Activity Coefficients of RbF in the RbF + RbBr + H2O and RbF +

Sep 23, 2016 - Key Laboratory of Macromolecular Science of Shaanxi Province, School of Chemistry and Chemical Engineering, Shaanxi Normal University, ...
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Activity Coefficients of RbF in the RbF + RbBr + H2O and RbF + RbNO3 + H2O Ternary Systems Using the Potentiometric Method at 298.2 K Xiaoting Huang, Shu’ni 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 S Supporting Information *

ABSTRACT: Thermodynamic properties of the RbF + RbBr + H2O and RbF + RbNO3 + H2O systems were determined by the potentiometric method at the total ionic strengths ranging from 0.0017 to 0.7005 mol·kg−1 for different ionic strength fractions yB of RbBr/RbNO3 with yB = 0.00, 0.30, 0.60, and 0.90, at 298.2 K. Combining the Nernst equation and Pitzer equation, the mean ionic activity coefficients of RbF and RbBr/RbNO3, the osmotic coefficients, and the excess Gibbs energies of the studied systems were calculated.

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INTRODUCTION The determination of the thermodynamic properties of the mixed-electrolyte systems is of great importance in the progress of thermodynamic theories and process design. On the other hand, it is also essential in the industrial chemistry, marine chemistry, and geological or biological processes. In the past few decades, many techniques have been used to study the thermodynamic properties of electrolytes in aqueous solutions, such as the isopiestic method,1,2 the hygrometric method,3−5 the potentiometric method,6−16,18,19 and so on. The potentiometric method was widely used to investigate the thermodynamic properties of electrolytes in aqueous solutions because of the simplicity and high speed. Using this method, the thermodynamic properties of many mixed electrolyte systems containing alkaline halides and ammonia halides have been explored. For example, Galleguillos-Castro et al.11 and Sirbu et al.12 both reported the thermodynamic properties of the NaCl+ Na2SO4 + H2O system by the potentiometric method at different temperatures. The activity coefficient of NaCl in the NaCl + Na2HCit + H2O ternary mixed-electrolyte system at multiple temperatures was studied by Ghalami-Choobaret al.13 Sang et al.14−16 determined the mean ionic activity coefficients of KBr in the KBr + K2SO4 + H2O and KBr + K2B4O7 + H2O systems and NaBr in the NaBr + SrBr2 + H2O system by potentiometric method at 298.15 K. In addition, the water activity of system containing iodide, KI + KNO3 + H2O, was measured by Galleguiloset al.17 with an electronic hydrometer at 298.15 K. Moreover, due to the similarity of NH4+ and alkaline metals, the thermodynamic properties of NH4Cl + CaCl2 + H2O and NH4Br + NaBr + © XXXX American Chemical Society

H2O mixed-electrolyte systems at 298 K were reported by Deyhimi et al.18,19 In our previous work, the thermodynamic properties of mixed-electrolyte systems containing RbCl or CsCl, such as RbCl + Rb2SO4/RbNO3 + H2O20,21 and CsCl + CaCl2/MgCl2 + H2O,22,23 were reported. However, the thermodynamic properties of heavy alkaline metal fluorides in mixed-electrolyte systems are not reported to date. As a continuation of our research, in this work, the thermodynamic properties of the RbF + RbBr + H2O and RbF + RbNO3 + H2O ternary mixedelectrolyte systems were studied at 298.2 K through potentiometric measurements. The Pitzer model was used to fit the experimental data. The mean ionic activity coefficients, the osmotic coefficients, and the excess Gibbs free energies of the investigated systems were obtained.

