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Fluid Phase Equilibria 336 (2012) 34–40

Contents lists available at SciVerse ScienceDirect

Fluid Phase Equilibria

journa l homepage: www.elsevier.com/locate/fluid

Osmotic and activity coefficients for the CsF + methanol or ethanol + water

ternary systems determined by potentiometric measurements

∗ ∗

Jing Tang, Lei Wang, Shu’ni Li , Quanguo Zhai, Yucheng Jiang, Mancheng Hu

Key Laboratory of Macromolecular Science of Shaanxi Province, School of Chemistry and Chemical Engineering, Shaanxi Normal University, Xi’an, Shaanxi 710062, PR China

a r t i c l e i n f o a b s t r a c t

Article history: The thermodynamic properties of CsF in the ROH (R = methyl or ethyl) + water mixtures were determined

Received 18 July 2012

using potentiometric measurements at 298.15 K with the mass fraction of ROH varying from 0.00 to 0.30.

Received in revised form 15 August 2012

The Pitzer, extended Debye–Hückel and Pitzer–Simonson–Clegg equations were successfully utilized

Accepted 19 August 2012

to fit the experimental data based on the molality and mole-fraction-composition scale. Except for the

Available online 25 August 2012

standard cell potentials and Pitzer parameters, the mean activity coefficients, osmotic coefficients and

standard Gibbs energies of transference of CsF from water to the methanol + water or ethanol + water

Keywords:

mixtures have also been discussed herein.

Activity coefficient

© 2012 Elsevier B.V. All rights reserved.

Osmotic coefficient CsF

Potentiometric measurements

1. Introduction (RbCl/CsCl + methanol/ethanol + water [10], RbCl/CsCl + ethylene

glycol/propylene glycol/glycerol [11,12]), we present herein the

It is well-known that the thermodynamic properties of elec- thermodynamic properties of CsF in mixed solvents with the mass

trolyte in aqueous or mixed solvents, such as activity coefficients, fraction of methanol or ethanol 0.10, 0.20, and 0.30 at 298.15 K.

osmotic coefficients, Gibbs excess energies and heat capacities The experimental data were well fitted to the Pitzer, the extended

are important for various industrial and environmental processes. Debye–Hückel, and Pitzer–Simonson–Clegg equations.

Especially, alkali metals in aqueous or aqueous-organic mixed

solvent are often selected as part of the research system. For exam-

ple, Hernández-Luis et al. have reported the experimental data 2. Equations

for NaCl [1], NaClO4 [2] and NaBF4 [3] in water or poly (eth-

ylene glycol) 4000 + H2O at temperatures of 288.15, 298.15, and The experimental mean activity coefficients of CsF in the

308.15 K by potentiometric measurements. The activity coefficients aqueous-organic mixtures were calculated from the following

of KCl in proline + water [4] and formamide + water [5] systems Nernstian equation

have been investigated by Ghalami-Choobar and co-workers.

Vera and co-workers have studied the individual ion activity 0

E = E + 2k ln(m±) (1)

coefficients of 1:1 electrolytes, such as KCl [6], NaNO3 + KNO3,

NaCl + KCl, and NaCl + NaBr [7], using potentiometric measure-

where E and m are the experimental values, which represent the

ments at 298.15 K. The ternary systems NaCl + CH3OH + H2O [8]

potential of the cell and the molality of CsF, respectively. ± is the

and NH4Br + NaBr + H2O [9] was also performed by Deyhimi and

mean activity coefficient of CsF; k = RT/F is the theoretical Nernstian

co-workers.

slope in which the symbols (R, T, and F) have their usual meanings.

Up to now, although the thermodynamic properties for a 0

E is the standard potential of the cell.

wide variety of alkali metal salts in organic-water mixtures have

Pitzer equations were used to describe the mean activity coef-

been explored, limited reports can be found for the rare-alkali

ficient in our calculation. For a 1–1 type electrolyte, the Pitzer

metal salts. As an extension of our work on the thermodynam-

equations for the mean activity coefficient (±) and osmotic coef-

ics of rubidium chloride and cesium chloride in mixed solvents

ficient (Ф) can be written as follows [13]:

2

ln ± = f + mB + m C (2)

∗

Corresponding authors. Tel.: +86 29 81530767; fax: +86 29 81530727.

