Potentiometric Investigation of the Thermodynamic Properties of Mixed

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

Potentiometric Investigation of the Thermodynamic Properties of Mixed Electrolyte Systems at 298.2 K: CsF + CsBr + H2O and CsF + CsNO3 + H2O Zhaodi Dou, Shuni Li,* Quanguo Zhai, Yucheng Jiang, and Mancheng Hu* Key Laboratory of Macromolecular Science of Shaanxi Province, School of Chemistry and Chemical Engineering, Shaanxi Normal University, Xi’ an, Shaanxi 710062, P. R. China Downloaded via UNIV OF LOUISIANA AT LAFAYETTE on September 23, 2018 at 03:30:55 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

S Supporting Information *

ABSTRACT: CsF + CsBr + H2O and CsF + CsNO3 + H2O mixed-electrolyte systems were investigated by the potentiometric method. The experimental data were modeled by connecting the Nernst equation with the Pitzer or Harned model. The mean ionic activity coefficients of CsF, γ±A, and CsBr or CsNO3, γ±B, were calculated. Moreover, other properties, such as mean ionic activity coefficients in pure and trace quantities (γ0 and γtr), osmotic coefficients, Φ, excess Gibbs energies, GE, and the change in excess Gibbs energy of the mixture, ΔGex m , were obtained and discussed.

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systems in the ionic strengths range of (0.01 to 0.70) mol·kg−1 is reported at 298.2 K. THe Harned model and the Pitzer model were used to obtain the mean ionic activity coefficients and other thermodynamic parameters for the mixed ternary systems.

INTRODUCTION Electrolyte solutions exist widely in nature and are highly regarded because of their wide application in the chemical, biological, and environmental industries.1,2 The design and optimization of industrial processes require a sufficient understanding of the behavior of the electrolyte solution.3 In recent years, numerous aqueous mixed-electrolyte systems containing chlorides were investigated by potentiometric method. For example, Bagherinia et al. studied the thermodynamic properties of CoCl2 + CoSO4 + H2O,4 MgCl2 + Mg(NO3)2 + H2O,5 and CoCl2 + Co(NO3)2 + H2O6 systems. Deyhimi et al. determined the thermodynamic properties of NH4Cl + LiCl + H2O,7 NaCl + MgCl2 + H2O,8 KCl + LiCl + H2O,9 and NH4Cl + CaCl2 + H2O10 systems. Sang et al. measured the mean activity coefficients of NaCl in NaCl + SrCl2 + H2O11 and NaCl + CdCl2 + H2O12 systems. Ghalami-Choobar et al. contributed not only to the thermodynamic properties of the quaternary (CaCl2 + Ca(NO3)2 + L-alanine + water)13 system but also to the systems containing ionic liquids ([EMIm]Br + LiBr + H2O).14 Moreover, the potentiometric studies on electrolytes in organic−water mixtures were also reported. For instance, Hernández-Luis et al. determined the mean activity coefficients of the system NaCl + trehalose/maltose/fructose/formamide + water.15−17 Lopes et al. reported the thermodynamic properties of NaCl + ethanol + water and KCl + ethanol + water.18,19 In our previous work, the phase behavior and activity coefficients of RbX/CsX (X = F, Cl) in organic solvent−water mixtures or in electrolyte systems20−22 were studied by potentiometric method. To continue our research, herein, a potentiometric investigation of the thermodynamic properties of the CsF + CsBr + H2O and CsF + CsNO3 + H2O mixed © XXXX American Chemical Society

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EXPERIMENTAL SECTION The descriptions of the chemicals are given in Table 1. CsF, CsBr, and CsNO3 with purity >99% were dried at 120 °C for use. Table 1. Chemicals Used in This Study chemical name CsF CsBr CsNO3

source Shanghai China Lithium Industrial Shanghai China Lithium Industrial Shanghai China Lithium Industrial

purity (mass fraction, stated by the supplier) >99% >99% >99%

purification method dried in vacuum dried in vacuum dried in vacuum

The solubility of CsF, CsBr, and CsNO3 in pure water is 35.6, 5.8, and 1.427 mol·kg−1 at 298.2 K.23 Ultrapure water was used in all experiments. Cesium-selective membrane electrode was prepared according to literature21 and evaluated as previously reported.22 The Cs-ISE was filled with 0.10 mol·L−1 CsF solution as the internal liquid. F-ISE was purchased from Jiangsu Electroanalytical Received: May 10, 2018 Accepted: September 10, 2018

