Mean Activity Coefficients of NaBr in NaBr + Na2SO4 + H2O Ternary

Mean Activity Coefficients of NaBr in NaBr + Na2SO4 + H2O Ternary System at 298.15 K Determined by Potential Difference Measurements ... Citation data...
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Mean Activity Coefficients of NaBr in NaBr + Na2SO4 + H2O Ternary System at 298.15 K Determined by Potential Difference Measurements Si-Yao Zhong,†,‡ Shi-Hua Sang,†,‡,* Jun-Jie Zhang,†,§ Wang-Yin Huang,†,‡ and Juan-Xin Hu†,‡ †

College of Materials and Chemistry & Chemical Engineering, Chengdu University of Technology, Chengdu 610059, P. R. China Mineral Resources Chemistry Key Laboratory of Sichuan Higher Education Institutions, Chengdu 610059, P. R. China § College of Environmental and Civil Engineering, Chengdu University of Technology, Chengdu 610059, P. R. China ‡

ABSTRACT: The mean activity coefficients of NaBr in the NaBr + Na2SO4 + H2O ternary system were determined at the total ionic strength ranging from (0.0500 to 3.0000) mol·kg−1 at 298.15 K by potential difference measurements from the galvanic cell without liquid junction: Na−ISE|NaBr(m1), Na2SO4(m2)| Br−ISE. The mean activity coefficients of NaBr were compared with those different ionic strength fractions yB of Na2SO4 with yB = (0.8, 0.6, 0.4, 0.2, and 0). The experimental results showed that Na−ISE and Br−ISE in this work had a good Nernst response, and the mean activity coefficients of NaBr in NaBr + Na2SO4 + H2O mixtures were calculated using the Nernst equation. Mixing interaction parameters of θBr−·SO42− and φNa+·Br−·SO42− in Pitzer’s equation, which had not been previously reported, were evaluated from the present measurements of the mean activity coefficients of NaBr. In addition, the osmotic coefficients, water activity, and the excess Gibbs energy of this system were calculated by the Pitzer’s equations.

1. INTRODUCTION The purpose of solution theory study is to illustrate the static nature (activity coefficient, permeability coefficient, heat capacity, enthalpy, entropy, etc.) and dynamic nature (conductivity, diffusion coefficient, etc.). With these theory formula is deduced to directly calculate a number of parameters about the nature of the electrolyte solution.1−3 Activity coefficients of electrolyte play an important role in thermodynamics, which reflect the deviation degree between the true solution and the ideal solution.4−6 There are many methods to measure activity coefficients of electrolyte solution, such as gas−liquid chromatography, kinetic method, dilute solution colligative method, conductivity method, solubility method, freezing point depression method, equal pressure method, and potential difference measurement. In this paper, we used potential difference measurement to determine the mean activity coefficients of solution. The emergence of ion-selective electrodes is undoubtedly an important advance in potential analysis. In recent years, the variety of ion-selective electrodes has increase rapidly; so far, more than 30 kinds of ion-selective electrohus. Thus they catch people’s attention.7−9 The Western Sichuan basin in China has abundant resources in underground brines,10 which contain a large amount of sodium, potassium, boron, and bromine. Bromine is an important industrial raw material, widely used in pharmaceutical, fire extinguishing agents, and other fields. Therefore, the study of the thermodynamic properties of brine is necessary. Research reports about activity coefficients calculated using the © XXXX American Chemical Society