ϕ ϕ 2 ϕ

˚ − 1 = f + mB + m C (3)

E-mail addresses: [email protected] (S. Li), [email protected] (M. Hu).

0378-3812/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.fluid.2012.08.015

Author's personal copy

J. Tang et al. / Fluid Phase Equilibria 336 (2012) 34–40 35

3 where −

S x1x2 2 1 f

ln = × (1 − f )W + × 2(x − x )U ± 2 12 1 2 12 1/2 f f

I 2 1/2 

f = −Aϕ + ln(1 + bI ) (2a)

1/2 2

+ b −

1 bI 2 f 1

  +[f (1 − 2x ) − 1]Z + (x W + x W )   S 12MX f 1 1MX 2 2MX

− − 1/2 1/2 2

+ −

(0) (1) [1 exp( ˛I )(1 ˛I 1/2˛ I)]

B = 2ˇ + 2ˇ (2b) + x1 × 3 2 x2

− + +

+ − + ˛2I [f (2 2x1 xS) xSf (3x1 x2) 2x2]U1MX   3f 2 3f 2

ϕ 3 2

=

× −

+ +

C 1.5C (2c) [f (2 2x2 xS) xSf (3x2 + x1) − 2x1]U2MX (7)

ϕ 1/2 1/2 and

f = −Aϕ(I /(1 + bI )) (3a)

1/2

−

ϕ (0) (1) 1/2 DH 2 1/2 IX (1 2IX )

= + − = −

B ˇ ˇ exp( ˛I ) (3b) ln ± A ln(1 + I ) +

X  X 1/2

+ 1 IX

(0) (1) ϕ  

ˇ , ˇ , and C are the parameters of the Pitzer equation. I

2 1/2

is the ionic strength, I = 1/2 (mZ ), where Z is the charge num- g(˛I )

+ 1/2 X 1 1/2

+ − xX BMX g(˛I ) − xX xM BMX + 1 − exp(−˛I )

ber of Cs and F . B and C represent the second and the X X 2IX 2IX

third virial coefficients, respectively. The term f accounts for the  

(8)

long-range (or Debye–Hückel) forces, while the B and C com-

prise the short-range forces. The variation of B with the ionic

(0) (1) By combining Eqs. (6) and (7), the mean activity coefficient of

strength is given by Eq. (2b) with the parameters ˇ and ˇ .

−1/2 the MX in mixed solvents is:

The parameters b and ˛ are equal to 1.2 and 2.0 kg mol , respec-

DH S

tively. Aϕ is the Debye–Hückel constant for the osmotic coefficient ln ± = ln ± + ln ± (9)

defined by

where W12 and U12 are the parameters for the alcohol (1) + water (2)

3/2 1/2 2 binary system; for methanol + water and ethanol + water mixtures,

1 2N0 e

A = × (4) the parameters are W12 = 0.4926, U12 = 0.0032 and W12 = 1.2051,

ϕ 3 1000 εKT

U = 0.2583 [20]. W and U are parameters for the solvent

    12 iMX iMX

i + MX binary system (i = 1 or 2); Z12MX and BMX are the parameters

where N0, , e, ε, K, and T are Avogadro’s number, the density

of Pitzer–Simonson–Clegg equation. ˛ is given as a fixed value of

of mixed solvent, electronic charge, the dielectric constant, Boltz-

13 [18].

mann’s constant, and the temperature. Eq. (4) can be simplified

In the above equations

as:

− + − = 2[1 (1 x) exp( x)]

6 1/2 −3/2 g(x) (7-1)

Aϕ = 1.4006 × 10  (εT) (5) x2

1

The value of Aϕ in pure water is 0.3915 [13] at 298.15 K. The Aϕ I = (x + x ) (7-2)

X 2 M X

value for the investigated ROH–water mixtures is obtained from

f = 1 − x (7-3)

the bibliography [10]. S

For 1–1 type electrolyte CsF, the extended Debye–Hückel 1/2

s

=

equation for the mean activity coefficient (±) is written as  2150 (7-4) εT [14,15]:  1/2 = 1000 Am1/2 AX Aϕ (7-5)