A

DOI: 10.1021/acs.jced.8b00383 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 2. Values of the Pitzer Parameters for CsF, CsBr, and CsNO3 at T = 298.2 K25 electrolyte

β(0) (kg·mol−1)

β(1) (kg·mol−1)

Cϕ (kg2·mol−2)

mmax (mol·kg−1)

ref

CsF CsBr CsNO3 CsF

0.1306 0.0279 −0.0758 0.1165

0.257 0.0139 −0.0669 0.2444

−0.0043 0.00004

3.2 5 1.4 0.7

25 25 25 this work

−0.0043

Instrument. The electrode pairs were calibrated to evaluate whether they were suitable for subsequent experiments. The cells used for calibration and measurement were as follows (a) Cs-ISE | CsF (mA0) | F-ISE (b) Cs-ISE | CsBr/CsNO3 (mB0) | F-ISE (c) Cs-ISE | CsF (mA), CsBr/CsNO3 (mB) | F-ISE in which, subscripts A and B refer to CsF and CsBr/CsNO3, m is the molality of electrolytes, and mA0 and mB0 refer to the value in pure water. First, cell (a) was used to determine the Nernst response of the electrode pair (Cs-ISE and F-ISE). Second, cell (b) was designed to describe the selectivity coefficient of the electrode pair to Br−/NO3−. Finally, cell (c) was performed to obtain the electromotive forces for CsF + CsBr/CsNO3 + H2O solutions. The whole experiment was performed at a constant temperature of 298.2 K using a thermostatic water bath. Samples were weighed using an analytical balance (Mettler Toledo-AL 204, Switzerland). The potentiometric determination was processed by a pH/mV meter (Orion-868, America).

Table 4. Adjustable Parameters of the Harned Model for the CsF + CsBr + H2O and CsF + CsNO3 + H2O Systems at T = 298.2 K and p = 0.1 MPaa I (mol·kg−1) 0.0100 0.0300 0.0600 0.1200 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.0100 0.0300 0.0600 0.1200 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000

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RESULTS AND DISCUSSION Calibration of the Electrode Pair. For cell (a), the Nernst equation can be written as

ln γ±A0

αAB

CsF + CsBr + H2O −0.1046 ± 0.0006 0.0235 ± 0.0005 −0.1552 ± 0.0009 0.0316 ± 0.0005 −0.1958 ± 0.0011 0.0431 ± 0.0004 −0.2485 ± 0.0008 0.0525 ± 0.0011 −0.2865 ± 0.0006 0.0752 ± 0.0015 −0.3162 ± 0.0004 0.0948 ± 0.0011 −0.3335 ± 0.0027 0.1147 ± 0.0001 −0.3447 ± 0.0024 0.1342 ± 0.0054 −0.3526 ± 0.0024 0.1557 ± 0.0068 −0.3573 ± 0.0041 0.1743 ± 0.0086 CsF + CsNO3 + H2O −0.1083 ± 0.0001 0.0066 ± 0.0003 −0.1569 ± 0.0001 0.0058 ± 0.0001 −0.1990 ± 0.0002 0.0138 ± 0.0004 −0.246 ± 0.0014 0.0290 ± 0.0013 −0.2827 ± 0.0007 0.0759 ± 0.0006 −0.3171 ± 0.0017 0.1267 ± 0.0024 −0.3377 ± 0.0067 0.1796 ± 0.0104 −0.3529 ± 0.0109 0.2302 ± 0.0199 −0.3629 ± 0.0143 0.2790 ± 0.0269 −0.3706 ± 0.0176 0.3223 ± 0.0335

σ 0.0006 0.0021 0.0018 0.0016 0.0012 0.0026 0.0034 0.0034 0.0033 0.0049 0.0002 0.0000 0.0008 0.0018 0.0010 0.0016 0.0063 0.0099 0.0132 0.0163

ln γ±A0 and αAB are the results of the linear fit by the Harned model. The expanded uncertainties are U(I) = 0.0002 mol·kg−1, U(T) = 0.1 K, and U(p) = 3 kPa (0.95 level of confidence). a

Figure 1. Response of Cs-ISE and F-ISE electrode pairs in pure water for the CsF + CsBr + H2O and CsF + CsNO3 + H2O systems at T = 298.2 K.

