Studies on Mean Activity Coefficients of NaBr in NaBrâSrBr2âH2O

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Studies on Mean Activity Coefficients of NaBr in NaBr−SrBr2−H2O Ternary System at 298.15 K by EMF Method Mei-Fang Zhou,†,‡ Shi-Hua Sang,*,†,‡ Jun-Jie Zhang,†,‡ Juan-Xin Hu,†,‡ and Si-Yao Zhong†,‡ †

College of Materials and Chemistry & Chemical Engineering, Chengdu University of Technology, Chengdu 610059, People’s Republic of China ‡ Mineral Resources Chemistry Key Laboratory of Sichuan Higher Education Institutions, Chengdu 610059, People’s Republic of China ABSTRACT: The mean activity coefficients for NaBr in the (NaBr + SrBr2 + H2O) ternary system were determined by electromotive force (EMF) measurements of the following cell without liquid junction: Na+− ISE−NaBr (mA), SrBr2 (mB)−Br−−ISE At the total ionic strengths ranging from 0.01 mol·kg−1 up to 2.00 mol·kg−1 at 298.15 K for different ionic strength fractions yB of SrBr2 with yB = (0.0, 0.2, 0.4, 0.6, and 0.8). The activity coefficient results were interpreted based on the Harned rule and Pitzer model. Furthermore, the Pitzer ion interaction parameters θNa+Sr2+ and φNa+Br−Sr2+ were calculated. those parameters obtained with the Pitzer model were used to calculate the values of the mean activity coefficients of SrBr2, the osmotic coefficients, solvent activity, and the excess Gibbs free energy for the whole series of the mixed electrolyte system that was studied.

1. INTRODUCTION Electrolyte solution exists widely in nature, and the study of the thermodynamics properties of mixed electrolytes solution is becoming more and more popular. The investigation of thermodynamic properties such as activity coefficients, osmotic coefficients, and excess free energy for the aqueous multicomponent electrolyte system is of much interest not only in developing new thermodynamic models and testing new electrolyte solution theories,1,2 but also, more importantly, in contributing thermodynamic data to the scientific literature.3−6 In the last decades, a series of ion-interaction models for electrolyte solution have been proposed to predict activity coefficient of each solute and osmotic coefficient of aqueous systems. One of the most famous and useful models is that proposed by Pitzer.7 Research reports about activity coefficients calculated using the Pitzer equation are increasing all over the word. Felipe et al.8 widely measured the thermodynamic of the NaCl + MgCl2 + H2O mixed system by EMF measurements at different temperatures. Héctor et al.9,10 studied the thermodynamic of the NaCl + CaCl2 + H2O system and NaCl + Na2SO4 + H2O system by EMF measurements at different temperatures. Pierrot et al.11 studied the activity coefficients of HCl in HCl − Na2SO4 solutions from 0 °C to 50 °C. Roy et al.12−14 studied the activity coefficients of the HCl + GdCl3 + H2O system from 5 °C to 55 °C and the thermodynamics of the system HCl + SmCl3 + H2O and the unsymmetrical mixed electrolyte HCl − SrCl2 with the application of Harned’s rule and the Pitzer equations. In the early stage, we studied the mean activity coefficients of NaBr in the NaBr + Na2SO4 + H2O system and NaBr + Na2B4O7 + H2O system and KBr in the KBr + K2B4O7 + H2O system and KBr + K2SO4 + H2O at 298.15K by electromotive force (EMF) techniques.15−18 © XXXX American Chemical Society

Although the thermodynamic properties of mixed-electrolyte solutions have been widely studied in the past decades, there remain numerous electrolytic systems for which these data are unreported or scarce. For example, the aqueous multicomponent electrolyte system (NaBr + SrBr2 + H2O), no report has been found on thermodynamic properties of NaBr + SrBr2 + H2O ternary system at 298.15 K. As we all know that strontiumcontaining brine has been found in Western Basin, in China.19 Strontium and their salts are very rare all over the world, so preliminary investigation of strontium salt solution chemistry is necessary for scientifically exploit these natural resources. In this work, we determined the activity coefficients of NaBr in the NaBr + SrBr2 + H2O ternary system by EMF measurement at 298.15 K, then the Pitzer’s ion-interaction parameters of θBr−Sr− and φNa+Br−Sr2+ and Harned interaction coefficients αAB and βAB were evaluated by using the activity coefficients of NaBr in the NaBr + SrBr2 + H2O ternary system. Furthermore, the osmotic coefficients, solvent activity, excess Gibbs free energy of this system were calculated.