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EXPERIMENTAL SECTION

Materials. Characterizations of all chemicals used in this work were listed in Table 1. The purity of the samples is greater than 99% (by mass fraction) as stated by the supplier. RbF, RbBr, and RbNO3 were dried in vacuum for 24 h at T = 393.2 K and stored in a desiccator before use. The solubility of RbF, RbBr, and RbNO3 in the water are 28.72 mol·kg−1 (0.75024 by mass at 293.2 K), 7.04 mol·kg−1 (0.53824 by mass at 298.2 K), and 4.41 mol·kg−1 (0.39424 by mass at 298.2 K), respectively. Received: May 16, 2016 Accepted: September 14, 2016

A

DOI: 10.1021/acs.jced.6b00398 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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water in this work and the reference27 is shown in Figure S2. Hence, the electrode pairs can be used for the electromotive measurements in this work. Determination of the F-ISE Selectivity Coefficient. The selective coefficient Kpot was calculated based on the following equation:

Table 1. Characterizations of All Chemicals Used in This Study compound RbF RbBr RbNO3

source

specification

purity (mass fraction)

purification method

A.R.

>99%

none

A.R.

>99%

none

Shanghai China Lithium Industrial Co., Ltd. Shanghai China Lithium Industrial Co., Ltd. Shanghai China Lithium Industrial Co., Ltd.

A.R.

>99%

K pot = [exp(E b − E0)/k]/[(mB0γ±B0)2 ]

(2)

where KPot indicates the selectivity coefficient of the F-ISE for Br−/NO3− ions. Eb stands for the EMF value of cell b. γ±B0 represents the mean activity coefficient of RbBr/RbNO3 as single salts in pure water at 298.2 K. The calculated results of KPot are much smaller than 1.0 × 10−4. The Pitzer Model. Cell c was used to determine the EMF values of the RbF + RbBr + H2O and RbF + RbNO3 + H2O ternary systems at 298.2 K and at different ionic strength I = mA + mB and ionic strength fraction yB = mB/(mA + mB). The Nernst equation of cell c has the following form:

none

Stock aqueous solutions of the mixed electrolyte were prepared by weight. Apparatus and Procedure. The Rb ion-selective electrode (Rb-ISE) and F-ISE were used in this work. The cells are as follows: Rb − ISE|RbF(mA0)|F − ISE

(a)

Ec = E0 + k ln[γ±2AmA (mA + mB) + K Potγ±2BmB(mA + mB)]

Rb − ISE|RbBr/RbNO3(mB0)|F − ISE

(b)

(3)

Rb − ISE|RbF(mA ), RbBr/RbNO3(mB)|F − ISE

(c)

where γ±A and γ±B are the mean activity coefficients of RbF and RbBr/RbNO3, respectively. Moreover, by neglecting the second term in the above equation because of such a small value of KPot, eq 3 can be simplified as

where mA0 and mA are the molalities of RbF in pure water and in the mixed solution, while mB0 and mB are the molalities of RbBr/RbNO3 in pure water and in the mixed solution, respectively. First, cell a was performed to calculate the Nernst response of the electrode pair. Second, cell b was used to determine the selectivity coefficient of the electrode pair. Finally, cell c was applied for the mixed-electrolyte solution with a series of different ionic strength fractions (yB) of RbBr/ RbNO3. All measurements were carried out in a double-walled glass vessel with the temperature control of 298.2 K. The electromotive force (EMF) measurements were obtained using a pH/mV meter (Orion-868, USA). In general, the EMF readings were taken with a fluctuation of 0.1 mV. To avoid fatigue of the electrodes, the whole experiment process was performed within 1.5 h.

Ec = E0 + k ln[γ±2AmA (mA + mB)]

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

Thus, the mean activity coefficients of RbF in the mixedelectrolyte solutions were obtained as given in Table 2. Harvie and Weare28 reorganized the Pitzer equation to simplify in calculating the activity coefficients for mixed electrolyte systems. Thus, the mean ionic activity coefficients and the osmotic coefficients can be given as follows:

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ln γ±A = (2mA + mB)βA(0) + mBβB(0) + (2mA + mB)g (2 I )

RESULTS AND DISCUSSION Calibration of the Electrode Pair Rb-ISE and F-ISE. The Nernst equation for cell a is Ea = E0 + 2k ln(mA0γ±A0)