2 Msol

log ± = − + cm + dm − log(1 + 0.002mM) + Ext (6)

1/2

1 + Bam  

IX means the ionic rational strength; xS is the mole fraction of the

where a is the ion size parameter, c and d are the ion-interaction total ions in the solution; s and ε are the density of solvent as well

parameters, M is the average molecular mass of mixed solvent as dielectric constant of the solvent; and Msol is the mean molecular

and Ext is the contribution of the extended terms and obtained mass of the solvent.

from Roy’s experience formula [16]. A and B are the Debye–Hückel Herein, the following Eq. (10) [19] is applied to the CsF + H2O

constants appropriate to the solvent given by: binary mixture to obtain the parameters BMX, W2MX and U2MX. In

this process, the concentration of CsF in aqueous solutions should

6 1/2

1.8247 × 10 ×  1/2 −1/2 be the mole fraction:

A = kg mol (6a)

(εT)3/2 1/2

−

2 1/2 IX (1 2IX )

± = − × + + ln AX ln(1 IX )

1/2  1/2

+

× − 1 I = 50.2901  1/2 −1/2 1 X B kg mol Å (6b) 1/2   (εT) 1/2

1/2 g(˛IX ) 1 1/2

+ xX BMX g(˛I ) − xX xM BMX × + 1 − exp(−˛I )

where , ε and T have their usual meaning [14,15]. X X

2IX 2IX

In this work, we also use the Pitzer–Simonson–Clegg equation  

to correlate the experiment data, and obtain the param- 2 2

+ − + −

(x2 1)W2MX 2x2(1 x2)U2MX (10)

eters of the model. This equation for electrolyte activity

coefficients was proposed by Pitzer, Simonson and Clegg

[17,18]. The mean ionic rational activity coefficient (±X) can be related

to the mean ionic molal activity coefficient (±) by:

The Pitzer–Simonson–Clegg model for a mixture of two neutral

species, 1 and 2, and a 1–1 type electrolyte has been discussed in

= ± +

±X (1 0.002Msolm) (11)

great details in Ref. [19]. For a MX (electrolyte) + alcohol (1) + water

where m is the molality of the solution.

(2) system, the mean activity coefficient ± MX can be written as

Author's personal copy

36 J. Tang et al. / Fluid Phase Equilibria 336 (2012) 34–40

3. Experimental

All primary stock solutions were prepared by weight using dou-

bly distilled water or the methanol + water and ethanol + water

mixed solvent. The analytical grade cesium fluoride was obtained

from Shanghai China Lithium Industrial Co. Ltd. with minimum

mass fraction of 0.9950. Methanol and ethanol were purchased

from Sinopharm Chemical Reagent Co. Ltd. with mass fraction

greater than 0.9950, respectively. These materials were used with-

out further purification. Double-distilled deionized water was used

in all experiments (water resistivity, 18.25 M cm).

The Cs ion-selective electrode (Cs-ISE) was a PVC membrane

−1

type based on valinomycin and was filled with 0.1 mol L CsF as the

−

internal liquid in K-ISE. F ion-selective electrode used was taken

by Jiangsu Jiangfen Electroanalytical Instrument Co. The electrode

was calibrated before the experiment, and the electrode showed

good Nernstian response. The cells used in this work are given as

follows:

Cs-ISE|CsF(m), H2O|F-ISE (I)

Cs-ISE|CsF(m), ROH(w), H2O(1 − w)|F-ISE (II)

The measurements carried out at different molalities of CsF in

aqueous-organic mixture of water and ROH at 298.15 ± 0.02 K. w

was varied between 0.00 and 0.30 in 0.10-unit steps. In the cells, w

is the mass fraction of ROH, and m is the molality of CsF. The solution

with various molalities was prepared by adding weighed amounts

of the CsF stock solution into the organic-water mixed solvent. The

injector was used to add the stock solution and the solvents to

a double-wall container. All the measurements were performed

under stirring conditions, and the temperature in the cell was

maintained constant within T = 298.15 K (0.02 K) by employing a

double-wall container enabling the circulation of water from a ther-

mostat. The potential readings were obtained on a pH/mV meter

(Orion-868, America). Voltage readings were taken as final when

they were constant, within 0.1 mV, for at least 5 min. The uncer-

tainty of the experimental of potential is ±0.1 mV.