Table 3. Nernst Response Results of the Electrode Pair CsISE and F-ISE at T = 298.2 K and p = 0.1 MPa system

E0/mV

k

σ

R2

CsF + CsBr + H2O CsF + CsNO3 + H2O

146.8 ± 0.1 85.5 ± 0.1

25.30 ± 0.04 25.37 ± 0.04

0.36 0.35

0.9999 0.9999

Figure 2. Plot of lnγ±A against ionic strength fractions yB in the system CsF + CsBr + H2O at T = 298.2 K (■, I = 0.0100; □, I = 0.0300; ●, I = 0.0600; ○, I = 0.1200; ▲, I = 0.2000; △, I = 0.3000; ▼, I = 0. 4000; ▽, I = 0.5000; ◆, I = 0.6000; ◇, I = 0.7000).

E0 is the standard potential. k is the Nernst response slope. σ is the standard deviation of the fitting. R2 is the determination coefficient. The expanded uncertainties are U(E0) = 0.2 mV, U(T) = 0.1 K, and U(p) = 3 kPa (0.95 level of confidence). a

Ea = E0 + 2k ln(mA0γ±A0)

(1)

in which E is the electromotive force, Ea represents the values of cell (a), and E0 is the standard potential. k = 25.69 mV refers to B



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Table 5. Values of the Mixing Interaction Parameters of the Pitzer Equation for the CsF + CsBr + H2O and CsF + CsNO3 + H2O Systems at T = 298.2 K and p = 0.1 MPaa system CsF + CsBr + H2O

a

CsF + CsNO3 + H2O

I/mol·kg−1

θF,Br

ΨCs,F,Br

σ

θF,NO3

ΨCs,F,NO3

σ

0.0100−0.7000

−0.09266

−0.1154

0.34

0.05977

−0.80109

0.59

Expanded uncertainties are U(I) = 0.0002 mol·kg − 1 , U(T) = 0.1 K, and U(p) = 3 kPa (0.95 level of con-

fidence).SD =

0.5

( n −1 1 ∑in=1 (Eexp − Ecal)2 )

the theoretical Nernst slope at 298.2 K. mA0 and γ±A0 are the molality and activity coefficient of CsF in pure water. By employing the Pitzer equation24 and the Pitzer ionic interaction parameters25 (listed in Table 2), γ±A0 can be calculated. E0 and 2k are the fitting parameters from eq 1, which can be calculated by plotting Ea versus ln αA0 (αA0 = mA0γ±A0) with linear regression, as shown in Figure 1. E0 and k (listed in Table 3) are 146.8 mV and 25.30 for the CsF + CsBr + H2O system and 85.5 mV and 25.37 for the CsF + CsBr + H2O system, respectively. Figure S1 plots the activity coefficient of CsF in pure water (γ±A0) in this work and ref 26, which suggests a good agreement. From the above experimental results, we can decide that the electrode pair (Cs-ISE and F-ISE) can be applied to the measurements in mixed-electrolyte solutions. Determination of the Thermodynamic Properties. Because of the selective permeation of ion-selective electrode, the selective coefficient Kpot of the F-ISE for Br−/NO3− ion was determined by separate solution method27 using cell (b). Kpot can be calculated according to K pot = [exp(E b − E0)/k ] /[(mB0γ±B0)2 ]

in which αAB, βAB, ... are adjustable Harned coefficients. γ±A and γ±A0 have the same meaning as in the Nernst equation. The fitting results of eq 5 with an adjustable parameter are given in Table 4. Figure 2 and Figure S2 show the natural logarithm of the experimental activity coefficients of CsF versus the ionic strength fraction, yB, for the mixed ternary systems of CsF + CsBr + H2O and CsF + CsNO3 + H2O. The results show a good linear relationship, indicating that CsF obeys the Harned model. Moreover, with increasing the total ionic strength, I, ln γ±A decreases. The Pitzer model28 is widely applied for single and mixedelectrolyte solutions to explain the ion interactions in solution. In this work, the rearranged equation by Harvie and Weare29 is applied as follows ln γ±A = (2mA + mB)βA(0) + mBβB(0) + (2mA + mB) g (2 I )βA(1) + mBg (2 I )βB(1) + (1.5mA 2 + 2mA mB + 0.5mB2)CΑϕ + mB(mA + mB)C Bϕ + mBθ + mB Eθ

