Mean Activity Coefficients of KBr in KBr+K2B4O7+H2O Ternary

Jan 21, 2014 - The mean activity coefficients of KBr in the KBr+K2B4O7+H2O ternary system were determined at the total ionic strength ranging from 0.0...
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Mean Activity Coefficients of KBr in KBr+K2B4O7+H2O Ternary System at 298.15 K Determined by the Electromotive Force Method Si-Yao Zhong,†,‡ Shi-Hua Sang,*,†,‡ Jun-Jie Zhang,†,§ and Cui Wei†,‡ †

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 KBr in the KBr+K2B4O7+H2O ternary system were determined at the total ionic strength ranging from 0.0100 mol· kg−1 to 2.0000 mol·kg−1 at 298.15 K by an electromotive force method from the cell without liquid junction: K-ISE|KBr(m1),K2B4O7(m2)|Br-ISE. The mean activity coefficients of KBr were compared with those different ionic strength fractions yB of K2B4O7 with yB = (0.8, 0.6, 0.4, 0.2, and 0). The experimental results showed that K-ISE and Br-ISE in this work had a good Nernst response, and the mean activity coefficients of KBr in KBr+K2B4O7+H2O mixtures were calculated using the Nernst equation. Mixing interaction parameters of θBr−·B4O5(OH)2− and φK+·Br−·B4O5(OH)2− in Pitzer’s equation, which had not been reported, 4 4 were evaluated from the present measurements of the mean activity coefficients of KBr. Then the osmotic coefficients, water activity, and excess Gibbs free energy of this system were calculated by the Pitzer’s equations. NaCl+KCl+H2O system at 318 K. Spah et al.16,17 studied the activity coefficients of CoCl2 and CuCl2 using EMF at 303.15 K and 313.15 K. Bagherinia et al.18 determined the activity coefficients of MgCl2 in the MgCl2+MgSO4+H2O system by EMF at 298.15 K. In our previous work, we studied the 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 EMF,19,20 we also studied multi-temperature phase diagrams in a series of subsystems of the NaCl+NaBr+Na2 SO4 +Na 2 B4 O 7 +KCl+ KBr+K2SO4+K2B4O7+H2O system for underground brine, that is, NaCl+Na2SO4+Na2B4O7+KCl+K2SO4+K2B4O7+H2O at 298 K;21 Na2B4O7+Na2 SO4+NaCl+H2O at 323 K;22 Na2SO4+Na2B4O7+K2SO4+K2B4O7+H2O at 323 K23 and NaBr +Na2SO4+KBr+K2SO4+H2O at 323 K.24 In general, 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, the phase diagram of the KBr+K2B4O7+H2O ternary system at 298.15 K has been reported;25 however, no report has been found on thermodynamic properties of the KBr +K2B4O7+H2O ternary system at 298.15 K. Therefore, in this work, the activity coefficients of KBr in the KBr+K2B4O7+H2O ternary system were determined by EMF measurement at 298.15 K and in (0.0100 to 2.0000) mol·kg−1 total ionic strength range, and the Pitzer’s ion interaction parameters of θBr−·B4O5(OH)2− 4 and φK+·Br−·B4O5(OH)42− were evaluated by using the activity

1. INTRODUCTION Electrolyte solutions are commonly found in nature. They have become favorable media for many organic and inorganic reactions, and are widely used in desalination, brine development, hydrometallurgy, earth science and environmental protection. Thus there is considerable scientific and technological interest in the thermodynamic properties of an electrolyte solution.1−3 The thermodynamic study of the electrolyte solution is also the thermodynamic basis of phase equilibria and chemical equilibrium calculations. In the past decades, a series of ion-interaction models have been proposed to predict the activity and osmotic coefficients of each electrolyte solution, of which the Pitzer equation is one of the most famous and useful model.4−6 The Western Sichuan basin in China has abundant resources in underground brines,7,8 which contain a large amount of sodium, potassium, boron, and bromine. Therefore, the study of the thermodynamic properties of brine is necessary. Research reports about activity coefficients calculated using the Pitzer equation are increasing all over the word. For example, Millero et al.9,10 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.11−13 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. With the application of Harned’s rule and the Pitzer equations, the thermodynamics of the HBr+NiBr2+H2O system from 5 °C to 55 °C were determined. Rodil et al.14 measured activity coefficients of MgCl2 in the MgCl2+CaCl2+ H2O and the MgCl2+BaCl2+H2O systems at 298.15 K by the electromotive force (EMF) method. Flesia et al.15 determined activity coefficients and osmotic coefficients of KCl in the © 2014 American Chemical Society