The cell I was used to calibrate the electrodes before the

measurements. Combined Nernst equation (1) with single 1–1

electrolyte Pitzer equation (2)–(4), we obtained the mean activ-

±

ity coefficient of CsF in the pure water. It showed a straight line Fig. 1. Plot of ln (CsF) vs. molalities m of CsF in CsF + methanol + water (a) and

CsF + ethanol + water (b) at 298.15 K. , Ref. [19]; *, w = 0.00; , w = 0.10; + w = 0.20;

when plot of E against ln(m±) produced. The value of k obtained

ଝ, w = 0.30.

by least-squares regression was 25.73 mV. It is clear that the val-

ues of k are close to the theoretical one (25.69 mV) of the Nernst

slope. For comparison, the published values [21] and our data for

the activity coefficients of CsF are both depicted in Fig. 1. This fig- Fig. 2, at the same ROH content, the mean activity coefficient of

ure shows that the experimental and the published data are in close CsF in methanol + water is higher than that in ethanol + water. This

agreement. So it is concluded that the electrode pairs we used have is due to the larger polarity of methanol compared with that of

a good Nernst response, and they are satisfactory enough for our ethanol.

study. The Pitzer parameters and extended Debye–Hückel parameters

were listed in Tables 3 and 4, respectively. The parameter a in

Table 4 is higher than the sum of crystallographic radii (2.95 A)˚

4. Results and discussion

[22] because of the ion salvation. Using Pitzer–Simonson–Clegg

equations with Nernstian equation, the parameters BMX, W2MX,

The mean activity coefficients and the osmotic coefficients of CsF

0

U2MX, W1MX, U1MX, Z12MX and E were obtained as shown in

in the ternary mixed system were calculated by Nernst equation (1)

Table 5. The parameters W12 and U12 for the methanol–water

and Pitzer equation (2)–(5). The values were listed in Tables 1 and 2.

and ethanol–water binary system were regressed from the Mar-

The variation of ln ± with the molalities of CsF is shown in Fig. 1. It

gules equations for the activity coefficients of the mixtures and the

can be seen that the activity coefficients for CsF decrease with the

known values were taken from the literature [23].

increasing of the molality of CsF. At the same time, when the molal-

The standard Gibbs energy of transference is one of the most

ity of CsF is fixed, the activity coefficients for CsF decrease with the

useful available thermodynamic properties for mixed solutions. It

increasing of alcohol in the mixed solvent. This phenomenon can

− 0

+ can be calculated from E values according to the following equa-

be explained by the fact that the interaction between Cs and F

tion [24]:

is enhanced with the increase of electrolyte concentration. More-

over, the dielectric constant of the mixed solvents decreased as the

ln w

ROH content increased. The values of osmotic coefficients (˚) share 0 0 0

G = F(E − E ) + 2RT (12)

t s w 

the same trend with the mean activity coefficient. As depicted in s  

Author's personal copy

J. Tang et al. / Fluid Phase Equilibria 336 (2012) 34–40 37

Table 1

Potential values, E, mean activity coefficient, ±, and osmotic coefficient, ˚, at different CsF molalities and w of methanol in (methanol + water) at 298.15 K.