(2)

where KPot is the selectivity coefficient. Subscript b and B are the corresponding values for cell (b) and electrolyte B (CsBr/ CsNO3). In our experiments, different mB0 was chosen to determine Eb and calculate KPot. After calculation, the mean value of KPot is much smaller than 1.0 × 10−4, which suggests that the electrode pair almost has no response to Br− or NO3−. Cell (c) was applied to determine the electromotive forces of the CsF + CsBr + H2O and CsF + CsNO3 + H2O mixed systems with different ionic strength (I = mA + mB) and ionic strength fraction (yB = mB/(mA+ mB). The Nernst equation of cell (c) has the following form

+ (mA mB + 0.5mB2)ψ + F

ln γ±B = (mA + mB)mA CAϕ + (0.5mA2 + 2mA mB + 1.5mB2) C Bϕ + mA βA(0) + (mA + 2mB)βB(0) + 21/2 /2(mA + 2mB)2 CAϕ + mA g (2 I )βA(1) + mA θ + (mA + 2mB)g (2 I )βB(1) + mA Eθ + (0.5mA2 + 1.5mA mB)ψ + F

+ (mA + mB)g ′(2 I )(mA βA(1) + mBβB(1))/I

where γ is the mean activity coefficient, A is for CsF, and B is for CsBr/CsNO3. Moreover, because of the negligible value of KPot, eq 3 can be written as

+ 2mA mBEθ′

(8)

ϕ = [mA (mA + mB)βA(0) + mB(mA + mB)βB(0)

or

+ mA (mA + mB) exp( −2 I )βA(1) + mB(mA + mB)

ln γ±A = (Ec − E0)/(2·k) − 1/2 ln[mA ·(mA + mB)]

exp( − 2 I )βB(1) + mA (mA + mB)2 CAϕ + mB

(4)

Thus the activity coefficients of CsF in mixed solutions, γ±A, for CsF + CsBr + H2O and CsF + CsNO3 + H2O systems can be calculated. The Harned model3 was also frequently used to obtain the mean ionic activity coefficients in mixed-electrolyte solutions. If the total ionic strength of the mixed solution remains unchanged, then the Harned model can be derived ln γ±A = ln γ±A0 − αAB·y B−βAByB2 − ···

(7)

F = −Aϕ[ I /(1 + 1.2 I ) + 2 ln(1 + 1.2 I )/1.2]

Ec = E0 + k · ln[γ±2A · mA · (mA + mB) + K Pot· γ±2B· mB · (mA + mB)] (3)

Ec = E0 + k· ln[γ±2A ·mA ·(mA + mB)]

(6)

(mA + mB)2 C Bϕ + 2mA mB(Eθ + θ + Eθ′I ) + 2mA mB(mA + mB)ψ − Aϕ I /(1 + 1.2 I )] /(mA + mB) + 1.0

(9)

Aϕ is called the Debye−Hückel constant with a value of 0.39209 at 298.2 K.30 Eθ and Eθ′ are the unsymmetrical higher-order electrostatic terms.31 Parameters Eθ and Eθ′ are zero for the systems of 1−1 and 1−1 mixed electrolytes. Pitzer parameters

(5) C



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Table 6. Electromotive Force, Eexp, the Experimental Mean Activity Coefficients of CsF, γ±A(CsF), the Calculated Mean Activity Coefficients of CsBr/CsNO3, γ±B (CsBr/CsNO3), the Osmotic Coefficients, Φ, and the Excess Gibbs Free Energies, GE, by the Pitzer Model for the CsF + CsBr + H2O and CsF + CsNO3 + H2O Systems at T = 298.2 K and p = 0.1 MPaa CsF + CsBr + H2O −1

−1

−1

I (mol·kg )

mA (mol·kg )

0.0020 0.0041 0.0062 0.0105 0.0149 0.0194 0.0308 0.0400 0.0602 0.1206 0.1993 0.3000 0.3997 0.4995 0.5992 0.6998

0.0020 0.0041 0.0062 0.0105 0.0149 0.0194 0.0308 0.0400 0.0602 0.1206 0.1993 0.3000 0.3997 0.4995 0.5992 0.6998

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0.0102 0.0294 0.0603 0.1205 0.1998 0.3000 0.3996 0.4999 0.6000 0.7001