2. EXPERIMENTAL SECTION The apparatus used in this experiment were an AL104 electronic balance (U.S. Mettler-Toledo Group) with an accuracy of 0.1 mg; a UPT-II-20T (Shanghai XiRen Scientific instrument Co., Ltd.) UPT type ultrapure water machine; a Pxsj-216 ion meter (Leici Precision Scientific Instrument Co., Ltd.) with a precision of ±0.1 mV; a JB-1 blender (Leici Precision Scientific Instrument Co., Ltd.); a Bilon-HW-05 (Beijing Bi-Lang Co., Ltd.) constant Received: July 15, 2014 Accepted: September 23, 2014

A

dx.doi.org/10.1021/je500655k | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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temperature water bath with an external circulation system for the circulation of water to keep the temperature constant and a precision of 0.1 K; a PNa-1-01 sodium ion selective electrode (Jiangfen Electroanalytical Instrument Co., Ltd.); a PBr-1-01 bromide ion selective electrode (Jiangfen Electroanalytical Instrument Co., Ltd.); a 801 reference electrode (Jiangfen Electroanalytical Instrument Co., Ltd.). Na+-ISE was soaked for 30 min in a 10−2 mol·L−1 NaCl aqueous solution and washed with deionized water to a blank potential, static reading was performed on testing; Br−-ISE was soaked for 2 h in a 10−3 mol·L−1 NaBr aqueous solution, then cleaned with deionized water; reference electrode was a double junction saturated calomel electrode with the salt bridge filled with a G. R. grade saturated solution of potassium chloride, and the foreign salt bridge was filled with a 0.1 mol·L−1 lithium acetate solution. Sodium bromide (NaBr) (Merck pro analysis, 99%) and strontium bromide (SrBr2·6H2O) (Aldrich, 98%) were heated at 378.15 K in an oven for about 3 h to 5 h, respectively, afterward stored over silica gel in desiccators and used without further purification. All aqueous solutions were prepared using UPT type ultrapure water machine that specific conductance was less than 0.055 μs·cm−1. Each concentration of the solutions was prepared at different ionic strength fractions yB of SrBr2 for each set of measurements by direct weighing of both the solute and the solvent. The cell arrangements in this work were as follows:

Figure 1. Plot of Ea vs ln a0±NaBr for calibration of sodium and bromine selective electrode pair at 298.15 K.

Figure 1 shown that the electrode constants E0 is 276.27 mV and the electrode response slope k is 25.442 and the coefficient of determination (R2) is 0.9994, so there really exists the good liner relation between Ea and ln a0±NaBr. The EMF values and molarities are listed in Table 1. As shown in Table 1, Ea linearly Table 1. Calibration of elecTrode Pair Na+−ISE and Br−−ISE mA0 0.0011 0.0051 0.0100 0.0505 0.1009 0.1994 0.4990 0.9998 2.0004 2.5010

(a) Na+−ISE|NaBr (mA0)|Br−−ISE (b) Na+−ISE|SrBr2 (mB0)|Br−−ISE (c) Na+−ISE|NaBr (mA), SrBr2 (mB)|Br−−ISE The above cells are without liquid junction. mA0 and mB0 were the molalities of NaBr and SrBr2 as single salts in water, respectively. mA and mB were the molalities of NaBr and SrBr2 in the mixture, respectively. The temperature in the cell was maintained constant within T = (298.15 ± 0.1) K until the electromotive force was balance, which changes less than 0.1 mV per 30 min. Before determining the activity coefficients of mixture, the electromotive force of cell (a) was measured so as to calibrate the electrode pair composing the cell (a) and, furthermore, obtain its standard potential and the Nernst response slope. Then the EMF of cell (b) was measured to obtain the selective coefficient (KPot Na,Sr). Finally, the electromotive force of cell (c) under different ionic strength was measured and all the determination concentration was from low to high.