a −1 b a −1 b

m (mol kg ) E (mV) ± ˚ m (mol kg ) E (mV) ± ˚

w = 0.00

0.0035 103.3 0.9382 0.9796 0.0760 253.5 0.8002 0.9401

0.0070 138.5 0.9165 0.9727 0.0870 260.3 0.7924 0.9384

0.0108 159.5 0.9000 0.9675 0.0984 266.0 0.7853 0.9371

0.0146 174.2 0.8872 0.9635 0.1135 272.9 0.7771 0.9357

0.0185 185.8 0.8763 0.9603 0.1289 279.1 0.7699 0.9347

0.0221 193.7 0.8678 0.9577 0.1481 285.6 0.7623 0.9338

0.0259 201.4 0.8598 0.9554 0.1710 292.5 0.7546 0.9332

0.0297 208.2 0.8527 0.9534 0.1971 299.4 0.7473 0.9330

0.0380 220.1 0.8395 0.9497 0.2276 306.0 0.7403 0.9333

0.0457 229.0 0.8293 0.9470 0.2615 312.7 0.7340 0.9340

0.0531 236.1 0.8208 0.9449 0.2979 319.0 0.7286 0.9351

0.0605 242.5 0.8134 0.9430 0.3373 325.1 0.7240 0.9367

0.0682 248.4 0.8065 0.9414 0.3868 331.8 0.7196 0.9391

w = 0.10

0.0022 110.4 0.9447 0.9814 0.0814 284.0 0.7525 0.9167

0.0066 164.0 0.9087 0.9692 0.0919 289.5 0.7424 0.9136

0.0087 178.0 0.8969 0.9652 0.1050 295.6 0.7312 0.9101

0.0110 189.2 0.8858 0.9614 0.1191 301.3 0.7204 0.9068

0.0131 197.8 0.8770 0.9584 0.1381 308.0 0.7077 0.9031

0.0152 204.9 0.8691 0.9557 0.1607 314.9 0.6947 0.8995

0.0173 211.2 0.8619 0.9532 0.1799 320.0 0.6850 0.8969

0.0194 216.8 0.8552 0.9510 0.2021 325.2 0.6750 0.8944

0.0238 226.6 0.8427 0.9467 0.2286 330.7 0.6645 0.8919

0.0282 234.6 0.8318 0.9430 0.2634 337.1 0.6527 0.8894

0.0325 241.3 0.8222 0.9398 0.3082 344.1 0.6398 0.8871

0.0369 247.2 0.8134 0.9368 0.3491 349.7 0.6299 0.8857

0.0415 252.8 0.8050 0.9340 0.4004 355.9 0.6194 0.8846

0.0483 259.9 0.7937 0.9302 0.4558 361.8 0.6099 0.8841

0.0553 266.1 0.7834 0.9268 0.4993 366.0 0.6035 0.8841

0.0619 271.4 0.7746 0.9239

w = 0.20

0.0034 149.1 0.9256 0.9746 0.0682 291.7 0.7330 0.9040

0.0073 186.9 0.8943 0.9636 0.0776 297.4 0.7203 0.8992

0.0088 196.1 0.8850 0.9603 0.0906 304.2 0.7046 0.8933

0.0105 204.6 0.8756 0.9570 0.1032 310.0 0.6911 0.8882

0.0120 211.1 0.8681 0.9542 0.1172 315.5 0.6777 0.8831

0.0136 217.0 0.8607 0.9516 0.1346 321.5 0.6629 0.8776

0.0153 222.6 0.8534 0.9489 0.1551 327.6 0.6476 0.8719

0.0184 231.5 0.8414 0.9445 0.1787 333.7 0.6321 0.8664

0.0217 239.2 0.8300 0.9404 0.2067 339.8 0.6163 0.8608