Received: October 13, 2013 Accepted: January 3, 2014 Published: January 21, 2014 455

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the activity of K+ and Br−, γ±KBr expresses the mean activity coefficient of KBr. The method and procedure is as follows: the total ionic strengths I (I = m1 + 3m2) ranges from 0.0100 mol·kg−1 to 2.0000 mol·kg−1, K2B4O7 of ionic strength score yB = 0.8, 0.6, 0.4, 0.3, 0.2 and 0, concentration from low to high close to capacity. The yB follows as yB = 3m2/(m1+ 3m2). Before determining the activity coefficients of the mixture, the electromotive force of cell (a) was measured so as to determine the standard electromotive force E0 and practical response slope κ. There κ = RT/F represented the theoretical Nernst slope. The R, F, and T were the gas constant, Faraday constant, and absolute temperature, respectively. The activity coefficients of pure KBr solution at 298.15 K were taken from the Handbook of Chemistry and Physics.26 Then the electromotive force of cell (b) under different ionic strengths was measured, and all the concentrations were determined from low to high. During measurement the experimental solution was under constant temperature (298.15 ± 0.1 K) until the electromotive force was steady and changed less than 0.1 mV in 30 min. For ionic activity coefficients the corresponding relations are

coefficients of KBr in the KBr+K2B4O7+H2O ternary system. Then the osmotic coefficients, water activity, excess Gibbs free energy of this system were calculated.

2. EXPERIMENTAL SECTION 2.1. Chemicals. The water for experiments was deionized water, with a conductivity less than 10−4 S·cm−1. All reagents were G.R. grade and were placed in an oven under 393 K for 2 h before using. 2.2. Apparatus. 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 BiLang 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.); 401 potassium ion selective electrode (Jiangsu Jiangfen Electroanalytical Instrument Co., Ltd.); PBr1-01 bromide ion selective electrode (Leici Precision Scientific Instrument Co., Ltd.); 50 mL glasses and other conventional glass instruments. 3. METHOD K-ISE was soaked for 30 min in 10−2 mol·L−1 KCl aqueous solution, and washed with deionized water to a blank potential around −160 mV, static reading when testing. Br-ISE was soaked for activation for 2 h in 10−3 mol·L−1 NaBr aqueous solution, then cleaned with deionized water, so that the cleaning potential was about 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·L−1 lithium acetate solution. First, the electromotive force of each single salt was determined so the electrode response slope of each electrode and the electrode constant were obtained. The salt composition with KBr single cell without liquid junction was K+ − ISE|KBr(m 0), H 2O|Br − − ISE

(γ±KBr)2 = γK+·γBr−

{γ±K B O (OH) }3 = (γK+)2 · γB O (OH) 2− 2 4 5

4 5

(A4)

4

+ m B4O5(OH)4 (2BK,B4O5(OH)4 + ZC K,B4O5(OH)4) + mK mBr C K,Br + mK m B4O5(OH)4 C K,B4O5(OH)4 + mBr m B4O5(OH)4 ψK,Br,B O (OH) 4 5

(A5)

4

ln γBr − = F + mK (2BK,Br + ZC K,Br) + mK mBr C K,Br + mK m B4O5(OH)4 C K,B4O5(OH)4

(a)

+ m B4O5(OH)4 (2ΦBr,B4O5(OH)4

0

Ea = E + κ ln a+a−

+ mK ψK,Br,B O (OH) ) 4 5

= E 0 + κ ln a0

(A6)

4

and (A1)

ln γB O (OH) 2− = 4F + mK (BK,B4O5(OH)4 + ZC K,B4O5(OH)4)

Where: a+, a−, a0, m0, and γ0±KBr, respectively, represent a single positive ion activity, negative ion activity, mean activity, molality, and activity coefficient, Ea indicates the battery electromotive force, E0 indicates the cell constant, κ indicates the electrode response slope. For the mixed salt, a cell without liquid junction can be composed of K+ − ISE|KBr(m1), K 2B4 O7 (m2), H 2O|Br− − ISE

4

ln γK+ = F + mBr (2BK,Br + ZC K,Br)

whose potential value was

= E 0 + 2κ ln m0γ0 ± KBr

(A3)