Pitzer equation are increasing all over the word, i.e., Millero et al.11,12 measured and calculated the solubilities of oxygen in aqueous solutions of KCl, K2SO4, and CaCl2 as a function of concentration and temperature, and determined the dissociation of TRIS in NaCl solutions by using Pitzer equations. Roy et al.13−15 studied the activity coefficients of the HCl + GdCl3 + H2O system from (278.15 to 328.15) K and the thermodynamics of the system HCl + SmCl3 + H2O with the application of Harned′s rule and the Pitzer equations, and the thermodynamics of the HBr + NiBr2 + H2O system from (278.15 to 328.15) K were determined. Sirbu, Galleguilos, and White et al.16−19 studied the activity coefficients of NaCl + Na2SO4 + H2O, KI + KNO3 + H2O, NaCl + Na2SO4 + H2O, and NaCl + Na2CO3 + H2O. Bagherinia et al.20 determined the activity coefficients of MgCl2 in the MgCl2 + MgSO4 + H2O system by potential difference measurements at 298.15 K. In our previous work, we studied mean activity coefficients of KBr in the KBr + K2SO4 + H2O ternary system and NaBr in the NaBr + Na2B4O7 + H2O system at 298.15 K by potential difference measurements.21,22 We also studied multi-temperature phase diagrams in a series of sub-system of the NaCl + NaBr + Na2SO4 + Na2B4O7 + KCl + KBr + K2SO4 + K2B4O7 + H2O system for underground brine, that is, NaCl + Na2SO4 + Na2B4O7 + KCl + K2SO4 + K2B4O7 + H2O at 298 K;23 Na2B4O7 + Na2SO4 + NaCl + H2O at 323 K;24 Na2SO4 + Received: January 15, 2014 Accepted: March 28, 2014

A

dx.doi.org/10.1021/je500046e | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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where a+, a−, a0±NaBr, m0, and γ0±NaBr, respectively, represent a single positive ion activity, negative ion activity, mean activity, molality, and activity coefficient, Ea indicates the galvanic potential difference, E0′ indicates the standard potential, k indicates the electrode response slope. For the mixed salt, a cell without liquid junction was

Na2B4O7 + K2SO4 + K2B4O7 + H2O at 323 K;25 NaBr + Na2SO4 + KBr + K2SO4 + H2O at 323 K;26 and NaBr + Na2SO4 + H2O at 323 K.27 Pitzer’s equations can be used to calculate the thermodynamic properties for underground brine, so we determined the thermodynamic properties of the underground brine system to predict the thermodynamic equilibrium for underground brine. So far, no report has been found on thermodynamic properties of the NaBr + Na2SO4 + H2O ternary system at 298.15 K containing both borate salts and bromine salts. Therefore, in this paper, the activity coefficients of NaBr in NaBr + Na2SO4 + H2O ternary system were determined by potential difference measurement at 298.15 K and in (0.0500 to 3.0000) mol·kg−1 total ionic strength range, and the Pitzer’s ion interaction parameters of θBr−·SO42− and φNa+·Br−·SO42− were evaluated by using the activity coefficients of NaBr in the NaBr + Na2SO4 + H2O ternary system. Then the permeability coefficients, water activity, excess Gibbs energy of this system were calculated.

Na + − ISE|NaBr(m1), Na 2SO4 (m2), H 2O|Br − − ISE

whose potential value is E b = E 0 ′ + k ln aNa+aBr− = E 0 ′ + k ln m1(m1 + 2m2)γ±NaBr 2

3. METHOD Br-ISE was soaked for activation for 2 h in 10−3 mol·dm−3 NaBr aqueous solution and then cleaned with deionized water to make the cleaning potential 160 mV. The reference electrode was a double-junction saturated calomel electrode with the salt bridge filled with G.R. grade saturated solution of potassium chloride and the foreign salt bridge filled with 0.1 mol·dm−3 lithium acetate solution. During the measurements, we use the same ion-selective electrodes. First, the potential difference of each single salt was determined so the electrode response slope of each electrode and the electrode constant were obtained. The salt composition with NaBr single cell without liquid junction was

(γ±NaBr)2 = γNa+·γBr− 2

4

(4)

4

ln γNa+ = F + mBr (2B Na,Br + ZC Na,Br) + mSO4 (2B Na,SO4 + ZC Na,SO4) + mNa mBr C Na,Br + mNa mSO4 C Na,SO4 + mBr mSO4 ψNa,Br,SO

4

(a)

(5)

ln γBr− = F + mNa (2B Na,Br + ZC Na,Br) + mNa mBr C Na,Br

Ea = E 0 ′ + k ln a+a−

+ mNa mSO4 C Na,SO4 + mSO4 (2ΦBr,SO4

= E 0 ′ + k ln a0 ± NaBr = E + 2k ln m0γ0 ± NaBr

(3)