ln αγ±NaBr

E mV

0.965 0.928 0.903 0.824 0.783 0.742 0.697 0.687 0.73 0.768

−13.7175 −10.7083 −9.4191 −6.3587 −5.0758 −3.8217 −2.1124 −0.7513 0.7573 1.3055

−74.2 1.2 38.2 115 145.9 184.3 226.3 258.6 291.7 306.1

increases with ln a0±NaBr increases, so we can say that the Na+− ISE and Br−−ISE have a good linear Nernst response, and it indicates that the electrode pairs used here have a satisfactory Nernst response and are well suitable for our measurements. 3.2. Determination of Na+−ISE Potentiometric Selec+ tivity Coefficient. KPot Na,Sr(selective coefficient of Na −ISE for 2+ Sr ) were influenced by the measurement method, the strength of solution and the influence of coexisting ions, so it is difficult to have a uniform value. Through combining the Nernst principle and reordering the relevant terms, the selective coefficient KPot Na,Sr was calculated according to eq 2

3. RESULTS AND DISCUSSION 3.1. Performance of the Electrode. According to the cell (a), the Ea (EMF values of NaBr) of pure NaBr solution at 0.0010 mol·kg−1 to 2.5000 mol·kg−1 at T = 298.15 K were determined by the Nernstian equation of cell (a) and it can be expressed as follows:

Pot 3/2 3/2 Eb = E0 + kNaBr ln KNa , Sr (2mB0 γ0 ± SrBr ) 2

(2)

in which γ0±NaBr2 refers to the mean ionic activity coefficient of pure SrBr2 solution at T = 298.15 K, the value of it can be taken from the Handbook of Chemistry and Physics.20 The Eb is the EMF value of cell (b) at each measurement. In this experiments, we chose seven measurements of mB0 from 0.0100 mol·kg−1 to 2.5000 mol·kg−1 to measure Eb, through experiments the average −4 value of KPot Na,Sr is found to be less than 10 . 3.3. Experimental Mean Activity Coefficient of NaBr in the Mixture. According to the cell (c), we experiment to acquire the EMF values Ec of NaBr in ternary system (NaBr + SrBr2 + H2O) at T = 298.15 K and at different ionic strength I = mA + 3mB ranging from 0.0100 mol·kg−1 to 2.0000 mol·kg−1, and ionic strength fraction yB = 3mB/(mA + 3mB) = 0.8, 0.6, 0.4, 0.2, 0.0, concentration from low to high close to capacity. The Nernstian equation of cell (c) can be written as eq 3

Ea = E 0 + κ ln a+a− = E 0 + κ ln a0 = E 0 + 2κ ln mA 0γ0 ± NaBr

γ±SrBr2

mol·kg−1

(1)

where k = RT/F is the electrode response slope. The R, F, and T, respectively represent the gas constant, Faraday constant, and absolute temperature, E0 stands for the standard electromotive force of cell (a) and γ0±NaBr is the mean activity coefficients of pure NaBr at 298.15 K at different mA0 values in water and it is taken from the Handbook of Chemistry and Physics20 through eq 1, the values of E0 and k at 298.15 K were determined. B



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where αAB and βAB represents the Harned interaction coefficient, they are adjustable parameters that depend only on the total ionic strength at a given pressure and temperature. γ±A0 is the mean activity coefficients of NaBr in pure solutions at the same total ionic strength as the mixture. The outcome is listed in Table 3

Table 2. Experimental Mean Activity Coefficients of NaBr in the Mixture at T = 298.15 K. I

yB

mol·kg−1 0.0101 0.0100 0.0101 0.0106 0.0101 0.0503 0.0496 0.0503 0.0512 0.0503 0.0997 0.1003 0.1003 0.1007 0.1017 0.1994 0.1997 0.2004 0.2007 0.2006 0.4998 0.4984 0.5000 0.5002 0.5002 0.9978 0.9992 1.0015 0.9979 1.0010 1.9970 1.9983 1.9977 2.0015 1.9977