(4)

βA(1) + mBg (2 I )βB(1) + (1.5mA + 2mB + 0.5mB2) CAϕ + mB(mA + mB)C Bϕ + mBθ + mB Eθ

(1)

+ (1.5mA mB + 0.5mB2)ψ + F

where Ea and E0 are the EMF readings and the standard potential of cell a, respectively. k = RT/F indicates the Nernst theoretical slope, and R, T, and F represent the universal gas constant, absolute temperature, and Faraday constant, respectively. γ±A0 is the mean ionic activity coefficient of RbF in pure water and mA0 is the molality of RbF in pure water. The values of γ±A0 were obtained through the Pitzer equation.25 The Pitzer ionic interaction parameters of RbF in pure water26 are listed in Table S1. Ea and mA0 are listed in Table 2. The relation between Ea and ln αA0 (the activity of RbF in pure water) is shown in Figure S1. Through linear regression, the values of E0, k, the standard deviation of the fitting (σ), and the linear correlation coefficient (R2) were calculated and given in Table S2. The obtained values of k for the two systems are close to the theoretical one of 25.69 mV (k = RT/F) of the Nernst slope. The comparison of the activity coefficient of RbF in pure

(5)

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

(6)

F = −Aϕ[ I /(1 + 1.2 I ) + 2 ln(1 + 1.2 I )/1.2] + (mA + mB)g ′(2 I )(mA βA(1) + mBβB(1))/I + 2mA mBEθ′ B

(7) DOI: 10.1021/acs.jced.6b00398 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 2. Electromotive Force Eexp, the Mean Activity Coefficients γ±A for RbF, and γ±B for RbBr/RbNO3, the Osmotic Coefficients Φ, and Excess Gibbs Free Energies GE for the RbF + RbBr + H2O and RbF + RbNO3 + H2O Ternary Systems at T = 298.2 K and p = 0.1 MPaa I (mol·kg−1)

mA (mol·kg−1)

γ±A

Eexp (mV)

0.0018 0.0038 0.0058 0.0093 0.0127 0.0188 0.0293 0.0390 0.0602 0.1196 0.1997 0.3000 0.4006 0.5007 0.5998 0.6994

0.0018 0.0038 0.0058 0.0093 0.0127 0.0188 0.0293 0.0390 0.0602 0.1196 0.1997 0.3000 0.4006 0.5007 0.5998 0.6994

−205.5 −168.0 −146.6 −123.3 −108.3 −88.9 −67.5 −53.5 −32.8 −0.1 23.8 43.2 57.0 67.7 76.6 84.4