(γ±Na SO )3 = (γNa+)2 ·γSO 2−

whose potential value was

0′

(2)

where m1 and m2, respectively, represent the molality of NaBr and Na2SO4 in mixed solution, aNa+ and aBr−, respectively, represent the activity of Na+ and Br−, γ±NaBr expresses the mean activity coefficient of NaBr. The method and procedure is as follows: the total ionic strength I (I = m1 + 3m2) ranges from (0.0500 to 3.0000) mol· kg−1; ionic strength fractions yB of Na2SO4 is (0.8, 0.6, 0.4, 0.2, and 0), concentration from low to high close to capacity. The yB follows as yB = 3m2/(m1 + 3m2). According to the different ionic strength fractions yB of Na2SO4 under different total ionic strength I, calculate the mass of NaBr and Na2SO4 that should be added to 30 g of deionized water, weigh the salts and deionized water on the electronic balance into a beaker, and placed on a stirred and stirred until dissolved, then put in a thermostatic circulating water bath, using ion meter for measuring. Before determining the activity coefficients of mixture, the potential difference of cell (a) was measured so as to determine the standard potential difference E0′ and practical response slope k. There k = RT/F represents the theoretical Nernst slope. R, F, and T are the gas constant, Faraday constant, and absolute temperature, respectively. The activity coefficients of pure NaBr solution at 298.15 K were taken from the Handbook of Chemistry and Physics.28 Then the potential difference of cell (b) under different ionic strengths was measured, and all of the concentrations were determined from low to high. During measurement, the experimental solution was under constant temperature (298.15 ± 0.1 K) until the potential difference was balance, which changes less than 0.1 mV in 30 min. For ionic activity coefficients the corresponding relations are

2. EXPERIMENTAL SECTION The water for experiments was deionized water, with a conductivity less than 1·10−4 S·m−1. Prior to use, the G.R. grade anhydrous Na2SO4 (mass fraction % > 99.5) from Tianjin Kemiou Chemical Reagent Co., Ltd. and NaBr salts (mass fraction % > 99.5) from Tianjin Guangfu Fine Chemical Research Institute were placed in an oven under 393 K for 2 h. Experimental apparatus were as follows: AL104 electronic balance (U.S. Mettler−Toledo Group, the smallest error value 0.0001 g); Pxsj-216 ion meter (Leici Precision Scientific Instrument Co., Ltd., accuracy ± 0.1 mV); Bilon-HW-05 thermostatic circulating water bath (Beijing Bi−Lang Co., Ltd., accuracy ± 0.1K); JB-1 stirrer (Leici Precision Scientific Instrument Co., Ltd., can automatically adjust the speed); 232-01 reference electrode (Leici Precision Scientific Instrument Co., Ltd.); 6801-01 sodium ion selective electrode (Leici Precision Scientific Instrument Co., Ltd.); PBr-1-01 bromide ion selective electrode (Leici Precision Scientific Instrument Co., Ltd.); 50 mL glasses and other conventional glass instruments.

Na + − ISE|NaBr(m0), H 2O|Br − − ISE

(b)

+ mNa ψNa,Br,SO ) 4

(1)

(6)

and B

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where EθBr,SO4 and Eθ′Br,SO4 can be calculated, and their values depend on the total ionic strength I and the valences (ZBr and ZSO4) of the ions. The equations are the following forms:

ln γSO 2− = 4F + mNa (B Na,SO4 + ZC Na,SO4) + 2mNa mBr 4

C Na,Br + 2mNa mSO4 C Na,SO4 + mBr (2ΦBr,SO4 + mNa ψNa,Br,SO )

J(χSO ,SO ) ⎤ J(χBr,Br ) ⎛ Z BrZ SO4 ⎞⎡ 4 4 ⎥ θ Br,SO4 = ⎜ − ⎟⎢J(χBr,SO4 ) − ⎥⎦ 2 2 ⎝ 4I ⎠⎢⎣

(7)

4

E

where

(17)