0 0.1957 0.3919 0.5987 0.7966 0 0.1958 0.3988 0.5937 0.7971 0 0.2032 0.3996 0.6003 0.7868 0 0.1993 0.4030 0.5999 0.7998 0 0.2000 0.4003 0.5998 0.8003 0 0.1999 0.4003 0.5996 0.7996 0 0.2001 0.4000 0.6003 0.7999

mA

mB

Ec

mol·kg−1

mol·kg−1

mV

0.0101 0.0079 0.0062 0.0043 0.0021 0.0503 0.0399 0.0303 0.0208 0.0102 0.0997 0.0799 0.0602 0.0403 0.0217 0.1994 0.1599 0.1197 0.0803 0.0401 0.4998 0.3987 0.2998 0.2002 0.0999 0.9977 0.7995 0.6006 0.3996 0.2006 1.9970 1.5985 1.1986 0.8000 0.3998

0 0.0007 0.0013 0.0021 0.0027 0 0.0032 0.0067 0.0101 0.0134 0 0.0068 0.0134 0.0202 0.0267 0 0.0133 0.0269 0.0401 0.0535 0 0.0332 0.0667 0.1000 0.1334 0 0.0666 0.1336 0.1995 0.2668 0 0.1333 0.2663 0.4005 0.5326

37.2 30.6 25.4 17.3 −3.2 114.5 108 100.5 90.7 71.1 146.8 140.8 133.2 122.4 106 179.6 174.2 166.5 155.9 137.4 224.7 218 210 199 180.1 257.8 253 247 238 221.5 294.8 291.4 286 277 260.6

γ±NaBr 0.9040 0.9407 0.9797 1.0212 1.0522 0.8273 0.8525 0.8700 0.8920 0.9132 0.7878 0.8072 0.8310 0.8534 0.8728 0.7502 0.7792 0.8026 0.8269 0.8494 0.7262 0.7389 0.7543 0.7738 0.7893 0.6972 0.7330 0.7792 0.8344 0.8881 0.7207 0.7797 0.8404 0.8964 0.9603

Table 3. Adjustable Parameters of the Harned Rule I 0.01 0.05 0.10 0.20 0.50 1.00 2.00

R2

−0.1020 −0.1884 −0.2394 −0.2866 −0.3206 −0.3622 −0.3270

0.2239 0.1351 0.1354 0.1838 0.0922 0. 2608 0.3996

−0.0382 −0.0117 −0.0040 −0.0370 0.0178 0.0528 −0.0536

0.9990 0.9974 0.9989 0.9993 0.9977 0.9992 0.9997

Table 4. Values of the Pitzer’s Pure-Electrolyte Parameters β0, β1, and Cφ for NaBr and SrBr2 at 298.15 K electrolyte

β(0) mol·kg

NaBr SrBr2

Cφ

β(1) −1

mol·kg

0.11077 0.32410

−1

0.13760 1.78223

mol·kg

σ

ref

0.00448 0.00086

25 25

−1

−0.00153 0.00344

and shown in Figure 2. Table 3 indicates the parameter αAB far outstripped βAB; that is, there was a linear response between ln γ±A0 and yB, and this linear response is shown in Figure 2. According to Figure 2, it was seen that γ±A0 in NaBr + SrBr2 + H2O system increased with the increase of the ionic strength fractions yB of SrBr2. 3.5. Pitzer Equation. In this article, we took the modified form of the Pitzer equation suggested by Harvie and Weare22,23 to fit the experimental data. For the mixed solution studied, the mean activity coefficients γ±NaBrand γ±SrBr2 and the osmotic coefficients Φ can be derived as follows after a series of substitutions and rearrangements. For ionic activity coefficients the corresponding relations (eqs 6 to 8) are

2

(3)

where γ±NaBr and γSrBr2 are the mean activity coefficient of NaBr and SrBr2 in the cell (c), respectively. Because KPot Na,Sr is so small that can be neglected without leading to an appreciable error, we get the simplified form of eq 3 (4)

Hence, the mean activity coefficients of NaBr can be calculated through eq 4, and the related results of cell (c) are listed in Table 2. 3.4. Harned Rule. The Harned model21 is one of the earliest known from which the activity coefficients of an electrolyte in a mixture can be expressed as a function of the molal concentration of the other electrolyte present. In relation to the studied electrolytic system, when the total ionic strength remains constant, the Harned rule can be simplified to eq 5 ln γ±A = ln γ±A 0 − αAB·yB − βAB ·yB2

βAB

Figure 2. Plot of ln γ±NaBr vs yB for different ionic strengths I.

