Fluid Phase Equilibria 226 (2004) 307–312

Study of thermodynamic properties of quaternary mixtureRbCl + Rb2SO4 + CH3OH + H2O by EMF measurement at 298.15 K

Zhang- Juna,∗, Gao Shi-Yangb, Xia Shu-Pingb, Yao- Yanb

a Department of Chemical Engineering, Henan University of Science and Technology, Luoyang 471003, PR Chinab Institute of Salt Lakes, Chinese Academy of Sciences, Xi’an 710043, PR China

Received 16 January 2004; accepted 1 October 2004

Abstract

The electromotive force (EMF) measurements of the cell: Rb-ion selective electrode (ISE)/RbCl (mA), Rb2SO4 (mB), CH3OH (X), H2O(1−X)/Ag AgCl with X= 10 wt.% on the quaternary system RbCl + Rb2SO4 + CH3OH + H2O were carried out at 298.15 K and over totalionic strengths from 0.0050 mol kg−1 up to near saturated concentration 2.5000 mol kg−1. The Rb-ISE and AgAgCl electrodes used in thisw xture wered respondingm y the Harnedr em©

K

1

tscwoac

teoem

am-F)iCl,5 Kentalame-aluesin-cteds

tical

ck-er-

Rb-e.thod

0d

ork were prepared in our laboratory and exhibited reasonably good Nernst response. The activity coefficients of RbCl in the miirectly determined. The experimental data were analyzed by using the Harned rule and Pitzer ion interaction model, and the corodel parameters required in the two equations for this system have been evaluated. It was found that the experimental results obe

ule and the Pitzer model can be used to describe the system satisfactorily. The activity coefficients of Rb2SO4, the osmotic coefficients of thixtures and the excess Gibbs free energy were also calculated.2004 Published by Elsevier B.V.

eywords:Activity coefficient; Osmotic coefficient; Mixed rubidium salt; Mixed solvent; EMF measurement

. Introduction

Introducing some organic solvents into aqueous elec-rolyte solutions, or adding some inorganic salts into mixedolvents (water + organic agent) can change the physical andhemical properties of the original systems to some extent,hich has been found to be very important in the contextf theoretical and application study of fluid chemistry, suchs the separation and purification of mixed salts[1,2], theoncentration distillation[3,4] and so on.

Up to now, most of the investigation on electrolyte solu-ions has been restricted to aqueous electrolyte systems, butlectrolyte systems with more than one solvents have receivednly minor attention. This is mainly due to the relatively easyxperimental methods and theoretical treatments for the for-er systems. Even so, the latter systems found in literature

∗ Corresponding author.E-mail address:zhjabc@mail.haust.edu.cn (Z. Jun).

usually involve only one salt, but not mixed salts. For exple, Koh et al.[5] reported their electromotive force (EMstudy results about ternary system alkali metal chloride (LNaCl, KCl, RbCl and CsCl) + methanol + water at 298.1by using amalgam electrodes. They fitted the experimdata to the Pitzer model, obtained the Pitzer model parters for the related single salts as well as the optimized vof α andβ constants. A conclusion was drawn from Koh’svestigation that the effect of changing the solvent is refleto larger extent by the different values ofAφ than by changein α andβ.

To our knowledge, the EMF measurements and theoretreatments on the system RbCl + Rb2SO4 + CH3OH + H2Oin the maximum range of total ionic strength are still laing. In previous work[6], we have investigated the thmodynamic behavior of RbCl and Rb2SO4 mixed salts inwater by means of a galvanic cell consisting of aion selective electrode and a AgAgCl reference electrodThe relevant results obtained indicate that the EMF me

378-3812/$ – see front matter © 2004 Published by Elsevier B.V.

oi:10.1016/j.fluid.2004.10.010

308 Z. Jun et al. / Fluid Phase Equilibria 226 (2004) 307–312

adopted was well suitable for the determination of the aque-ous system. In this part, the preliminary EMF study forRbCl + Rb2SO4 + CH3OH + H2O quaternary system at rela-tively lower methanol content was made. The activity coeffi-cients were experimentally determined at total ionic strengthsof 0.005, 0.01, 0.05, 0.1, 0.5, 1.0, 1.5, 2.0 and 2.5 mol kg−1

and at 298.15 K. The ionic strength fraction for Rb2SO4, yB,in the system studied was selected as 0.0, 0.2, 0.4, 0.6 and0.8 in order to assign experiments and treat results more ra-tionally and conveniently.