⎤ ⎡ I1/2 1/2 ⎥ F = −A ⎢ (2/ b )ln(1 bI ) + + ⎦ ⎣ (1 + bI1/2) ⌀

⎛ Eθ ⎞ ⎛ Z Z ⎞⎡ Br,SO4 ⎟ + ⎜ Br SO4 ⎟⎢χ J ′(χBr,SO ) = −⎜⎜ Br,SO4 2 ⎟ 4 ⎝ I ⎠ ⎝ 8I ⎠⎢⎣ χSO ,SO J ′(χSO ,SO ) ⎤ χBr,Br J ′(χBr,Br ) 4 4 4 4 ⎥ − − ⎥⎦ 2 2 (18)

E

θ′Br,SO4

′ ′ 4 + mBr mSO4 Φ′Br,SO4 + mNa mBr B Na,Br + mNa mSO4 B Na,SO (8) −1/2

where I is the ionic strength, the constants b = 1.2 mol · kg1/2, and A⌀ = 0.391475 mol−1/2·kg1/2 is the value of the Debye−Hückel limiting−law slope for an aqueous solution at T (1) = 298.15 K.29,30 Values of the Pitzer parameters β(0) M,X, βM,X and Ø CMX for NaBr and Na2SO4 at 298.15 K are from ref 31. For the {(1 − yB)NaBr + yBNa2SO4}(aq) system, the osmotic coefficient equation is

where

+

(19)

J(χ ) = χ[4 + 4.581χ −0.7237 exp(− 0.0120χ 0.528 )]−1

(20)

4

⎛ ⎞⎡⎛ −A⌀I 3/2 ⎞ 2 ⎟⎟⎢⎜ ⎟ ⌀ = 1 + ⎜⎜ 1/2 ⎝ mNa + mBr + mSO4 ⎠⎢⎣⎝ 1 + bI ⎠ ⌀ mNa mBr (B Na,Br

χBr,SO = 6Z BrZ SO4A⌀I1/2

J ′(χ ) = [4 + 4.581χ −0.7237 exp(− 0.0120χ 0.528 )]−1 + [4 + 4.581χ −0.7237 exp(− 0.0120χ 0.528 )]−2

+ ZC Na,Br) + mNa mSO4

[4.581χ exp(− 0.0120χ 0.528 )(0.7237χ −1.7237

⌀ (B Na,SO + ZC Na,SO4) + mBr mSO4 {Φ⌀Br,SO4 4

⎤ + mNa ψNa,Br,SO }⎥ 4 ⎥ ⎦

+ 0.0120· 0.528χ −0.472 χ −0.7237 )]

The excess Gibbs energy (G ) and activity of water (aw) are calculated from the following relations

(9)

GE = RT[2m1(1 − ⌀ + ln γ±NaBr) + 3m2

where Z is given by Z = mNa + mBr + 2mSO4, where mNa = m1 + 2m2, mBr = m1, and mSO4 = m2. BØM,X, BM,X, CMX, and B′M,X are defined as the following which depend on ionic strength

(1 − ⌀ + ln γ±Na SO )] 2

and

⎪

⎪

⎪

⎪

4. RESULTS AND DISCUSSION According to m0 (molality of NaBr) and Ea (the potential difference value of NaBr), the γ0±NaBr (activity coefficients of NaBr at 298.15 K accessing physical chemistry handbook) was determined and collected in Table 1, and a diagram (Figure 1) was drawn. The expanded uncertainties (U) of the measured potential difference are 0.0914 mV (K = 2). As shown in Figure 1, Ea linearly increases with ln a0±NaBr increases, and R2 = 0.999, so the Na+-ISE and Br−-ISE have a

(11) ⌀ CMX

(2 |Z MZ X|1/2 )

(12)

⎧ 2⎡1 − ⎜⎛1 + αI1/2 + α2I ⎟⎞ exp(−αI1/2)⎤ ⎫ ⎥⎦ ⎪ ⎪ ⎢⎣ ⎝ 2 ⎠ (1) ⎬ βM,X ⎨− 2 αI

Table 1. Values for Potential Difference Ea, Activity Logarithm ln α0±NaBr, and Mean Ionic Activity Coefficient γ0±NaBr of NaBr in Aqueous Solutions versus NaBr Molality m0 at 298.15 K