0.0071 0.0206 0.0422 0.0844 0.1399 0.2100 0.2797 0.3499 0.4200 0.4901

0.0031 0.0088 0.0181 0.0362 0.0600 0.0900 0.1199 0.1500 0.1800 0.2100

0.0100 0.0305 0.0594 0.1197 0.1997 0.3002 0.4000 0.4998 0.6000 0.6998

0.0040 0.0122 0.0238 0.0479 0.0799 0.1201 0.1600 0.1999 0.2400 0.2799

0.0060 0.0183 0.0356 0.0718 0.1198 0.1801 0.2400 0.2999 0.3600 0.4199

0.0100 0.0293 0.0603 0.1198 0.1997 0.2997 0.3998 0.5004 0.6001 0.7001

0.0010 0.0029 0.0060 0.0120 0.0200 0.0300 0.0400 0.0500 0.0600 0.0700

0.0090 0.0264 0.0543 0.1078 0.1798 0.2697 0.3598 0.4504 0.5401 0.6301

I (mol·kg−1)

mA (mol·kg−1)

mB (mol·kg−1)

yB = 0.00 0.0016 0.0031 0.0050 0.0106

0.0016 0.0031 0.0050 0.0106

mB (mol·kg )

0 0 0 0

Eexp (mV) yB = 0.00 −172.0 −135.0 −114.7 −88.8 −72.0 −59.3 −37.1 −24.7 −5.3 27.2 50.7 69.9 83.7 94.4 103.2 110.9 yB = 0.30 −99.9 −48.7 −14.7 17.5 40.8 59.6 72.7 83.2 91.7 98.9 yB = 0.60 −115.4 −61.7 −30.4 2.0 25.3 43.7 56.7 66.8 75.0 81.9 yB = 0.90 −150.6 −99.2 −65.3 −33.7 −10.8 7.4 20.3 30.2 38.0 44.8 CsF + CsNO3 + H2O

γ±A

γ±B

0.952 0.934 0.921 0.901 0.886 0.874 0.851 0.836 0.813 0.773 0.746 0.728 0.718 0.713 0.711 0.711

Φ

GE (J·mol−1)

0.984 0.978 0.974 0.968 0.963 0.960 0.953 0.949 0.943 0.935 0.933 0.935 0.940 0.945 0.952 0.959

−0.32 −0.95 −1.74 −3.78 −6.24 −9.08 −17.54 −25.30 −44.74 −115.27 −223.79 −377.79 −539.52 −706.35 −874.80 −1044.92

0.895 0.852 0.814 0.769 0.735 0.710 0.691 0.680 0.670 0.662

0.899 0.844 0.796 0.743 0.701 0.665 0.639 0.618 0.600 0.584

0.967 0.950 0.937 0.924 0.916 0.911 0.908 0.906 0.904 0.903

−3.63 −16.78 −46.32 −120.73 −239.22 −409.61 −594.84 −793.32 −1000.67 −1215.93

0.888 0.839 0.801 0.754 0.717 0.686 0.666 0.650 0.637 0.626

0.899 0.839 0.793 0.738 0.693 0.655 0.628 0.605 0.587 0.570

0.966 0.947 0.933 0.916 0.903 0.893 0.886 0.880 0.874 0.869

−3.58 −18.12 −46.82 −125.07 −253.14 −440.20 −647.23 −871.46 −1110.98 −1362.89

0.882 0.833 0.791 0.744 0.702 0.671 0.649 0.630 0.613 0.601

0.898 0.840 0.789 0.732 0.686 0.647 0.619 0.597 0.579 0.564

0.966 0.946 0.929 0.910 0.895 0.882 0.874 0.867 0.861 0.857

−3.65 −17.47 −49.34 −130.47 −266.54 −466.50 −691.49 −937.27 −1197.09 −1472.14

Eexp (mV)

γ±A

γ±B

Φ

GE (J·mol−1)

−244.4 −209.9 −187.8 −150.9

0.957 0.941 0.928 0.901

D

0.986 0.981 0.976 0.968

−0.29 −0.80 −1.51 −3.85



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Table 6. continued CsF + CsNO3 + H2O I (mol·kg−1) yB = 0.00 0.0145 0.0204 0.0302 0.0401 0.0599 0.1193 0.2002 0.2999 0.3998 0.5002 0.6000 0.7000 yB = 0.30 0.0100 0.0305 0.0600 0.1217 0.1999 0.2999 0.4002 0.5000 0.5999 0.7001 yB = 0.60 0.0100 0.0299 0.0602 0.1198 0.2000 0.2997 0.4001 0.4999 0.5999 0.7000 yB = 0.90 0.0098 0.0301 0.0599 0.1198 0.2000 0.3002 0.3998 0.4998 0.6001 0.7001

mA (mol·kg−1)

mB (mol·kg−1)