2. Experimental

Rubidium sulfate (Rb2SO4), analytical grade, was twicerecrystallized from water before use. Rubidium chloride(RbCl) was made from rubidium carbonate (Rb2CO3) of an-alytical grade and was further treated with several effectivesteps up to more than 99.5% purity. Then both salts wereheated at 473 K in an oven for about 5–8 h, afterwards storedover silica gel in a desiccator before use. The methanol waschromatographically pure and directly used without furtherpurification. Water used was deionized and then redistilledin the presence of a small amount of KMnO4. Its specificconductance was less than 1.0× 10−4 s m−1.

s aP opera s con-s beend et theg nc e ands res-o

anda in ad con-s at rate.

R

R

w anoli

liq-u dR The

mA andmB were the molalities of RbCl and Rb2SO4 in themixture, respectively.

Each concentration of the above solutions in all cells wasprepared by directly weighing the materials using a Sartoriuselectronic balance whose accuracy was 0.1 mg. In general, foreach run the EMF reached a stable equilibrium value with afluctuation of±0.2 mV after 1–2 h at all ionic strengths.

At first, the electromotive force (EMF) of cell (a) wasmeasured so as to calibrate the electrode pair composing thecell (a), and furthermore obtain its standard potential and theNernst response slope. And then the EMF of cell (c) wasmeasured in the order (from low to high) of ionic strengthfraction (yB) of Rb2SO4 in the solutions. Finally, the EMFof cell (b) was measured to compute the selective coefficient(Kpot).

3. Results and discussion

3.1. The calibration of electrode pair Rb-ISE andAg AgCl

For the cell (a), 15 measurements ofmA0 from0.0050–4.6139 mol kg−1 (saturated) were selected to deter-mine each corresponding potential (Ea). The Nernst equationf

E

o

wiT abso-l ni ntsa me-t .A ofR es ere-f tlyu es ithaa usta in-ee EMFv nsts V,r iation( and0 et , it isc tisfac-

The Rb ion-selective electrode (Rb-ISE), which waVC membrane type based on valinomycin and a prmount potassium tetraphenylboron as active agent, watructed in our laboratory. The related technique hasescribed elsewhere[7]. The Ag AgCl electrode was th

hermal-electrolytic type prepared by us according touidance described by Ives and Janz[8]. They both have beealibrated before use, and showed good Nernst responselectivity. The ion analyzer used was Orion 868, whoselution was± 0.1 mV.

The cell consisted of a Rb ion-selective electroden Ag AgCl reference electrode in the solution placedouble-walled glass vessel whose temperature was heldtant within 298.15± 0.02 K by circulation of water fromhermostat, and stirred by a magnetic stirrer at constant

The cell arrangements in this work were as follows[9]:

b-ISE/RbCl(mA0),CH3OH(X),H2O(1−X)/Ag AgCl (a)

b-ISE/Rb2SO4(mB0),CH3OH(X),H2O(1−X)/Ag AgCl

(b)

Rb-ISE/RbCl(mA),Rb2SO4(mB),CH3OH(X),

H2O(1−X)/Ag AgCl (c)

hereX= 10 wt.% designates the mass fraction of methn the mixed solvents.

These galvanic cells contained a single liquid withoutid junction. Here,mA0 andmB0 were molalities of RbCl anb2SO4 as single salt in the mixed solvents, respectively.

or cell (a) can be expressed as:

a = E0 + k ln aRbCl (1)

r Ea = E0 + k ln(m2A0γ

2±A0)

herek=RT/F represents theoretical Nernst slope. TheaRbCls the activity of RbCl in the mixed solvents. TheR, F and

are the universal gas constant, Faraday constant andute temperature, respectively. Theγ±A0 refers to the meaonic activity coefficient of pure RbCl in the mixed solvet differentmA0; its values were calculated from the para

ers recommended by Kim and Frederich[10] when neededccording to Koh et al.[5], since the Pitzer parametersbCl in the mixed solvents CH3OH (10 wt.%) + water arlightly changed in comparison with those in water, thore theγ±A0 value calculated from RbCl in water is direcsed as the substitution of that in the mixed solvent. ThE0