= E 0 + κ ln mA (mA + 2mB)γ±2NaBr + K Pot ·γ±2/3 ·mB1/2 · SrBr

Ec = E 0 + κ ln mA (mA + 2mB)γ±2NaBr

αAB

mol·kg−1

Ec = E 0 + κ ln αNa+·αBr −

(mA + 2mB)

lnγ±A0

(0) (0) ln γ±NaBr = 2mA + mBβNaBr + mBβSrBr + 2(mA + mB) 2

× g (2

(1) I )βNaBr

1 + mBg (2 I )βSrBr

2

φ 2mB2)CNaBr

+

(1.5mA2

+

2 φ CSrBr + mBθ + mBE θ 2 2(mA mB + 2mB2)

+ 4mA mB +

+ (1.5mA mB + mB2)φ + F

(5) C

(6)



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Table 5. Values of the Pitzer mixing interaction parameters θNa+Sr2+, φNa+Br−Sr2+ for the NaBr + SrBr2 + H2O ternary system at 298.15 K. I mol·kg

θNa+Sr2+

φNa+Br−Sr2+

R2

ref

0.0168

−0.8337

0.9715

This work

−1

0.0100−2.0000

Table 6. Mean Activity Coefficients γ±SrBr2, the Osmotic Coefficients Φ, Solvent Activity aW and Excess Gibbs Free Energies GE at T = 298.15 K I mol·kg

yB −1

0.0101 0.0100 0.0101 0.0106 0.0101 0.0503 0.0496 0.0503 0.0512 0.0503 0.0997 0.1003 0.1003 0.1007 0.1017 0.1994 0.1997 0.2004 0.2007 0.2006 0.4998 0.4984 0.5000 0.5002 0.5002 0.9978 0.9992 1.0015 0.9979 1.0010 1.9970 1.9983 1.9977 2.0015 1.9977

γ±SrBr2 mol·kg

0 0.1957 0.3919 0.5987 0.7966 0 0.1958 0.3988 0.5937 0.7971 0 0.2032 0.3996 0.6003 0.7868 0 0.1993 0.4030 0.5999 0.7998 0 0.2000 0.4003 0.5998 0.8003 0 0.1999 0.4003 0.5996 0.7996 0 0.2001 0.4000 0.6003 0.7999

Φ

aW

GE·104

0.9671 0.9637 0.9598 0.9535 0.9472 0.9407 0.9358 0.9288 0.9204 0.9095 0.9286 0.9223 0.9150 0.9056 0.8942 0.9193 0.9119 0.9035 0.8939 0.8818 0.9218 0.9050 0.8915 0.8812 0.8737 0.9495 0.8980 0.8644 0.8511 0.8597 1.0259 0.8356 0.7239 0.6976 0.7733

0.9996 0.9997 0.9997 0.9997 0.9998 0.9983 0.9985 0.9987 0.9988 0.9990 0.9967 0.997 0.9974 0.9977 0.9980 0.9934 0.9941 0.9948 0.9955 0.9962 0.9835 0.9855 0.9872 0.9889 0.9906 0.9664 0.9713 0.9754 0.9788 0.9816 0.9288 0.9473 0.9592 0.9654 0.9672

−0.0003 −0.0003 −0.0003 −0.0004 −0.0004 −0.0031 −0.0032 −0.0033 −0.0035 −0.0034 −0.008 −0.0083 −0.0086 −0.0088 −0.0090 −0.0206 −0.0211 −0.0216 −0.0219 −0.0221 −0.0819 −0.0764 −0.0734 −0.0715 −0.0706 −0.3158 −0.2516 −0.2073 −0.1785 −0.1651 −1.8045 −1.206 −0.7852 −0.5212 −0.3824

−1

0.8196 0.8187 0.8166 0.8125 0.8155 0.6917 0.6887 0.6840 0.6811 0.6822 0.6332 0.6260 0.6216 0.6187 0.6175 0.5785 0.5688 0.5620 0.5586 0.5582 0.5119 0.4980 0.4894 0.4865 0.4892 0.4299 0.4187 0.4168 0.4248 0.4418 0.2248 0.2363 0.2618 0.3047 0.3743