4 5

4

+ 2mK mBr C K,Br + 2mK m B4O5(OH)4 C K,B4O5(OH)4 + mBr (2ΦBr,B4O5(OH)4 + mK ψK,Br,B O (OH) ) 4 5

4

(A7)

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

(b)

whose potential value is

′ + mK m B4O5(OH)4 BK,B ′ 4O5(OH)4 + mK mBr BK,Br

E b = E 0 + κ ln αK+·αBr− = E 0 + κ ln m1(m1 + 2m2)γ±2KBr

+ mBr m B4O5(OH)4 Φ′Br,B4O5(OH)4

(A2)

(A8) −1/2

where I is the ionic strength, the constants b = 1.2 mol ·kg1/2 and a = 2.0 mol−1/2·kg1/2, and A⌀ = 0.391475 mol−1/2·kg1/2 is the

where m1 and m2, respectively, represent the molality of KBr and K2B4O7 in mixed solution, αK+ and αBr−, respectively, represent 456

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⎛ Z BrZ B4O5(OH)4 ⎞⎡ J(χBr,Br ) θ Br,B4O5(OH)4 = ⎜ ⎟⎢J(χBr,B4O5(OH)4 ) − ⎢ 4I 2 ⎝ ⎠⎣

value of the Debye−Hückel limiting-law slope for an aqueous solution at T = 298.15 K.27,28 Values of the Pitzer parameters (1) ⌀ β(0) M,X, βM,X, and CMX for KBr and K2B4O5(OH)4 at 298.15 K are from references 29 and 30. For the {(1 − yB)KBr + yBK2B4O7}(aq) system, the osmotic coefficient equation is

E

−

E

+ mK mBr (B⌀K,Br + ZC K,Br) + mK m B4O5(OH)4 (B⌀K,B4O5(OH)4 + ZC K,B4O5(OH)4) ⎤ + mK ψK,Br,B O (OH) }⎥ 4 5 4 ⎥ ⎦

−

(A9)

χBr,Br J ′(χBr,Br ) 2

mBr = m1;

m B4O7 = m2

(A19)

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

(A20)

The quantities BM,X, CMX, and BM,X ′ are defined to have the following dependences on ionic strength:

+ [4 + 4.581χ −0.7237 exp(− 0.0120χ 0.528 )]−2 4.581χ exp( −0.0120χ 0.528 )(0.7237χ −1.7237 + 0.0120

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

(A10)

× 0.528χ −0.472 χ −0.7237 )

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

⎪

⎪

⎪

GE = RT[2m1(1 − ⌀ + ln γ±KBr) + 3m2 (1 − ⌀ + ln γ±K B O (OH) )]

⌀ CMX

2 4 5

1/2

(2 |Z MZ X|

) ⎜

(A22)

4

and

(A12)

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

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

(A23)

⎟

4. RESULTS AND DISCUSSION Using m0 (molality of KBr) and Ea (the EMF value measuring KBr), the γ0±KBr (activity coefficients of KBr at 298.15 K accessing the Handbook of Chemistry and Physics26) was determined and collected in Table 1, and a diagram (Figure 1)

(A13)

I

where M denotes K+ and X denotes Br− or B4O5(OH)42−; ZM and ZX are the valences of ions M and X; these mixing functions are related to the mixing parameters by Φ⌀Br,B4O5(OH)4

(A21)

The excess Gibbs free energy (GE) and activity of water (aW) are calculated from the following relations:

(A11)

′ = BM,X

4

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

B⌀M,X,

CMX =

χB O (OH) ,B O (OH) J ′(χB O (OH) ,B O (OH) ) ⎤ 4 5 4 4 5 4 4 5 4 4 5 4 ⎥ ⎥⎦ 2 (A18)

χBr,B O (OH) = 6Z BrZ B4O5(OH)4A⌀I1/2 4 5

mK = m1 + 2m2 ;

and

−

where

where Z is given by Z = mK + mBr + 2m B4O7 ;

(A17)

⎛ Eθ ⎞ ′ O (OH) = − ⎜ Br,B4O5(OH)4 ⎟ θ Br,B ⎜ ⎟ 4 5 4 I ⎝ ⎠ ⎛ Z BrZ B4O5(OH)4 ⎞⎡ +⎜ ⎟⎢χBr,B4O5(OH)4 J ′(χBr,B4O5(OH)4 ) 8I 2 ⎝ ⎠⎢⎣