tands for the experimental standard EMF of cell (a). Wseries of sets ofEa, mA0 and γ±A0, then we plottedEa

gainst lnaRbCl so as to check their linear relationship. Js shown inFig. 1, it is clear that there really exists good lar relationship betweenEa and lnaRbCl. TheE0 andkcan bevaluated using linear regression method. By means ofalueEa for eachmA0, the regressed values of the Nerlope (k) and the standard EMF (E0) are 25.52 and 139.7 mespectively; the corresponding root mean square devRMSD) and linear correlation coefficient are 0.1605.9999, respectively. The obtained value ofkgets quite clos

o theoretical one (25.69) of the Nernst slope. Thereforeoncluded that the electrode pairs used here have a sa

Z. Jun et al. / Fluid Phase Equilibria 226 (2004) 307–312 309

Fig. 1. The response of Rb-ISE and AgAgCl electrode pair in the mixedsolvents.

tory Nernst response and are well suitable for the measure-ments.

3.2. The selective coefficient of AgAgCl electrode forSO42− ion

The Ag AgCl electrode is, indeed, also an ion selectiveelectrode. Its selectivity for Cl− is not unique in the mix-ture of RbCl and Rb2SO4, whereas it may be disturbed bySO4

2−. So, in this case, the disturbance extent, that is, theselective coefficientKpot of electrode Ag AgCl for SO4

2−should be determined firstly. Through combining the Nernstprinciple and reordering the relevant terms, theKpot for thegiven system can be calculated from the formula:

Kpot = [exp{(Eb − E0)/k}][2(mB0γ±B0)3/2]

(2)

in whichγ±B0 refers to the mean ionic activity coefficient ofpure Rb2SO4 in the mixed solvents at 298.15 K, and its valuewas likewise treated as the pure Rb2SO4 in water as theγ±A0.TheEb is the EMF value of cell (b) at each measurement.Here, we chose four sets ofmB0 (0.1, 0.5, 1.0, 1.2 mol kg−1)to measureEb. Through calculation the average value ofKpot

is found to be less than 1.0× 10−4.

3t

lues( ntsay nad

E

Table 1The experimental mean activity coefficients of RbCl in the mixture at298.15 K

I (mol kg−1) yB mA

(mol kg−1)mB

(mol kg−1)Em (mV) γ±RbCl

0.005 0.0 0.0050 0.0000 −134.8 0.92330.2 0.0040 0.0003 −142.6 0.92370.4 0.0030 0.0007 −151.4 0.91780.6 0.0020 0.0010 −163.8 0.92470.8 0.0010 0.0013 −184.6 0.9171

0.01 0.0 0.0100 0.0000 −100.9 0.89690.2 0.0080 0.0007 −108.3 0.89480.4 0.0060 0.0013 −117.7 0.89840.6 0.0040 0.0020 −130.4 0.88960.8 0.0020 0.0027 −150.1 0.8891

0.05 0.0 0.0500 0.0000 −24.6 0.79990.2 0.0400 0.0033 −32.2 0.79820.4 0.0300 0.0067 −41.5 0.79590.6 0.0200 0.0100 −54.2 0.79180.8 0.0100 0.0133 −74.3 0.7895

0.10 0.0 0.1000 0.0000 7.1 0.74420.2 0.0800 0.0067 −0.6 0.74040.4 0.0600 0.0133 −9.6 0.74440.6 0.0400 0.0200 −22.4 0.73820.8 0.0200 0.0267 −42.2 0.7394

0.50 0.0 0.5000 0.0000 78.6 0.60410.2 0.4000 0.0333 71.2 0.60480.4 0.3000 0.0667 61.3 0.59690.6 0.2000 0.1000 47.9 0.58530.8 0.1000 0.1333 27.7 0.5820

1.00 0.0 1.0000 0.0000 109.3 0.55120.2 0.8000 0.0667 101.1 0.54320.4 0.6000 0.1333 91.3 0.53720.6 0.4000 0.2000 77.7 0.52470.8 0.2000 0.2667 56.6 0.5125