⎪ ⎭

⎪ ⎩

I

(13)

where M denotes K+ and X denotes Br−or SO42−; ZM and ZX are the valences of ions M and X; these mixing functions are related to the mixing parameters by Φ⌀Br,SO4 = θBr,SO4 + Eθ Br,SO4 + IEθ′Br,SO4

(14)

ΦBr,SO4 = θBr,SO4 + Eθ Br,SO4

(15)

and Φ′Br,SO4 = Eθ′Br,SO4

(23)

(10)

1/2 ⎧ ) exp( −αI1/2)] ⎫ (0) (1) [1 − (1 + αI ⎬ ⎨ + 2βM,X BM,X = βM,X 2 αI ⎭ ⎩

B′M,X =

(22)

4

aW = exp[(− 18.0513/1000)(2m1 + 3m2)⌀]

⌀ (0) (1) BM,X = βM,X + βM,X exp( −αI1/2)

CMX =

(21)

E

(16) C

m0/mol·kg−1

γ0±NaBr

ln a0±NaBr

Ea/mV

0.0108 0.0521 0.1163 0.6703 1.0670 1.4879 2.0169 3.0953

0.903 0.824 0.782 0.697 0.687 0.719 0.73 0.812

−9.260 −6.296 −4.795 −1.522 −0.621 0.135 0.774 1.843

0.6 98.9 137.1 216.0 235.1 258.4 273.2 299.0

dx.doi.org/10.1021/je500046e | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 3. Values for the Total Ionic Strengths I, Stoichiometric Ionic Strength Fraction of Na2SO4 yB, Molality of NaBr and Na2SO4 m1,m2, Respectively, Potential Difference Eb, Mean Activity Coefficient of NaBr γ±NaBr in NaBr + Na2SO4 + H2O Ternary System at 298.15 K

Figure 1. Response curve of Na+−ISE|NaBr (m0), H2O|Br−−ISE galvanic vs NaBr at 298.15 K.

good linear Nernst response, and the measured potential difference value is true and reliable. The electrode constants and the electrode response slope are listed in Table 2. Table 2. Standard Potential E0′ and the Electrode Response Slope k of Na+-ISE|NaBr(m0), H2O|Br−-ISE Galvanic at 298.15 K E0′/mV

κ

R2

253.6

24.70

0.999

The weight molar concentration m1, m2 and the potential difference Eb of mixed solution are listed in Table 3. According to the electrode constants E0′, the electrode response slope k and the potential difference Eb, the mean activity coefficient γ±NaBr of mixed solution can be calculated according to eq 2, the results are also shown in Table 3. The relationship between the mean activity coefficients γ±NaBr of mixed solution and the ionic strength scores yB of Na2SO4 is shown in Figure 2. Seen from Table 3, in a mixed solution containing Na2SO4, lnγ±NaBr decreases with the increase of I within the range of I less than 1.000 mol·kg−1, lnγ±NaBr increases with the increase of I within the range of I more than 1.000 mol·kg−1. As shown in Figure 2, when the I is constant, lnγ±NaBr changes little with the increase of yB, indicating that the activity coefficients of NaBr almost depend on the total ionic strength (not the concentration). Values of the Pitzer parameters (β(0), β(1), and CØ)for pure NaBr and pure Na2SO4 are listed in Table 4. According to measured values Eb of NaBr + Na2SO4 + H2O system and the Pitzer model formula, the Pitzer parameters θBr−·SO2− and 4 + − 2− φNa ·Br ·SO4 were calculated using Matlab linear regression method on the basis of eqs 2−23. The results are shown in Table 5. The osmotic coefficient, water activity, excess Gibbs energy results of NaBr + Na2SO4 + H2O ternary system at 298.15 K are listed in Table 6. The relationship of osmotic coefficient and total ionic strength of NaBr + Na2SO4 + H2O ternary system are shown in Figure 3. As shown in Table 6, when the I is constant, the osmotic coefficient Φ and excess Gibbs energy GE decreases with the increase of yB, water activity aW increases with the increase of yB; when the yB is constant, the osmotic coefficient Φ decreases at the beginning and then increases with the increase of I, water