0.0249 245.7 0.8199 0.9367 0.2359 345.4 0.6020 0.8560

0.0283 251.5 0.8102 0.9331 0.2695 351.0 0.5877 0.8515

0.0333 259.1 0.7973 0.9283 0.3144 357.5 0.5715 0.8468

0.0380 265.1 0.7863 0.9242 0.3527 362.4 0.5597 0.8438

0.0446 272.5 0.7725 0.9190 0.4010 367.8 0.5471 0.8411

0.0511 278.7 0.7603 0.9144 0.4580 373.4 0.5346 0.8393

0.0588 285.0 0.7472 0.9094 0.5225 379.1 0.5230 0.8386

w = 0.30

0.0017 130.6 0.9406 0.9797 0.0608 299.7 0.7098 0.8906

0.0051 184.7 0.9002 0.9653 0.0689 305.1 0.6957 0.8846

0.0066 196.9 0.8876 0.9607 0.0781 310.5 0.6812 0.8783

0.0082 207.1 0.8759 0.9564 0.0900 316.5 0.6643 0.8710

0.0097 215.3 0.8661 0.9528 0.1085 324.3 0.6413 0.8608

0.0112 222.1 0.8572 0.9495 0.1265 330.6 0.6219 0.8521

0.0148 235.4 0.8384 0.9423 0.1480 337.0 0.6016 0.8429

0.0162 239.8 0.8318 0.9398 0.1769 344.1 0.5781 0.8321

0.0192 247.7 0.8189 0.9349 0.2075 350.4 0.5569 0.8222

0.0223 254.7 0.8069 0.9302 0.2428 356.5 0.5358 0.8124

0.0256 261.0 0.7953 0.9256 0.2814 362.1 0.5160 0.8031

0.0289 266.6 0.7846 0.9214 0.3212 367.1 0.4983 0.7948

0.0351 275.4 0.7666 0.9141 0.3631 371.7 0.4820 0.7871

0.0399 281.1 0.7541 0.9091 0.4195 377.1 0.4630 0.7783

0.0462 287.7 0.7393 0.9029 0.4777 381.9 0.4462 0.7706

0.0527 293.5 0.7254 0.8972 0.5555 387.4 0.4270 0.7619

a −1

The error in molality value was ±0.0001 mol kg .

b

The error in emf value was ±0.1 mV.

0 0

where Gt is the standard Gibbs energy of transference of CsF. Gt values are listed in Tables 3–5. It can be seen that the val-

0 0 0 0

Ew and Es are the standard of electromotive force of the cell in pure ues of the E and Gt obtained from different models are similar.

water and in mixed solvents, respectively. w and s are density Fig. 3 shows the relationship of the standard transfer Gibbs energy

0 0

of water and mixed solvents, respectively. Based on Eq. (12), the Gt and the ratio of w in the mixed solvent. Gt are all positive

Author's personal copy

38 J. Tang et al. / Fluid Phase Equilibria 336 (2012) 34–40

Table 2

Potential values, E, mean activity coefficient, ±, and osmotic coefficient, ˚, at different CsF molalities and w of ethanol in (ethanol + water) at 298.15 K.