Eexp (mV)

γ±A

γ±B

Φ

GE (J·mol−1)

0.964 0.959 0.953 0.949 0.943 0.935 0.933 0.935 0.940 0.945 0.952 0.959

−6.19 −9.63 −16.73 −25.70 −44.39 −113.80 −225.03 −377.59 −539.86 −707.30 −876.17 −1045.18

0.0145 0.0204 0.0302 0.0401 0.0599 0.1193 0.2002 0.2999 0.3998 0.5002 0.6000 0.7000

0 0 0 0 0 0 0 0 0 0 0 0

−135.5 −119.0 −100.1 −86.5 −67.4 −34.8 −10.4 8.4 22.2 33.0 41.9 49.5

0.887 0.872 0.852 0.836 0.814 0.774 0.746 0.728 0.718 0.713 0.711 0.711

0.0070 0.0213 0.0420 0.0852 0.1399 0.2099 0.2801 0.3500 0.4199 0.4901

0.0030 0.0091 0.0180 0.0365 0.0600 0.0900 0.1200 0.1500 0.1800 0.2100

−162.7 −108.7 −76.6 −43.5 −20.8 −2.8 9.6 19.2 27.0 33.6

0.896 0.853 0.816 0.772 0.736 0.699 0.669 0.647 0.629 0.614

0.897 0.834 0.783 0.716 0.659 0.603 0.555 0.512 0.471 0.432

0.967 0.949 0.936 0.921 0.908 0.895 0.882 0.867 0.850 0.830

−3.55 −17.95 −47.44 −127.90 −256.34 −450.05 −672.59 −920.60 −1194.06 −1494.39

0.0040 0.0120 0.0241 0.0479 0.0800 0.1199 0.1600 0.2000 0.2400 0.2800

0.0060 0.0179 0.0361 0.0719 0.1200 0.1798 0.2401 0.3000 0.3599 0.4200

−177.0 −124.0 −90.8 −58.7 −36.0 −18.8 −6.8 1.9 9.0 15.0

0.894 0.852 0.814 0.769 0.721 0.675 0.641 0.609 0.584 0.563

0.895 0.831 0.775 0.706 0.643 0.585 0.536 0.494 0.455 0.419

0.966 0.946 0.929 0.908 0.887 0.866 0.843 0.820 0.793 0.764

−3.69 −18.30 −50.69 −137.50 −287.81 −517.24 −789.19 −1098.10 −1444.70 −1829.54

0.0010 0.0030 0.0060 0.0120 0.0200 0.0300 0.0400 0.0500 0.0600 0.0700

0.0088 0.0271 0.0539 0.1079 0.1800 0.2702 0.3598 0.4498 0.5401 0.6301

−213.4 −158.9 −126.5 −94.4 −72.4 −55.8 −44.6 −36.1 −29.4 −23.8

0.892 0.851 0.809 0.761 0.704 0.650 0.609 0.576 0.547 0.524

0.894 0.827 0.769 0.695 0.630 0.571 0.524 0.485 0.451 0.421

0.965 0.941 0.921 0.895 0.870 0.845 0.824 0.803 0.782 0.761

−3.67 −19.38 −53.71 −149.82 −319.73 −585.24 −898.56 −1258.05 −1660.27 −2101.80

a I is the total ionic strength in pure water or mixed solution, I = mA + mB. mA is the molality of CsF in pure water or mixed solution (moles of CsF per kilogram of water). mB is the molality of CsBr/CsNO3 in pure water or mixed solution (moles of CsBr or CsNO3 per kilogram of water). yB is the ionic strength fractions of CsBr/CsNO3 in pure water or mixed solution, yB = mB/(mA + mB). Expanded uncertainties are U(I) = 0.0002 mol· kg−1, U(E) = 0.2 mV, U(γ) = 0.02, U(Φ) = 0.02, U(GE) = 0.02, U(T) = 0.1 K, and U(p) = 3 kPa (0.95 level of confidence).