I/mol·kg−1

yB

m1/ mol·kg−1

m2/ mol·kg−1

Eb/mV

γ±NaBr

0.0503 0.0506 0.0502 0.0500 0.0499 0.1003 0.1000 0.1000 0.0997 0.0997 0.1998 0.2021 0.2009 0.2004 0.1997 0.5017 0.5025 0.5017 0.4986 0.4990 0.9985 0.9997 0.9990 1.0010 0.9995 2.0039 1.9999 2.0013 1.9974 1.9972 3.0039 2.9963 2.9962 2.9920 2.9968

0.8017 0.6034 0.3965 0.1970 0.0000 0.7997 0.5993 0.3986 0.2001 0.0000 0.7990 0.6043 0.4054 0.2018 0.0000 0.8004 0.6016 0.4011 0.1998 0.0000 0.8002 0.6003 0.4007 0.2000 0.0000 0.7999 0.5994 0.4001 0.2003 0.0000 0.7998 0.6004 0.4002 0.2002 0.0000

0.0100 0.0201 0.0303 0.0402 0.0499 0.0201 0.0401 0.0601 0.0797 0.0997 0.0402 0.0800 0.1195 0.1600 0.1997 0.1001 0.2002 0.3005 0.3990 0.4990 0.1995 0.3996 0.5987 0.8008 0.9995 0.4010 0.8012 1.2007 1.5974 1.9972 0.6014 1.1974 1.7971 2.3930 2.9968

0.0134 0.0102 0.0066 0.0033 0.0000 0.0267 0.0200 0.0133 0.0066 0.0000 0.0532 0.0407 0.0272 0.0135 0.0000 0.1339 0.1008 0.0671 0.0332 0.0000 0.2663 0.2001 0.1334 0.0667 0.0000 0.5343 0.3996 0.2669 0.1333 0.0000 0.8008 0.5996 0.3997 0.1997 0.0000

54.3 73.3 84.8 93.2 99.7 84.5 103.0 114.6 122.8 129.9 116.5 135.5 146.7 155.2 161.5 158.5 177.1 188.4 196.7 203.5 189.2 208.4 220.4 229.3 236.4 228.4 247.3 259.1 267.9 274.8 252.0 270.7 282.4 291.1 297.9

0.876 0.871 0.864 0.859 0.853 0.811 0.804 0.799 0.792 0.791 0.781 0.778 0.771 0.765 0.753 0.737 0.730 0.721 0.717 0.711 0.693 0.694 0.697 0.695 0.696 0.769 0.768 0.767 0.767 0.764 0.831 0.828 0.825 0.823 0.816

Figure 2. Plot of mean activity coefficient logarithm ln γ±NaBr. vs stoichiometric ionic strength fraction of Na2SO4 yB at different ionic strengths of the NaBr + Na2SO4 + H2O ternary system at 298.15 K.

activity aW and excess Gibbs energy GE decreases with the increase of I. D

dx.doi.org/10.1021/je500046e | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 4. Values of the Pitzer Parameters (β(0), β(1), and CØ) for Pure NaBr and Na2SO4 at 298.15 K electrolyte

β(0)/kg·mol−1

β(1)/kg·mol−1

CØ/kg2·mol−2

mmax/mol·kg−1

σ

ref

NaBr Na2SO4

0.110 77 0.046 04

0.137 60 0.933 50

−0.001 53 −0.004 83

9.000 1.750

0.004 48 0.001 12

31 31

Table 5. Pitzer Parameters θBr−·SO42− and φNa+·Br−·SO42− for the NaBr + Na2SO4 + H2O Ternary System at 298.15 K I/mol·kg−1

θBr−·SO42−

φNa+·Br−·SO42−

R2

ref

0.0050−3.0000

0.2002

0.0568

0.9414

this work

Table 6. Values for the Total Ionic Strengths I, Stoichiometric Ionic Strength Fraction of Na2SO4 yB, Mean Activity Coefficient of Na2SO4 γ±Na2SO4, Osmotic Coefficient Ø, Water Activity aW, and Excess Gibbs Energy GE for the NaBr + Na2SO4 + H2O Ternary System at 298.15 K I/mol·kg−1

yB

γ±Na2SO4

Φ

aW

GE/kJ·mol−1

0.0503 0.0506 0.0502 0.0500 0.0499 0.1003 0.1000 0.1000 0.0997 0.0997 0.1998 0.2021 0.2009 0.2004 0.1997 0.5017 0.5025 0.5017 0.4986 0.4990 0.9985 0.9997 0.9990 1.0010 0.9995 2.0039 1.9999 2.0013 1.9974 1.9972 3.0039 2.9963 2.9962 2.9920 2.9968