0.0107 0.0304 0.0599 0.1200 0.2005 0.2994 0.4000 0.4997 0.5998 0.6998

0.0075 0.0213 0.0419 0.0840 0.1404 0.2096 0.2800 0.3498 0.4198 0.4899

−126.0 −75.3 −43.1 −10.6 12.7 30.6 43.2 52.7 60.3 66.6

0.0100 0.0301 0.0601 0.1196 0.1997 0.3003 0.4000 0.4998 0.5997 0.6998

0.0040 0.0121 0.0240 0.0478 0.0799 0.1201 0.1600 0.1999 0.2399 0.2799

−144.9 −90.7 −58.2 −26.5 −3.4 13.7 25.5 34.3 41.2 47.0

0.0101 0.0305 0.0605 0.1202 0.1999 0.2999 0.4004 0.5004 0.6003 0.6999

0.0010 0.0031 0.0060 0.0120 0.0200 0.0300 0.0400 0.0500 0.0600 0.0700

−180.1 −126.0 −94.0 −62.6 −40.3 −23.8 −12.4 −4.2 1.9 7.1

0.0017 0.0034 0.0053 0.0105 0.0141 0.0206

0.0017 0.0034 0.0053 0.0105 0.0141 0.0206

−202.5 −167.0 −144.6 −110.1 −96.4 −77.9

RbF + RbBr + H2O yB = 0.00 0.9465 0.9258 0.9222 0.9097 0.8915 0.8793 0.8580 0.8460 0.8218 0.7820 0.7467 0.7255 0.7111 0.7008 0.6960 0.6949 yB = 0.30 0.8944 0.8491 0.8076 0.7596 0.7157 0.6796 0.6503 0.6265 0.6054 0.5866 yB = 0.60 0.8834 0.8388 0.7931 0.7394 0.6946 0.6448 0.6092 0.5789 0.5519 0.5296 yB = 0.90 0.8770 0.8330 0.7846 0.7278 0.6760 0.6216 0.5814 0.5459 0.5126 0.4865 RbF + RbNO3 + H2O yB = 0.00 0.9402 0.9397 0.9260 0.9101 0.8869 0.8722 C

γ±B

Φ

GE (J·mol−1)

0.9532 0.9337 0.9198 0.9014 0.8871 0.8668 0.8403 0.8210 0.7883 0.7266 0.6706 0.6173 0.5727 0.5331 0.4970 0.4630

0.9848 0.9788 0.9747 0.9693 0.9654 0.9600 0.9536 0.9493 0.9430 0.9347 0.9315 0.9322 0.9351 0.9390 0.9435 0.9483

−0.28 −0.86 −1.60 −3.16 −4.96 −8.72 −16.35 −24.52 −44.83 −114.62 −226.23 −382.42 −549.78 −722.61 −896.63 −1072.82

0.8955 0.8393 0.7913 0.7314 0.6782 0.6289 0.5871 0.5499 0.5152 0.4823

0.9654 0.9470 0.9311 0.9102 0.8889 0.8649 0.8399 0.8133 0.7843 0.7527

−3.91 −17.45 −45.37 −118.21 −235.89 −399.37 −579.81 −768.08 −963.74 −1163.97

0.8993 0.8412 0.7939 0.7376 0.6887 0.6440 0.6080 0.5762 0.5469 0.5191

0.9658 0.9450 0.9269 0.9026 0.8766 0.8462 0.8152 0.7823 0.7466 0.7080

−3.53 −17.47 −46.42 −120.78 −242.70 −418.27 −609.63 −813.57 −1027.73 −1249.88

0.8992 0.8419 0.7965 0.7437 0.7006 0.6639 0.6362 0.6138 0.5944 0.5771

0.9661 0.9464 0.9306 0.9112 0.8938 0.8766 0.8609 0.8458 0.8303 0.8144

−3.63 −17.99 −47.64 −124.69 −250.87 −434.31 −638.94 −857.86 −1089.22 −1330.39

0.9533 0.9348 0.9191 0.8880 0.8716 0.8470

0.9853 0.9800 0.9757 0.9678 0.9640 0.9587

−0.26 −0.71 −1.38 −3.78 −5.77 −9.92

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Table 2. continued I (mol·kg−1)

mA (mol·kg−1)

Eexp (mV)