a −1 b a −1 b

m (mol kg ) E (mV) ± ˚ m (mol kg ) E (mV) ± ˚

w = 0.10

0.0039 144.2 0.9262 0.9752 0.0593 274.9 0.7744 0.9239

0.0075 176.5 0.9011 0.9667 0.0648 279.0 0.7673 0.9216

0.0094 187.1 0.8910 0.9632 0.0717 283.7 0.7591 0.9189

0.0112 195.9 0.8825 0.9603 0.0784 287.7 0.7517 0.9165

0.0130 203.0 0.8748 0.9577 0.0873 292.7 0.7427 0.9136

0.0147 209.1 0.8682 0.9555 0.0977 297.8 0.7331 0.9105

0.0165 214.5 0.8618 0.9533 0.1101 303.2 0.7227 0.9071

0.0183 219.4 0.8558 0.9513 0.1261 309.3 0.7108 0.9033

0.0214 227.1 0.8464 0.9481 0.1439 315.3 0.6989 0.8995

0.0248 234.0 0.8371 0.9449 0.1629 320.8 0.6876 0.8959

0.0280 239.7 0.8292 0.9423 0.1837 326.1 0.6766 0.8924

0.0312 244.9 0.8219 0.9398 0.2053 331.0 0.6661 0.8890

0.0349 250.2 0.8141 0.9372 0.2339 336.8 0.6537 0.8849

0.0387 255.0 0.8067 0.9347 0.2619 341.7 0.6427 0.8812

0.0435 260.6 0.7981 0.9318 0.2967 347.2 0.6303 0.8768

0.0491 266.1 0.7890 0.9288 0.3511 354.4 0.6130 0.8702

0.0540 270.6 0.7817 0.9264

w = 0.20

0.0015 123.3 0.9473 0.9824 0.0457 289.5 0.7759 0.9232

0.0032 161.1 0.9255 0.9750 0.0511 294.6 0.7665 0.9197

0.0048 181.8 0.9107 0.9700 0.0569 299.4 0.7571 0.9163

0.0065 196.6 0.8980 0.9657 0.0625 303.8 0.7487 0.9131

0.0080 206.6 0.8885 0.9625 0.0696 308.6 0.7389 0.9094

0.0096 215.7 0.8795 0.9594 0.0769 313.1 0.7294 0.9058

0.0112 222.9 0.8714 0.9567 0.0858 317.9 0.7188 0.9016

0.0127 229.3 0.8645 0.9543 0.0957 322.7 0.7079 0.8973

0.0140 233.9 0.8589 0.9524 0.1071 327.7 0.6964 0.8927

0.0154 238.3 0.8533 0.9505 0.1204 332.8 0.6840 0.8876

0.0171 243.3 0.8469 0.9483 0.1363 338.1 0.6704 0.8819

0.0200 250.8 0.8370 0.9448 0.1565 344.1 0.6549 0.8752

0.0228 257.1 0.8283 0.9418 0.1775 349.4 0.6402 0.8687

0.0255 262.4 0.8206 0.9391 0.2010 354.6 0.6253 0.8619

0.0284 267.3 0.8129 0.9364 0.2306 360.3 0.6084 0.8540

0.0314 272.1 0.8055 0.9338 0.2643 365.8 0.5912 0.8457

0.0360 278.5 0.7951 0.9301 0.3021 371.1 0.5739 0.8372

0.0402 283.6 0.7864 0.9269 0.3480 376.7 0.5553 0.8279

w = 0.30

0.0016 151.1 0.9376 0.9789 0.0516 316.4 0.7252 0.9007

0.0047 203.9 0.8978 0.9651 0.0582 321.7 0.7128 0.8956

0.0064 218.7 0.8827 0.9598 0.0648 326.4 0.7013 0.8909

0.0078 229.0 0.8721 0.9560 0.0725 331.3 0.6891 0.8858

0.0093 236.9 0.8620 0.9524 0.0815 336.3 0.6759 0.8802

0.0107 243.9 0.8535 0.9493 0.0922 341.5 0.6617 0.8741

0.0122 250.0 0.8451 0.9463 0.1043 346.7 0.6471 0.8677

0.0133 254.1 0.8394 0.9442 0.1189 352.2 0.6311 0.8605

0.0149 259.5 0.8316 0.9414 0.1358 357.6 0.6145 0.8529

0.0173 266.5 0.8208 0.9374 0.1537 362.6 0.5987 0.8454

0.0202 273.8 0.8091 0.9331 0.1756 368.0 0.5812 0.8370

0.0223 278.4 0.8013 0.9302 0.1992 373.0 0.5644 0.8287

0.0250 283.6 0.7920 0.9267 0.2251 377.7 0.5478 0.8204

0.0279 288.6 0.7828 0.9232 0.2540 382.4 0.5313 0.8118

0.0318 294.6 0.7714 0.9188 0.2863 386.9 0.5147 0.8031

0.0354 299.5 0.7617 0.9151 0.3183 390.9 0.4999 0.7953

0.0408 305.9 0.7484 0.9099 0.3571 395.1 0.4838 0.7867

0.0460 311.3 0.7367 0.9053 0.4135 400.4 0.4635 0.7758

a ± −1

The error in molality value was 0.0001 mol kg .

b

The error in emf value was ±0.1 mV.

Table 3

(0) (1) 0 0 −1

Pitzer parameters, ˇ , ˇ , and C , standard potential, E , standard deviation, SD, and standard Gibbs energy, Gt (kJ mol ) and w of methanol or ethanol in the mixed

solvents at 298.15 K.

(0) (1) ϕ 0 0 −1

ROH (w) ˇ ˇ C E (mV) SD (mV) Gt (kJ mol )

0.00 0.1306 0.2570 −0.0043 397.7 0.27 0

CsF + methanol + water

0.10 0.1217 −0.0743 −0.0260 427.7 0.13 2.98

0.20 0.0708 −0.2529 0.0341 445.8 0.07 4.81

0.30 0.0226 −0.4164 −0.0048 461.4 0.13 6.40

CsF + ethanol + water

0.10 0.1351 −0.0470 −0.1784 433.4 0.08 3.52

0.20 −0.2591 0.5894 0.1938 461.3 0.07 6.29

0.30 −0.1552 0.2169 0.0967 485.5 0.11 8.71

Author's personal copy

J. Tang et al. / Fluid Phase Equilibria 336 (2012) 34–40 39

Table 4

0

Values of E , and the Debye–Hückel parameters for CsF in methanol + water and ethanol + water mixtures at 298.15 K.