for electrolytes in pure water are taken from the literature.25 θF,Br/NO3 and ψCs,F,Br/NO3 are ionic interaction parameters. In this paper, θF,Br/NO3 and ψCs,F,Br/NO3 are obtained through the method described by Khoo et al.32 by utilizing all of the experimental data in a least-squares fitting. The results are listed in Table 5. Hence, the mean ionic activity coefficients from Pitzer model are calculated and shown in Table 6. The relation between γ±A and I is given in Figure 3a and Figure S3. At a given yB, γ±A decreases

with increasing I. That is, more electrolytes are added to the solution with increasing I. Thus the ion−ion interaction (association) plays a dominant role in the solution. γ±A decreases when the ionic strength fraction, yB, changes from 0.0 to 0.9. This suggests that Br− or NO3− replaces F− ions in the mixed solution, resulting in the lower effective concentration of CsF in the mixed solution. Figure 3b and Figure S4 are the plots of the activity coefficients of electrolyte B, γ±B, versus the ionic E



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Figure 5. Plot of ln γ against total ionic strength, I, in the system CsF + CsBr + H2O at T = 298.2 K (■, ln γ±A0(CsF); ○, ln γ±Atr(CsF); ▲, ln γ±B0(CsBr/CsNO3); ▽, ln γ±Btr(CsBr/CsNO3)).

Figure 3. Plot of γ±A (a) and γ±B (b) against total ionic strength, I, in the systems CsF + CsBr + H2O at T = 298.2 K (□, yB = 0.00; ○, yB = 0.30; △, yB = 0.60; ▽, yB = 0.90).

Figure 6. Plot of ΔGex m against yB in the systems CsF + CsBr + H2O at T = 298.2 K (□, I = 0.10 mol·kg−1; ○, I = 0.30 mol·kg−1; △, I = 0.50 mol· kg−1; ▽, I = 0.70 mol·kg−1).

strength, I, for the investigated systems. The variation of γ±B is similar to that of γ±A when increasing yB in the solution. That is, Br− or NO3− replaces the F− ions, decreasing both γ±A and γ±B. Moreover, the degree of activity changing with yB for γ±A is more sensitive than that of γ±B. This could be caused by the competition of association and solvation. The ion−ion interaction (association) is influenced by the radius of the ion (the crystal radius of the ions, r(F−) = 1.36 Å, r(Br−) = 1.95 Å, r(NO3−) = 2.64 Å).33 Meanwhile, solvation effect (ion−solvent interaction) is also dependent on the radius of the ion. For example, hydration free energies, ΔhydG* of Br− (−315 kJ· mol−1) and NO3− (−300 kJ·mol−1) are much smaller than those of F− (−465 kJ·mol−1).34 Increasing yB strongly affects the interaction between Cs+ and F− because of the smaller radius of F−. However, for the changing of γ±B, more electrolyte B in the

Figure 4. Comparisons of γ±A and γ±B at ionic strength fraction yB = 0.30 at T = 298.2 K (□, CsF + CsBr + H2O; ○, CsF + CsNO3 + H2O). F



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The change in excess Gibbs energy of the mixture, ΔGex m , can be given by the following equation38−41

solution is equal to the increasing concentration of B. The association and hydration lead to the decreasing trend of γ±B changing with yB. Figure S5 is the plot of the osmotic coefficients, Φ, versus ionic strength, I. It can be observed that Φ is reduced with increasing yB and increasing I. Moreover, plots of γ±A and γ±B versus ionic strength I at yB = 0.30 for CsF + CsBr + H2O and CsF + CsNO3 + H2O systems are given in Figure 4. γ±A and γ±B for CsF + CsBr + H2O system are always bigger than those for CsF + CsNO3 + H2O system. This is caused by the smaller radius and larger hydration free energies of Br− than those of NO3−. Comparisons of γ±A at yB = 0.30 for systems CsF + CsBr + H2O in this work and CsF + CsCl + H2O in ref 35 are depicted in Figure S6. It can be seen that γ±A in the CsF + CsBr + H2O system are smaller than those in the CsF + CsCl + H2O system. This is also the result of the competition between the cation−anion interaction (dependent on the radius of ion) and the hydration ability of ion (dependent on the hydration free energies). The smaller radius (r(Cl−) = 1.81 Å)33 and stronger hydration ability (ΔhydG* of the Cl− is −340 kJ·mol−1)34 of Cl− than Br− lead to the smaller activity coefficients in CsF + CsCl + H2O than those in the CsF + CsBr + H2O system. The comparison of the osmotic coefficients, Φ, at yB = 0.30 is depicted in Figure S7. It shows a similar changing trend as γ±A and γ±B. To consider the influence of one electrolyte on the other in the mixed-electrolyte solutions, the activity coefficients under extreme conditions (in pure or in the trace) can be evaluated.36,37 When the electrolyte is in pure water, the activity coefficient can be marked as γi0 (mi = I), whereas when the electrolyte is in the trace, the influence of the other electrolyte becomes greatest at mi = 0, corresponding to the activity coefficient γitr. Using eqs 6 and 7, values of ln γ at limits for CsF (yB = 0 and yB = 1) and for CsBr/CsNO3 (yB = 1 and yB = 0) are plotted in Figure 5 and Figure S8. First, ln γ0 and ln γtr both decrease with the increase in ionic strength, I, which means that the ion−ion interaction increases with more electrolytes in the mixed solution. For electrolyte A (CsF), the curve of ln γA0 lies above ln γAtr, which indicates that the replacement of F− by Br−or NO3− increases the ion−ion interaction and decrease the ion−solvent interaction. However, for CsBr and CsNO3, ln γB0 is less than ln γBtr, which suggests that the ion−solvent interaction is of dominance as Br− or NO3− replacing F−. Therefore, the overall trend of γ0 and γtr is a net effect of ion−ion interaction and ion−solvent interaction. The excess Gibbs free energy, GE, is usually used to express the deviations of aqueous electrolyte solution properties from the ideal solution properties. For the mixed-electrolyte solution, GE can be calculated by the following equation