0.0293 0.0400 0.0593 0.1195 0.2001 0.2994 0.3997 0.4993 0.6001 0.7002

0.0293 0.0400 0.0593 0.1195 0.2001 0.2994 0.3997 0.4993 0.6001 0.7002

−60.8 −45.6 −26.7 6.2 30.6 49.8 63.7 74.5 83.5 91.2

0.0105 0.0299 0.0601 0.1195 0.1993 0.3003 0.4003 0.5000 0.6006 0.7005

0.0073 0.0209 0.0421 0.0837 0.1395 0.2102 0.2802 0.3500 0.4205 0.4903

−120.0 −69.5 −37.0 −6.6 13.9 29.4 39.2 46.5 52.3 56.9

0.0094 0.0295 0.0604 0.1200 0.1999 0.2997 0.3999 0.5000 0.6000 0.6999

0.0038 0.0118 0.0242 0.0480 0.0799 0.1199 0.1600 0.2000 0.2400 0.2800

−139.9 −85.1 −52.3 −23.5 −4.5 8.8 17.2 23.2 27.9 31.5

0.0099 0.0299 0.0602 0.1194 0.2002 0.3000 0.4001 0.4999 0.5997 0.7003

0.0010 0.0030 0.0060 0.0119 0.0200 0.0300 0.0400 0.0500 0.0600 0.0700

−173.5 −120.7 −89.3 −61.5 −43.4 −31.2 −23.5 −18.1 −14.1 −10.7

γ±A yB = 0.00 0.8575 0.8445 0.8225 0.7758 0.7456 0.7249 0.7118 0.7035 0.6976 0.6947 yB = 0.30 0.9025 0.8470 0.7935 0.7223 0.6461 0.5803 0.5269 0.4864 0.4534 0.4252 yB = 0.60 0.8990 0.8367 0.7751 0.6847 0.5954 0.5146 0.4543 0.4085 0.3731 0.3431 yB = 0.90 0.8866 0.8247 0.7559 0.6557 0.5569 0.4713 0.4107 0.3652 0.3291 0.3012

γ±B

Φ

GE (J·mol−1)

0.8202 0.7926 0.7516 0.6580 0.5663 0.4770 0.4021 0.3387 0.2833 0.2357

0.9536 0.9489 0.9432 0.9347 0.9315 0.9322 0.9351 0.9390 0.9435 0.9484

−16.33 −25.34 −43.97 −114.46 −226.87 −381.40 −548.39 −720.11 −897.25 −1074.32

0.8896 0.8221 0.7572 0.6709 0.5863 0.5010 0.4297 0.3676 0.3123 0.2637

0.9624 0.9378 0.9117 0.8708 0.8200 0.7536 0.6821 0.6039 0.5174 0.4238

−3.82 −17.38 −46.95 −122.46 −246.51 −427.67 −625.74 −836.73 −1060.24 −1290.14

0.8960 0.8269 0.7643 0.6854 0.6101 0.5360 0.4733 0.4180 0.3681 0.3228

0.9625 0.9329 0.9012 0.8508 0.7876 0.7062 0.6183 0.5228 0.4190 0.3066

−3.34 −17.62 −49.43 −131.01 −268.06 −470.39 −699.43 −948.75 −1214.90 −1495.26

0.8948 0.8298 0.7729 0.7032 0.6398 0.5823 0.5364 0.4975 0.4630 0.4315

0.9629 0.9373 0.9120 0.8758 0.8352 0.7888 0.7428 0.6958 0.6467 0.5948

−3.67 −18.52 −51.31 −137.90 −288.92 −513.79 −771.81 −1055.77 −1362.67 −1691.83

a I (I = mA + mB) is the total ionic strength. mA is the molality of RbF in pure water or mixtures. yB (yB = mB/(mA + mB)) is the ionic strength fractions of RbBr/RbNO3. The expanded uncertainties are U(m) = 0.0002 mol·kg−1; U(E) = 0.02 mV; U(γ) = 0.02; U(T) = 0.1 K; U(p) = 3 kPa (0.95 level of confidence).

298.2 K. Eθ and Eθ′ are the unsymmetrical higher-order electrostatic terms and can be calculated according to Pitzer.30 The meanings of all of the other symbols were detailed above. The Pitzer parameters of pure RbBr/RbNO3 in water still come from the literature.26 The mixing ionic interaction parameters (θF,Br/NO3, ψRb,F, Br/NO3) were calculated by eq 5 and given in Table 3. Thus, the mean ionic activity coefficient γ±B for RbBr/ RbNO3 and the osmotic coefficients Φ were obtained by combining eqs 6 and 8 as given in Table 2. Figures 1 and 2 are the plots of the mean ionic activity coefficient γ±A for RbF and γ±B for RbBr/RbNO3 against total ionic strength I for the studied systems. It is clear that γ±A and γ±B both decrease with the increase of the total ionic strength I at a constant ionic

