalab, A.; Vera, J. H. Mean Activity Coefficients In the Ternary NaCl−NaNO3−H2O and NaBr−NaNO3−H2O Systems at 298.15 K. J. Chem. Eng. Data 1991, 36, 332−340. (11) Kozlowski, Z.; Bald, A.; Gregorowicz, J. Thermodynamic studies of NaCl solutions in water+methanol mixtures by means of a galvanic cell containing glass sodium electrode. J. Electroanal. Chem. Interfacial Electrochem. 1990, 288 (1−2), 75−82. (12) Weingartner, H.; Braun, B. M. J.; Schmoll, M. Determination of transference numbers with ion-selective electrodes. Transference numbers and activity coefficients of concentrated aqueous solutions of potassium fluoride. J. Solution Chem. 1987, 16, 419−431. (13) Robinson, R. A.; Stokes, R. H. Ionic hydration and activity in electrolyte solutions. J. Am. Chem. Soc. 1948, 70, 1870−1878. (14) Hernandez-Luis, F.; Morales, J. W.; Graber, T. A.; Galleguillos, H. R. Activity coefficients of NaNO3 in poly(ethylene glycol) 4000water mixtures at (288.15, 298.15, and 308.15) K. J. Chem. Eng. Data 2010, 55, 4082−4087. (15) Pitzer, K. S.; Kim, J. J. Thermodynamics of electrolytes. IV. Activity and osmotic coefficients for mixed electrolytes. J. Am. Chem. Soc. 1974, 96, 5701−5707. (16) Roy, R. N.; Rice, S. A.; Vogel, K. M.; Roy, L. N.; Millero, F. J. Activity coefficients for HCl-BaCl2-H2O at different temperatures and effects of higher order electrostatic terms. J. Phys. Chem. 1990, 94 (19), 7706−7710. (17) Zhou, M. F.; Sang, S. H.; Zhang, J. J.; Hu, J. X.; Zhong, S. Y. Studies on Mean Activity Coefficients of NaBr in NaBr-SrBr2H2O.Ternary System at 298.15 K by potential difference method. J. Chem. Eng. Data 2014, 59, 3779−3784. (18) Zhou, M. F.; Sang, S.-H.; Liu, Q.-Z.; Wang, D.; Fu, C. Mean Activity Coefficients of NaCl in NaCl-SrCl2-H2O Ternary System at 298.15 K Determined by Potential Difference Measurements. J. Chem. Eng. Data 2015, 60 (11), 3209−3214. (19) Wang, D.; Wen, X. H.; Zhang, W. Y.; Sang, S. H. Thermodynamic study in NaNO3-Cd(NO3)2-H2O ternary system at 298.15 K by potential difference method. J. Chem. Eng. Data 2017, 62 (4), 1232−1239. (20) Zhong, S. Y.; Sang, S. H.; Zhang, J. J. Mean activity coefficients of KCl in the KCl-K2B4O7-H2O ternary system at 308.15 K by an potential difference method. Chem. Res. Chin. Univ. 2013, 29, 1189− 1192. (21) Greenberg, J. P.; Møller, N. The Prediction of Mineral Solubilities in Natural Waters: A Chemical Equilibrium Model for the Na-K-Ca-Cl-SO4-H2O System to High Concentration from 0 to 250°C. Geochim. Cosmochim. Acta 1989, 53, 2503−2518. (22) Steiger, M. Thermodynamic properties of SrCl2(aq) from 252 to 524 K and phase equilibria in the SrCl2-H2O system: Implications for thermo chemical heat storage. J. Chem. Thermodyn. 2018, 120, 106−110.

F

DOI: 10.1021/acs.jced.8b00491 J. Chem. Eng. Data XXXX, XXX, XXX−XXX