Figure 3. Plot of the osmotic coefficients Φ of water against total ionic strength I of the NaBr + SrBr2+ H2O ternary system at different ionic strength fraction yB of SrBr2 in the mixture at T = 298.15 K.

kJ·mol

Figure 4. Plot of the values of the mean activity coefficients γ±SrBr2 for SrBr2 against total ionic strength I of the NaBr + SrBr2 + H2O ternary system at different ionic strength fraction yB of SrBr2 in the mixture at T = 298.15 K.

⎧ 2ln(1 + 1.2 I ) ⎫ I ⎬ F = − Aφ ⎨ + 1.2 ⎭ ⎩ 1 + 1.2 I (1) (1) )/I + (mA + 2mB)g ′(2 I )(mAβNaBr + mBβSrBr 2

+

(0) (0) Φ = [mA (mA + 2mB)βNaBr + mB(mA + 2mB)βSrBr

2

+ mA (mA + 2mB)exp( −2 exp( −2 +

(0) (0) + 4mA βNaBr + (2mA + 8mB)βSrBr

2 (1) + 4mA g (2 I )βNaBr φ 2mA + 2mB2CSrBr 2

+ (2mA + 8mB)g (2

+ (6mA mB + mA2 )φ + 6F

+ 2mA θ +

1 I )βSrBr 2

(1) I )βNaBr

+ mB(mA + 2mB)

φ + mA (mA + 2mB) CNaBr 2

2 + 2mA mB( Eθ + θ + Eθ′I ) φ 2mBmA + 2mB2CSrBr 2

+ 2mA mB(mA + 2mB)φ − AφI1.5/(1 + 1.2 I )]

2

1 I )βSrBr 2

(8)

In these eqs 6−8, I = mA + 3mB are the total ionic strength on a molality scale, Aφ denotes the Debye−Huckel parameter for the osmotic function with value of 0.3915 kg1/2·mol−1/2 for an aqueous solution at T = 298.15 K.24 The β0, β1, and Cφ are the parameters of the Pitzer equation for single salt electrolyte solutions. These parameters were taken from the literature25 and are presented in Table 4. The Pitzer’s ion-interaction parameters of θNa+Sr2+and φNa+Br−Sr2+ indicate the unknown mixing ioninteraction parameters, which should be determined.

⎛ 2 ⎞⎟ φ 3ln γ±SrBr = 4(mA + 2mB)⎜⎜mA CNaBr + φ ⎟ 2 2mBCSrBr ⎝ 2⎠

+

2mAm BEθ′

/(mA + 1.5mB) + 1

(9)

where the EθNa,Sr2 and its ionic strength derivative Eθ′Na,Sr2′ stand for the unsymmetrical higher-order electrostatic terms of the Pitzer equation, which can be calculated according to the empirical formula,6 and their values depend only on the total ionic

2mAE θ (7) D



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other mean of symbols as above mention. The results of GE and aW are listed in Table 6. Figure 3 shows the plot of the osmotic coefficient against total ionic strength. It can be seen that the osmotic coefficient of water is reduced by increasing the ionic strength fraction yB of SrBr2 in the mixture. Figures 4 to 6 show the changes of the mean activity coefficients of SrBr2, solvent activity, and the excess Gibbs free energy plots as a function of total ionic strength for the entire mixed electrolyte systems investigated, respectively. Figure 6 shows that the excess Gibbs free energy of solution is reduced by increasing total ionic strength.

Figure 5. Plot of the solvent activity aW against total ionic strength I of the NaBr + SrBr2+ H2O ternary system at different ionic strength fraction yB of SrBr2 in the mixture at T = 298.15 K.