ΔGmex = RTI 2yB (1 − yB )[g0 + I(1 − 2yB )g1]

(11)

in which all of the symbols have their usual meanings. The trends of ΔGex m changing with the ionic strength, I, are plotted in Figure 6 and Figure S10. With increasing the total ionic strength, I, ΔGex m first decreases and then increases with a minimum at yB = 0.5. The symmetrical figures suggest that the binary interactions are of importance in the investigated systems.28

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CONCLUSIONS The potentiometric method was employed to investigate the thermodynamic properties of the CsF + CsBr + H2O and CsF + CsNO3 + H2O mixed-electrolyte systems at 298.2 K. Pitzer ioninteraction model was used to model the two systems and determine the CsF mean activity coefficients and Pitzer mixing ionic interaction parameters, θF,Br/NO3 and ψCs,F,Br/NO3. The mean ionic activity coefficients of CsF decrease with increasing the ionic strength and the concentration of CsBr/CsNO3 in the mixed-electrolyte solution. Moreover, the mean ionic activity coefficients of CsF, γ±A, in the CsF + CsBr + H2O system are bigger than those in the CsF + CsNO3 + H2O system.

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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.8b00383.

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Plots of activity coefficient of CsF in pure water; plots of ln γ±A from Harned model; plots of γ±A and γ±B; osmotic coefficients, Φ; comparison of Φ and GE from Pitzer model; plots of the extreme activity coefficients γ0 and γtr; and the change in excess Gibbs energy of the mixture, ΔGex m , for mixed electrolyte systems at T = 298.2 K and p = 0.1 MPa (PDF)

AUTHOR INFORMATION

Corresponding Authors

*S.L.: Tel: +86-29-81530767. Fax:+86-29-81530727. E-mail: [email protected]. *M.H.: E-mail: [email protected]. ORCID

Shuni Li: 0000-0002-6614-9241 Quanguo Zhai: 0000-0003-1117-4017 Mancheng Hu: 0000-0003-2920-0439 Funding

GE = 2RT[mA (1 − ϕ + ln γ±A ) + mB(1 − ϕ + ln γ±B)]

This work was supported by the National Natural Science Foundation of China (nos. 21571120 and U1607116) and the Fundamental Research Funds for the Central Universities (GK201701003)

(10)

The calculated GE was listed in Table 6. Figure S9 is the plot of GE versus I for CsF + CsBr + H2O and CsF + CsNO3 + H2O systems. It can be seen that GE values are always less than zero for both the binary system (yB = 0) and ternary systems. Moreover, GE decreases with increasing I and yB. This means that the mixing process is easier when more electrolytes are added to the mixed solution. Figure S7 is the graphical comparison of GE at yB = 0.30 for CsF + CsBr + H2O and CsF + CsNO3 + H2O as a function of ionic strength, I. It shows a larger value for the system CsF + CsBr + H2O than for CsF + CsNO3 + H2O.

Notes

The authors declare no competing financial interest.

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REFERENCES

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Potentiometric Investigation of the Thermodynamic Properties of Mixed

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