1.50 0.0 1.5000 0.0000 127.4 0.52390.2 1.2000 0.1000 119.2 0.51630.4 0.9000 0.2000 108.5 0.50170.6 0.6000 0.3000 94.6 0.48710.8 0.3000 0.4000 73.2 0.4730

2.00 0.0 2.0000 0.0000 140.6 0.50890.2 1.6000 0.1333 131.8 0.49570.4 1.2000 0.2667 121.1 0.48160.6 0.8000 0.4000 106.8 0.46390.8 0.4000 0.5333 85.1 0.4479

2.50 0.0 2.5000 0.0000 151.1 0.50010.2 2.0000 0.1667 142.1 0.48520.4 1.5000 0.3333 130.7 0.46510.6 1.0000 0.5000 116.3 0.44710.8 0.5000 0.6667 93.9 0.4258

whereγ±A andγ±B respectively refer to the mean activitycoefficient of RbCl and Rb2SO4 in the cell (c). SinceKpot isso small that the second term within brackets on the right ofthe Eq.(3)can be neglected without leading to an appreciableerror, so the Eq.(3) reduces to

Em = E0 + k ln{mA(mA + 2mB)γ2±A} (4)

.3. Experimental mean activity coefficients of RbCl inhe mixture

The cell (c) was employed to determine the EMF vaEm) of RbCl and Rb2SO4 as mixed salts in the mixed solvet 298.15 K in different ionic strengthI and mole fractionB. Here,yB = IB/I = 3mB/(mA + 3mB). Experimental meactivity coefficients of RbCl (seeTable 1) in the mixture areerived from the following Nernst equation:

m = E0 + k ln{γ2±AmA(mA + 2mB)

+Kpotγ3/2±Bm

1/2B (mA + 2mB)} (3)

310 Z. Jun et al. / Fluid Phase Equilibria 226 (2004) 307–312

Table 2The parameters of Harned equation

I (mol kg−1) ln γ±A0 αAB βAB 103 ×RMSD

0.0050 −0.0800 9.80× 10−4 6.50× 10−3 4.680.0100 −0.1091 2.97× 10−3 1.82× 10−2 3.770.0500 −0.2231 1.13× 10−2 7.32× 10−3 0.890.1000 −0.2961 7.91× 10−3 1.78× 10−4 4.050.5000 −0.5012 2.54× 10−2 3.55× 10−2 6.441.0000 −0.5963 4.71× 10−2 5.39× 10−2 2.551.5000 −0.6449 8.79× 10−2 5.41× 10−2 3.422.0000 −0.6753 1.23× 10−1 4.68× 10−2 1.792.5000 −0.6922 1.53× 10−1 6.07× 10−2 2.40

After arrangements, it becomes

ln γ±A = Em − E0

2k− 1

2 ln {mA(mA + 2mB)}. (5)

Accordingly, the mean activity coefficients of RbCl in theabove mixture can be calculated through Eq.(5), and therelated results of the cell (c) are collected inTable 1.

4. The application and testing of some electrolytesolution theories

4.1. Harned rule

The Harned rule[11] is one of the earliest proposed andthe simplest-formed treatments for strong electrolyte solu-tion. When the total ionic strength keeps constant, the ac-tivity coefficient of an electrolyte in the mixture is a simplefunction of the ionic strength fractionyB of the solution. Inrelation to the electrolytic system studied, the Harned rulecan be written as:

ln γ±A = ln γ±A0 − αAByB − βABy2B − · · · (6)

whereαAB andβAB represents the Harned interaction coef-fi andtF on-s its gher( udet stemq

4

tzerm ld bsti-t ginalPγ n

Fig. 2. Plot of lnγ±RbCl againstyB in the mixture: (�) I = 0.005; (�) I = 0.01;(�) I = 0.05; (�) I = 0.1; (�) I = 0.5;(�) I = 1.0; (�) I = 1.5; ( ) I = 2.0; (�)I = 2.5.

be given as the following Eqs. (7)–(10):

ln γ±RbCl = 2(mA +mB)β(0)RbCl +mBβ

(0)Rb2SO4

+2(mA+mB)g(2√I)β(l)

RbCl+mBg(2√I)β(1)