4. CONCLUSION The thermodynamic investigation of the NaBr + SrBr2 + H2O ternary system was studied by EMF method using Na+−ISE and Br−−ISE at 298.15 K. The mean activity coefficients of NaBr in pure and mixed solution were determined by the cells without liquid junction. According to the obtained electrode constant and the response slope, the mean activity coefficients of NaBr in NaBr + SrBr2 + H2O system were calculated using the Nernstian equation. Pitzer ion interaction parameters θNa+Sr2+ and φNa+Br−Sr2+ were calculated. And then the osmotic coefficients Φ, solvent activity aW, and the Gibbs free energy GE of the system were calculated using these mixing parameters and Pitzer equations. The results showed that the Pitzer model can be used to describe this aqueous system satisfactorily. The Harned rule was applied to the (NaBr + SrBr2 + H2O) ternary system. The experimental results obey the Harned rule. The results of present investigations indicate that both thermodynamic models could correlate the experimental results and the result in this work can provide basic thermodynamic reference data for further research applications.

Figure 6. Plot of the excess Gibbs free energy GE for mixed electrolyte solution against total ionic strength I of the NaBr + SrBr2 + H2O ternary system at different ionic strength fraction yB of SrBr2 in the mixture at T = 298.15 K.

strength I and the valences of the ions of like sign. The empirical formulas are the following forms: E

θ Na , Sr2 =

■

J(χSr , Sr ) ⎤ J(χNa , Na ) ⎛ ZNaZSr ⎞⎡ 2 2 ⎥ ⎜ ⎟⎢J(χ ) − − ⎝ 4I ⎠⎢⎣ Na , Sr2 2 2 ⎥⎦

Corresponding Author

(10)

*E-mail: [email protected]; [email protected]. Tel.: +86-28-8407-9634. Fax: +86-28-8407-9074.

⎛ Eθ ⎞ ⎛ Z Z ⎞⎡ Na , Sr2 E ⎟ + ⎜ Na Sr ⎟⎢χ J′(χNa , Na ) θ Na , Sr2′ = −⎜⎜ ⎟ Na , Sr2 2 ⎝ I ⎠ ⎝ 8I ⎠⎢⎣ χSr , Sr J′(χSr , Sr ) ⎤ χNa , Na J′(χNa , Na ) 2 2 ⎥ − − 2 2 2 2 ⎥⎦ (11)

Funding

This project was supported by the National Natural Science Foundation of China (41373062), the Specialized Research Fund (20125122110015) for the Doctoral Program of Higher Education of China (KLSLRC-KF-13-HX-5), Fund of Key Laboratory of Salt Lake Resources and Chemistry, Chinese Academy of Sciences (Qinghai Institute of Salt Lakes).

and all the other parameters are constants and they have their usual significance.1,5,7 Through eq 6, the mixing ionic parameters θNa+Sr2+ and φNa+Br−Sr2+ were evaluated by using multiple linear regression technique and are given in Table 5. Then, the activity coefficients of SrBr2 fractions were calculated by substituting the regressed mixing ionic parameters from eq 7. These outcomes are also together listed in Table 6. The excess Gibbs free energy (GE) and solvent activity (aW) are calculated from the following relations:

Notes

The authors declare no competing financial interest.

■

REFERENCES

(1) Pitzer, K. S. Thermodynamics of electrolytes. I. Theoretical basis and general equations. J. Phys. Chem. 1973, 77, 268−277. (2) Harned, H. S.; Robinson, R. A. Multicomponent Electrolyte Solutions; Pergamon Press: London, 1968. (3) 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. (4) Pitzer, K. S.; Mayorga, G. Thermodynamics of electrolytes. III. Activity and osmotic coefficients for 2−2 electrolytes. J. Solution Chem. 1974, 3, 539−546. (5) 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. (6) Pitzer, K. S. Thermodynamics of electrolytes. V. Effects of higher order electrostatic terms. J. Solution Chem. 1975, 3, 249−265.

G E = RT[νAmA (1 − Φ + ln γA) + νBmB(1 − Φ + ln γB)] (12)

⎡ mi ⎤ ⎥ aW = exp⎢ −Φ·MW ·∑ ⎢⎣ 1000 ⎥⎦ i

AUTHOR INFORMATION

(13)

Where mA and mB are total number of anions and cations of the electrolyte produced by dissociation of one molecule of NaBr and SrBr2, respectively. MW and mi are the molecular mass of water (18.0153 g·mol−1), molality of the solute species. Then E



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Studies on Mean Activity Coefficients of NaBr in NaBrâSrBr2âH2O

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