⎛ ⎞⎡⎛ −A⌀I 3/2 ⎞ 2 ⎟⎟⎢⎜ ⎟ ⌀ = 1 + ⎜⎜ 1/2 ⎝ mK + mBr + m B4O5(OH)4 ⎠⎢⎣⎝ 1 + bI ⎠

+ mBr m B4O5(OH)4 {Φ⌀Br,B4O5(OH)4

J(χB O (OH) ,B O (OH) ) ⎤ 4 5 4 4 5 4 ⎥ ⎥⎦ 2

E

= θBr,B4O5(OH)4 + θ Br,B4O5(OH)4

Table 1. The Electromotive Force and Activity Coefficient of KBr Criterion Solution at 298.15 Ka

′ O (OH) + I θ Br,B 4 5 4 E

(A14)

ΦBr,B4O5(OH)4 = θBr,B4O5(OH)4 + Eθ Br,B4O5(OH)4

(A15)

and ′ O (OH) Φ′Br,B4O5(OH)4 = Eθ Br,B 4 5 4

(A16)

where the quantity EθBr,B4O5(OH)4 and its ionic strength derivative θBr,B ′ 4O5(OH)4 can be calculated, and their values depend only the total ionic strength I and the valences of the ions of like sign, in this case ZBr and ZB4O5(OH)4. The equations are the following forms:

m0/mol·kg−1

γ0±KBr

ln a0±KBr

Ea/mV

0.0013 0.0052 0.0100 0.0499 0.1001 0.1998 0.5002 1.0003 2.9989

0.965 0.934 0.903 0.824 0.772 0.772 0.657 0.617 0.595

−13.424 −10.673 −9.416 −6.381 −5.120 −3.738 −2.226 −0.965 1.158

19.9 90.2 120.1 197.8 229.3 264.6 303.9 337.6 390.4

E

m0 is the molality of pure KBr aqueous solutions, γ0±KBr is the activity coefficients of KBr at 298.15 K from the Handbook of Chemistry and Physics,26 a0±KBr is the activity of pure KBr aqueous solutions, and Ea is the battery electromotive force of pure KBr aqueous solutions. a

457

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Table 3. The Mean Activity Coefficients of KBr in KBr +K2B4O7+H2O Ternary System at 298.15 Ka I

Figure 1. The response curve of K+-ISE−Br−-ISE battery vs KBr at 298.15 K.

Table 2. Electrode Constant and Electrode Response to Slopea E0/mV

κ

R2

360.6

25.43

0.999

E is the cell constant, κ is the electrode response slope.

a 0

Figure 2. Plot of ln γ±KBr vs yB at different ionic strengths of the KBr +K2B4O7+H2O ternary system at 298.15 K: ◆, I = 0.0100 mol·kg−1; ■, I = 0.0200 mol·kg−1; ▲, I = 0.1000 mol·kg−1; ×, I = 0.2000 mol·kg−1; ∗, I = 0.5000 mol·kg−1; ●, I = 1.0000 mol·kg−1; +, I = 2.0000 mol·kg−1.

m1

m2

Eb

mol·kg−1

yB

mol·kg−1

mol·kg−1

mV

γ±KBr

0.0100 0.0100 0.0100 0.0102 0.0100 0.0199 0.0200 0.0200 0.0202 0.0201 0.0998 0.1000 0.0998 0.1024 0.1006 0.1991 0.2004 0.2003 0.2050 0.2021 0.4986 0.4989 0.4995 0.4989 0.5008 1.0078 1.0006 1.0159 0.9973 0.9994 2.0029 2.0025 2.0016 2.0039 1.9997

0.8006 0.5993 0.4010 0.2019 0.0000 0.7992 0.5968 0.4054 0.1986 0.0000 0.7996 0.5989 0.4019 0.2040 0.0000 0.7992 0.5965 0.4061 0.1985 0.0000 0.7996 0.5969 0.4027 0.2001 0.0000 0.7996 0.5943 0.3921 0.1996 0.0000 0.8002 0.5981 0.3960 0.1989 0.0000

0.0020 0.0040 0.0060 0.0082 0.0100 0.0040 0.0081 0.0119 0.0162 0.0201 0.0200 0.0401 0.0597 0.0815 0.1006 0.0400 0.0808 0.1189 0.1643 0.2021 0.0999 0.2011 0.2983 0.3991 0.5008 0.2020 0.4059 0.6175 0.7982 0.9994 0.4002 0.8047 1.2090 1.6052 1.9997