Rb2SO4

+(1.5m2A + 4mAmB + 2m2

B)CφRbCl

+√

2

2(mAmB + 2m2B)Cφ

Rb2SO4+mBθ +mB

Eθ

+(1.5mAmB +m2B)ψ + F (7)

3 lnγ±Rb2SO4

= 4(mA+2mB)

(mAC

φ

RbCl+√

2

2mBCφ

Rb2SO4

)+ 4mAβ

(0)RbCl

+(2mA + 8mB)β(0)Rb2SO4

+√

2

2(mA + 2mB)2Cφ

Rb2SO4

+4mAg(2√I)β(1)

RbCl + (2mA + 8mB)g(2√I)β(1)

Rb2SO4

+2mAθ + 2mAEθ + (m2

A + 6mAmB)ψ + 6F (8)

F = −A{ √

I√ + 2 ln(l + 1.2√I)}

h ix-t ance[

cients which are dependant upon both ionic strengthemperature. The outcomes, listed inTable 2and shown inig. 2, indicate that at lower ionic strengths the relatihip between lnγ±A andyB basically appears linear, butlightly get curved when the ionic strength becomes hiI > 1.50 mol kg−1). From the above results we can conclhat the Harned rule can be applied to describe the title syuite well.

.2. Pitzer model

In this article, we adopted the modified form of the Piodel suggested by Harvie et al.[12] to fit the experimentaata. For the mixed system studied, after a series of su

utions and rearrangements of related terms of the oriitzer equation, the mean activity coefficientsγ±RbCl and±Rb2SO4 and the osmotic coefficientsΦ of the system ca

φl + 1.2 I 1.2

+(mA + 2mB)g′(2√I)

(mAβ

(1)RbCl +mBβ

(1)Rb2SO4

I

)

+2mIAmBEθ′ (9)

ereI =mA + 3mB denotes the total ionic strength in the mure, and all the other symbols have their usual signific13].

Z. Jun et al. / Fluid Phase Equilibria 226 (2004) 307–312 311

Φ =

mA(mA + 2mB)β(0)RbCl +mB(mA + 2mB)β(0)

Rb2S04+mA(mA + 2mB) exp (−2

√I)β(1)

RbCl

+(√

2/2mB)(mA + 2mB)2CφRb2SO4+ 2mAmB(Eθ + θ+Eθ′I)

+2mAmB(mA + 2mB)ψ − Aφ(I1.5)/(1 + 1.2√I)

mA + 1.5mB+ 1. (10)

In these equations, theEθ and Eθ′ stand for the asym-metrical higher-order electrostatic terms of the Pitzer equa-tion, which can be calculated according to the empirical for-mula [14] suggested by Pitzer. It is worth noting that herethe value ofAφ should be calculated according to the for-

mulaAφ = (2πN0dw/1000)1/2[(e2/DkT )3/2/3], where the

involved symbols have special meanings[12], but the em-pirical constantsα andβ still take the values as 2 and 1.2,respectively, because the changes caused by solvent changingfrom water to mixed solvent are almost negligible[5].

The Pitzer’s mixing interaction parameters (θCl SO4,ψCl SO4 Rb), by taking into account the contribution ofhigher-order electrostatic terms, were evaluated by usingmultiple linear regression technique. In this case, it is as-sumed thatθCl SO4 andψCl SO4 Rb are independent of ionicstrength. TheTable 3lists the values of the regressed Pizter’smixing parametersθCl SO4 andψCl SO4 Rb and correspond-ing root mean square deviation (RMSD).

The activity coefficients of Rb2SO4 and the osmotic co-e erec eterso re-s

ntsΦ .

ouldc hicha usedd

5

ivens tion[

�

TV

I

θ

ψ

1

Table 4The mean activity coefficients of Rb2SO4 in the mixture, osmotic coefficientsof the mixture and excess free energies of mixing

I (mol kg−1) yB γ±Rb2SO4 Φ �mGE (J kg−1)

0.005 0.0 0.8431 0.9734 00.2 0.8456 0.9703 0.05890.4 0.8441 0.9651 0.04270.6 0.8463 0.9607 0.02990.8 0.8482 0.9552 −0.00016

0.01 0.0 0.7903 0.9639 00.2 0.7914 0.9586 0.11660.4 0.7946 0.9537 0.17550.6 0.7950 0.9466 0.07980.8 0.7951 0.9379 −0.0695