ϕ = [mA (mA + mB)βA(0) + mB(mA + mB)βB(0) + mA (mA + mB) exp( −2 I )βA(1) + mB(mA + mB) exp( −2 I )βB(1) + mA (mA + mB)2 CAϕ + mB(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

(8)

where Aφ stands for the Debye−Hückel constant for the osmotic coefficient, which has a definite value of 0.3920929 at D

DOI: 10.1021/acs.jced.6b00398 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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strength fraction yB in the mixed-electrolyte solution. The variation is the typical phenomenon as presented in the other systems, such as NaCl + Na2HCit + H2O,13 KBr + K2B4O7 + H2O,15 RbCl + Rb2SO4/RbNO3 + H2O,20,21 CsCl + CaCl2/ MgCl2 + H2O,22,23 and so on. With the increasing of the concentration of electrolyte, the electrostatic interaction between the electrolyte ions is enhanced. As well, γ±A is reduced with the increase of the ionic strength fraction yB at a constant total ionic strength I for the studied systems. Similar results can be found in the systems NaCl + Na2HCit + H2O13 and RbCl + RbNO3 + H2O.21 While γ±B increases with the increasing of the ionic strength fraction yB at a constant total ionic strength I in this work. The similar phenomenon was observed in our previous work.20,22,23 However, different trends were presented in the other systems, such as NaCl + Na2HCit + H2O,13 KBr + K2B4O7 + H2O,15 and NaBr + SrBr2 + H2O.16 Such phenomenon may be caused by the properties, such as the radius, hydration ability, and electronegativity of the cations and anions. What’s more, it can be seen that the gap of the activity coefficients γ±A between yB = 0.0 and yB = 0.30 in RbF + RbNO3 + H2O is much larger than that in RbF + RbBr + H2O system. This may be interpreted by the difference of hydration ability of the anion in the solution. Because the radius of the nitrate ion (2.64 Å)31 is much greater than fluoride ion (1.36 Å),31 the hydration ability of nitrate ion is far less than that of fluoride ion. Therefore, with the addition of RbNO3, the free water in the solution increases, and then the effective concentration of RbF decreases. Thus, the mean ionic activity coefficient of RbF, γ±A, in the RbF + RbNO3 + H2O system decreases significantly compared with the value in pure water.32 The plot of the osmotic coefficients Φ against total ionic strength I is given in Figure S3. Moreover, to understand the effect of anion on the activity coefficients, a comparison was plotted in Figure 3 at the ionic strength fractions yB = 0.30 in the RbF + RbBr + H2O and RbF + RbNO3 + H2O systems. It shows that γ±A (the activity coefficient of RbF) and γ±B (the

Table 3. Values of the Mixing Interaction Parameters of the Pitzer Equation for the RbF + RbBr + H2O and RbF + RbNO3 + H2O Ternary Systems at T = 298.2 K and p = 0.1 MPa I (mol·kg−1) 0.0100−0.7000 σ

θF,Br

ψRb,F,Br

−0.34206 −0.36788 0.00904

θF,NO3

ψRb,F,NO3

−0.90842 −1.00555 0.04668

Figure 1. Plot of γ±A against ionic strength I in the RbF + RbBr + H2O and RbF + RbNO3 + H2O systems at T = 298.2 K (□, yB = 0.00; ○, yB = 0.30; △, yB = 0.60; +, yB = 0.90).

Figure 2. Plot of γ±B against ionic strength I in the RbF + RbBr + H2O and RbF + RbNO3 + H2O systems at T = 298.2 K (□, yB = 0.00; ○, yB = 0.30; △, yB = 0.60; +, yB = 0.90).