0.8017 0.6034 0.3965 0.1970 0.0000 0.7997 0.5993 0.3986 0.2001 0.0000 0.7990 0.6043 0.4054 0.2018 0.0000 0.8004 0.6016 0.4011 0.1998 0.0000 0.8002 0.6003 0.4007 0.2000 0.0000 0.7999 0.5994 0.4001 0.2003 0.0000 0.7998 0.6004 0.4002 0.2002 0.0000

0.6586 0.6602 0.6647 0.6699 0.6763 0.5807 0.5850 0.5907 0.5985 0.6079 0.5006 0.5057 0.5154 0.5274 0.5423 0.3974 0.4103 0.4275 0.4493 0.4751 0.3285 0.3507 0.3788 0.414 0.4577 0.2721 0.3121 0.3633 0.4295 0.5161 0.2498 0.3093 0.3898 0.4994 0.6522

0.8968 0.9119 0.9242 0.9334 0.9409 0.8720 0.8921 0.9073 0.9190 0.9286 0.8468 0.8720 0.8917 0.9072 0.9193 0.8169 0.8561 0.8847 0.9059 0.9217 0.8046 0.8624 0.9024 0.9306 0.9496 0.8185 0.9114 0.9711 1.0071 1.0259 0.8563 0.9840 1.0609 1.0998 1.1106

0.9990 0.9988 0.9987 0.9985 0.9983 0.9981 0.9978 0.9974 0.9970 0.9967 0.9963 0.9956 0.9949 0.9941 0.9934 0.9912 0.9892 0.9873 0.9855 0.9836 0.9828 0.9785 0.9744 0.9702 0.9664 0.9652 0.9550 0.9455 0.9369 0.9288 0.9459 0.9284 0.9125 0.8988 0.8870

−0.0362 −0.0362 −0.0356 −0.0356 −0.0357 −0.0953 −0.0936 −0.0931 −0.0929 −0.0938 −0.2456 −0.2447 −0.2403 −0.2394 −0.2405 −0.839 −0.8111 −0.7915 −0.7792 −0.7859 −2.0368 −1.9209 −1.8400 −1.8053 −1.8049 −4.8206 −4.3167 −3.9737 −3.7695 −3.7285 −7.7503 −6.5983 −5.7846 −5.3072 −5.2023

Figure 3. Plot of the osmotic coefficients Ø. against total ionic strength I of the NaBr + Na2SO4 + H2O ternary system at different yB at T = 298.15 K.

activity of the single salt was drawn. The results indicated that the Nernst electrode has a good linear response and that the obtained electrode constant and response slope are true and reliable. The potential difference of the NaBr + Na2SO4 + H2O system was measured at 298.15 K. According to the obtained electrode constant and the response slope, the mean activity coefficients of NaBr in the NaBr + Na2SO4 + H2O system were calculated using the Nernst equation. Pitzer ion interaction parameters θBr−·SO42− and φNa+·Br−·SO42−, the osmotic coefficients Ø, water activity aw, and the Gibbs energy GE of the system were calculated by a Matlab linear regression method. This theoretical calculation provides a supplementary role for the study of the phase equilibrium of the NaBr + Na2SO4 + H2O system, which provides a foundation for later research on the theory of phase equilibrium.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This project was supported by the National Natural Science Foundation of China (41373062 and 40973047), the Specialized Research Fund (20125122110015) for the Doctoral Program of Higher Education of China, and the youth science and technology innovation team of Sichuan Province, China (2013TD0005).

5. CONCLUSION In this paper, we determined the average activity coefficients of NaBr + Na2SO4 + H2O ternary system by potential difference measurements from a galvanic cell without liquid junction. The main research contents and results are as follows: The potential difference of single salt NaBr was measured at 298.15 K, the diagram of the potential difference and the

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