0.05 0.0 0.6219 0.9323 00.2 0.6264 0.9221 1.30580.4 0.6295 0.9104 1.45040.6 0.6323 0.8975 0.74290.8 0.6344 0.8821 −0.3682

0.10 0.0 0.5347 0.9150 00.2 0.5401 0.9010 3.28810.4 0.5448 0.8861 3.85450.6 0.5481 0.8690 1.87550.8 0.5502 0.8493 −1.0183

0.50 0.0 0.3310 0.8776 00.2 0.3393 0.8476 29.26010.4 0.3460 0.8173 30.72650.6 0.3512 0.7865 13.10280.8 0.3548 0.7543 −5.6870

1.00 0.0 0.2535 0.8712 00.2 0.2627 0.8263 73.80880.4 0.2704 0.7837 70.18340.6 0.2764 0.7426 21.78570.8 0.2806 0.7023 −14.0714

1.50 0.0 0.2128 0.8743 00.2 0.2225 0.8163 125.7530.4 0.2307 0.7634 105.64960.6 0.2372 0.7146 15.712380.8 0.2419 0.6682 −29.36297

2.00 0.0 0.1861 0.8812 00.2 0.1962 0.8111 181.00310.4 0.2048 0.7494 130.14090.6 0.2118 0.6945 −12.37830.8 0.2170 0.6429 −56.8988

2.50 0.0 0.1667 0.8903 00.2 0.1770 0.8085 236.32420.4 0.1860 0.7395 137.73810.6 0.1935 0.6797 −69.15320.8 0.1991 0.6234 −102.0849

fficients for the mixture at different ionic strengths walculated by substituting the regressed mixing parambtained from this work into the Pitzer equation. Theseults are together given inTable 4.

TheFig. 3shows the relation between osmotic coefficieof the mixture and the total ionic strengthI of the systemAs seen from the above results, the Pitzer equation c

orrelate the experimental data with very small errors, wlso tested the stability and suitability of our electrodesuring the experiments.

. Excess Gibbs free energy of mixing for the system

The excess Gibbs free energies of mixing for the gystem have been calculated by using the following rela15]:

mGE = 2mART

{ln

(γ±A

γ±A0

)+ YA(ΦA −Φ)

}

+3mBRT

{ln

(γ±B

γ±B0

)+ YB(ΦB −Φ)

}

able 3alues of the mixing interaction parameters of the Pitzer equation

(mol kg−1) 0.01–2.5000

Cl SO4 −0.09167

Cl SO4 Rb −0.001266

03 × RMSD 3.24

312 Z. Jun et al. / Fluid Phase Equilibria 226 (2004) 307–312

Fig. 3. Plot of osmotic coefficientΦ against ionic strengthI in the mixture:(�) yB = 0.0; (�) yB = 0.2; (�) yB = 0.4; (�) yB = 0.6; (�) yB = 0.8.

whereγ±A0 andΦA respectively refer to the mean activitycoefficient and osmotic coefficient of RbCl in the mixed so-lution at same total ionic strength as the mixture. TheYAis the mole fraction of RbCl in the mixture and subscript Bsymbolizes Rb2SO4. The calculated results are also listed inTable 4.

6. Conclusion

The galvanic cell consisting of a Rb-ion selective electrodeand a Ag AgCl reference electrode can be used to measurethe EMF with great precision, not only for aqueous mixedelectrolyte solution but also for mixed solvent electrolyte sys-tem, provided the content of methanol in the system is nottoo high.

The Pitzer equation and Harned rule, which initially wereproposed to treat aqueous electrolyte systems, are still suit-able for the electrolyte solution in the mixed solvents. Inaddition, the Pitzer parameters of single salts in water can

be directly used to the mixed solvent system without lead-ing to an appreciable error. But theAφ, or the Debye–Huckelconstant for the osmotic coefficient, should be given the cor-responding values according to its relation with dielectricconstants and density of the mixed solvents.

Acknowledgement

The authors are indebted to Prof. Wu Guo-Liang for his as-sistance in the preparation of Rb-ISE. This project are finan-cially supported by the national natural science foundationof China (Grant No.: 20271051)

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