0.0027 0.0020 0.0013 0.0007 0.0000 0.0053 0.0040 0.0027 0.0013 0.0000 0.0266 0.0200 0.0134 0.0070 0.0000 0.0530 0.0398 0.0271 0.0136 0.0000 0.1329 0.0993 0.0671 0.0333 0.0000 0.2686 0.1982 0.1328 0.0664 0.0000 0.5342 0.3993 0.2642 0.1329 0.0000

73.0 93.0 104.8 115.1 121.5 105.3 125.3 136.6 146.2 153.0 183.9 203.7 215.4 225.4 231.7 216.9 237.1 248.8 259.5 266.1 255.2 275.3 287.5 296.9 304.2 287.1 307.2 320.6 328.6 336.1 319.1 339.5 352.1 361.5 369.4

0.920 0.919 0.912 0.909 0.904 0.864 0.860 0.852 0.844 0.838 0.809 0.807 0.802 0.794 0.788 0.776 0.774 0.773 0.773 0.772 0.659 0.659 0.661 0.663 0.659 0.610 0.613 0.617 0.618 0.618 0.577 0.581 0.584 0.587 0.595

a

I is the total ionic strengths; yB is the stoichiometric ionic strength fraction of K2B4O7 in the mixtures; m1, m2 respectively represent the molality of KBr and K2B4O7 in mixed solution; Eb is the battery electromotive force of mixed solution; γ±KBr is the mean activity coefficient of KBr in the mixtures.

reliable. The electrode constants and the electrode response slope are listed in Table 2. The weight molar concentration m1, m2 and the electromotive force Eb of mixed solution are listed in Table 3. According to the electrode constants E0, the electrode response slope κ, and the electromotive force Eb, the mean activity coefficient γ±KBr of mixed solution can be calculated according to eq A2; the results are shown in Table 3. The relationship between the mean activity coefficients γ±KBr of mixed solution and the ionic strength scores yB of K2B4O7 is shown in Figure 2. Seen from Table 3, in a mixed solution containing K2B4O7, ln γ±KBr decreases with the increase of I. It is shown that in the ternary system KBr+K2B4O7+H2O, the greater is the concentration of the solution, the smaller is the mean activity coefficient of KBr. As shown in Figure 2, when the I is constant, with the increase of yB, ln γ±KBr changed little, indicating that the activity

Figure 3. Plot of the osmotic coefficients of water against total ionic strength of the KBr+K2B4O7+H2O system at different yB at T = 298.15 K: ●, yB = 0; ∗, yB = 0.2; ◆, yB = 0.4; ▲, yB = 0.6; ■, yB = 0.8.

was drawn. In Figure 1, it can be seen that there is a good linear response between ln a0±KBr and Ea. As shown in Figure 1, Ea linearly increases with ln a0±KBr increases, and R2 = 0.999, so the K+-ISE and Br−-ISE have a good linear Nernst response, and the measured EMF value is true and 458

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Table 4. Values of the Pitzer Parameters for KBr and K2B4O5(OH)4 at 298.15 K C⌀

mmax

kg·mol

kg·mol

−1

kg ·mol−2

mol·kg−1

σ

0.05592 −0.022

0.22094

−0.00162

5.500

0.00036

β(0)

β(1) −1

electrolyte 29

KBr K2B4O5(OH)430

2

According to EMF measured values Eb of KBr+K2B4O7+H2O system and the Pitzer model formula, the Pitzer parameters θBr−·B4O5(OH)2− and φK+·Br−·B4O5(OH)2− were calculated using a Matlab 4 4 linear regression method on the basis of eq A2−A23. The results are shown in Table 5. The osmotic coefficient, water activity, excess Gibbs free energy results of the KBr+K2B4O7+H2O ternary system at 298.15 K are listed in Table 6. The relationship of osmotic coefficient and total ionic strength of KBr+K2B4O7+H2O ternary system are shown in Figure 3.