Figure 3. Comparison of γ±A and γ±B at ionic strength fractions yB= 0.30 at T = 298.2 K (□, RbF + RbBr + H2O; ○, RbF + RbNO3 + H2O). E

DOI: 10.1021/acs.jced.6b00398 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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CONCLUSION In this paper, the thermodynamic properties of the RbF + RbBr + H2O and RbF + RbNO3 + H2O ternary systems were reported by the potentiometric method for different ionic strength fractions yB of RbBr/RbNO3 with yB = 0.00, 0.30, 0.60, and 0.90, at 298.2 K. The experimental data were fitted using the Pitzer model. The mean ionic activity coefficients of RbF, γ±A, and RbBr/RbNO3, γ±B, the osmotic coefficients, and the excess Gibbs free energies of the systems were calculated. With the increasing of total ionic strength, γ±A and γ±B both decreased because of the electrostatic interaction between cations and anions. However, with the increasing of ionic strength fraction in the mixed-electrolyte solution, γ ±A decreased, and γ±B increased. Moreover, γ±A and γ±B in the RbF + RbBr + H2O system were larger than that in RbF + RbNO3 + H2O system at a constant ionic strength fraction. The difference on the thermodynamic properties may be caused by the different hydration abilities of anions in the studied systems. The results in this paper may enrich the thermodynamic properties for alkaline metal salt solutions.

activity coefficient of RbBr or RbNO3) in the RbF + RbBr + H2O system are larger than that of in the RbF + RbNO3 + H2O system. The radius of Br− (1.95 Å)31 is smaller than that of NO3− (2.64 Å),31 so the hydration ability of Br− is stronger than that of NO3−. Thus, the free water in the RbF + RbBr + H2O system is reduced, and the effective concentration of RbF and RbBr (in the RbF + RbBr + H2O system) increase, which lead to the difference in activity coefficient.32 Figure S4 is the comparison of the osmotic coefficients (yB = 0.30) for the two systems, showing a similar trend as that of the mean ionic activity coefficients γ±A and γ±B. Excess Gibbs Free Energy. The excess Gibbs free energy (GE) represents the nonideal behaviors of real systems. The values of excess Gibbs free energies (GE) were determined using the following equation: GE = 2RT[mA (1 − Φ + ln γ±A ) + mB(1 − Φ + ln γ±B)] (9)

where γ±A, γ±B, and Φ represent the mean ionic activity coefficient of RbF, RbBr/RbNO3, and the osmotic coefficient in the mixed-electrolyte solution. The results of GE are given in Table 2. The plot of the excess Gibbs free energies of the mixture GE against the total ionic strength I is depicted in Figure 4, which indicates that the values of GE are always negative. Moreover, GE decreases when the ionic strength fractions yB increase. In addition, a comparison of GE at the ionic strength fractions yB = 0.30 for the two systems is also depicted in Figure S4, which shows GE of the RbF + RbBr + H2O system is larger than that of the RbF + RbNO3 + 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.6b00398. Values of the Pitzer parameters for RbF, RbBr, and RbNO3 at T = 298.2 K and p = 0.1 MPa; calibration results of the electrode pairs at T = 298.2 K and p = 0.1 MPa; plot of the response results of Rb-ISE and F-ISE electrode pairs at 298.2 K; plots of activity coefficient of RbF in pure water, osmotic coefficients Φ, and comparison of Φ and GE for the RbF + RbBr + H2O and RbF + RbNO3 + H2O systems at 298.2 K (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*Tel.: +86-29-81530767; fax: +86-29-81530727; e-mail: [email protected]. *E-mail: [email protected]. Funding

This work was supported by the National Natural Science Foundation of China (nos. 21571120 and 21301114). Notes

The authors declare no competing financial interest.

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REFERENCES

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Figure 4. Plot of excess Gibbs free energies GE against ionic strength I in the RbF + RbBr + H2O and RbF + RbNO3 + H2O systems at T = 298.2 K (□, yB = 0.00; ○, yB = 0.30; △, yB = 0.60; +, yB = 0.90). F

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DOI: 10.1021/acs.jced.6b00398 J. Chem. Eng. Data XXXX, XXX, XXX−XXX