Table 5. Pitzer Parameters for the KBr+K2B4O7+H2O Ternary System at 298.15 K I/mol·kg−1

θBr−·B4O5(OH)2− 4

φK+·Br−·B4O5(OH)2− 4

R2

0.0100−2.0000

0.2364

−0.1464

0.9677

Table 6. The Osmotic Coefficient, Water Activity, and Excess Gibbs Free Energy of KBr+K2B4O7+H2O at 298.15 Ka I/mol·kg−1

yB

γ±K2B4O5(OH)4

⌀

aW

GE/kJ·mol−1

0.0100 0.0100 0.0100 0.0102 0.0100 0.0199 0.0200 0.0200 0.0202 0.0201 0.0998 0.1000 0.0998 0.1024 0.1006 0.1991 0.2004 0.2003 0.2050 0.2021 0.4986 0.4989 0.4995 0.4989 0.5008 1.0078 1.0006 1.0159 0.9973 0.9994 2.0029 2.0025 2.0016 2.0039 1.9997

0.8006 0.5993 0.4010 0.2019 0.0000 0.7992 0.5968 0.4054 0.1986 0.0000 0.7996 0.5989 0.4019 0.2040 0.0000 0.7992 0.5965 0.4061 0.1985 0.0000 0.7996 0.5969 0.4027 0.2001 0.0000 0.7996 0.5943 0.3921 0.1996 0.0000 0.8002 0.5981 0.3960 0.1989 0.0000

0.8046 0.8054 0.8069 0.8069 0.8108 0.7420 0.7431 0.7455 0.7477 0.7521 0.5512 0.5558 0.5625 0.5673 0.5794 0.4581 0.4644 0.4731 0.4819 0.4971 0.3370 0.3475 0.3600 0.3763 0.3952 0.2535 0.2669 0.2813 0.3021 0.3259 0.1819 0.1934 0.2093 0.2296 0.2569

0.9419 0.9506 0.9574 0.9624 0.9673 0.9217 0.9338 0.9428 0.9505 0.9569 0.8538 0.8791 0.8984 0.9134 0.9273 0.8169 0.8509 0.8759 0.8972 0.9149 0.7636 0.8131 0.8493 0.8797 0.9045 0.7211 0.7858 0.8338 0.8721 0.9060 0.6700 0.7461 0.8100 0.8677 0.9259

0.9998 0.9998 0.9997 0.9997 0.9996 0.9996 0.9995 0.9995 0.9994 0.9993 0.9982 0.9978 0.9974 0.9970 0.9966 0.9965 0.9957 0.9950 0.9940 0.9934 0.9918 0.9898 0.9879 0.9859 0.9838 0.9844 0.9803 0.9758 0.9722 0.9679 0.9714 0.9630 0.9542 0.9451 0.9355

−0.0036 −0.0036 −0.0035 −0.0037 −0.0036 −0.0100 −0.0099 −0.0098 −0.0099 −0.0098 −0.1013 −0.0990 −0.0967 −0.0986 −0.0950 −0.2673 −0.2607 −0.2536 −0.2553 −0.2459 −0.9452 −0.9009 −0.8661 −0.8342 −0.8149 −2.4309 −2.2579 −2.1763 −2.0294 −1.9540 −6.0080 −5.5502 −5.1540 −4.8238 −4.5024

5. CONCLUSION In this paper, we determined the average activity coefficients of KBr+K2B4O7+H2O ternary system by the EMF method from a battery cell without liquid junction. The main research contents and results are as follows: The electromotive force of single salt KBr was measured at 298.15 K, the diagram of the electromotive force and the 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 electromotive force of the KBr+K2B4O7+H2O system was measured at 298.15 K. According to the obtained electrode constant and the response slope, the mean activity coefficients of KBr in the KBr+K2B4O7+H2O system were calculated using the Nernst equation. Pitzer ion interaction parameters θBr−·B4O5(OH)2− 4 and φK+·Br−·B4O5(OH)2− , the osmotic coefficients ⌀, water activity aW, 4 and the Gibbs free 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 KBr+K2B4O7+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]. Funding

This project was supported by the National Natural Science Foundation of China (41373062, 40973047), the Specialized Research Fund (20125122110015) for the Doctoral Program of Higher Education of China, and the Open Fund (PLC201204) of the State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation (Chengdu University of Technology).

a

I is the total ionic strengths; yB is the stoichiometric ionic strength fraction of K2B4O7 in the mixtures; γ±K2B4O5(OH)4 is the mean activity coefficient of K2B4O5(OH)4 in the mixtures; ⌀, aW, and GE are the osmotic coefficients, water activity, and excess Gibbs free energy of this system calculated by Pitzer’s equations, respectively.

Notes

The authors declare no competing financial interest.

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REFERENCES

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