−1 2 −2 0 0 −1

ROH (w) a (Å) c (kg mol ) d (kg mol ) E (mV) SD Gt (kJ mol )

0.00 4.1325 0.0968 −0.0022 397.4 0.27 0

CsF + methanol + water

0.10 3.2069 −0.0014 0.0553 427.2 0.13 2.96

0.20 3.3222 −0.1024 0.0827 444.7 0.36 4.73

0.30 3.6083 −0.3307 0.2662 460.6 0.23 6.35

CsF + ethanol + water

0.10 3.2554 0.0018 −0.0149 433.0 0.17 3.49

0.20 4.8459 −0.1735 0.0037 460.8 0.13 6.24

0.30 4.3220 −0.2997 0.1921 484.9 0.15 8.65

Table 5

0 0 −1

Pitzer–Simonson–Clegg parameters, BMX, W1MX, W2MX, Z12MX, U1MX, U2MX, E (mV), SD(mV), Gt (kJ mol ) and w of methanol/ethanol in (methanol/ethanol + water) at 298.15 K.

w 0 0.10 0.20 0.30

CsF + methanol + water

BMX −51.5151 W2MX 109.1940

U2MX 120.5618

Z12MX 1011.7344 698.9224 415.0274

W1MX −1477.1238 −1053.7215 −666.0228

U1MX −1878.5031 −1385.6282 −903.1991

0

E (mV) 399.1 429.0 447.1 462.4

SD (mV) 0.29 0.08 0.15 0.14

0 −1

Gt (kJ mol ) 0.00 2.97 4.80 6.36

CsF + ethanol + water

BMX −51.5151 W2MX 109.1940 U2MX 120.5618

− −

Z12MX 14.9190 31.1878 348.4701

W1MX −7.3816 −16.8239 −558.1030

U1MX −1.3836 −2.9480 −735.4621

0

E (mV) 399.1 434.7 462.9 487.0

SD (mV) 0.29 0.29 0.11 0.20

0 −1

Gt (kJ mol ) 0.00 3.52 6.31 8.72

obviously, which indicates that the transference of CsF from decrease in hydration of in the mixed solvent. For a given mass frac-

0

water to the methanol/ethanol + water mixed solvents is not tion percentage, Gt of CsF + ethanol + water was larger than that

spontaneous. And Fig. 3 also shows that as the mass fraction of CsF + methanol + water system because the methanol + water

of methanol/ethanol in the mixed solvents increases, the solva- mixture had higher dielectric constant than ethanol + water

tion capacity decreases [25]. This phenomenon would indicate a mixture.

Fig. 2. Natural logarithm of the mean activity coefficient (ln ±) for CsF in 0.10



mass fraction of methanol + water and ethanol + water at 298.15 K. , Methanol; Fig. 3. Variation of standard Gibbs energy of transference with mass fraction of

 ᭹ ᭹, ethanol. methanol/ethanol in methanol/ethanol + water at 298.15 K. , Methanol; , ethanol.

Author's personal copy

40 J. Tang et al. / Fluid Phase Equilibria 336 (2012) 34–40

5. Conclusion [4] B. Ghalami-Choobar, S. Mirzaie, J. Mol. Liq. 169 (2012) 124–129.

[5] B. Ghalami-Choobar, V. Mahdavi, S. Pourpanah, J. Solut. Chem. 41 (2012) 89–99.

[6] E. Lladosa, A. Arce, G. Wilczek-Vera, J.H. Vera, J. Chem. Thermodyn. 42 (2010)

Using the galvanic cell consisting of Cs-ISE and F-ISE electrodes, 244–250.

we determined the potential of CsF in the water + ROH (R = methyl [7] E. Rodil, A. Arce, G. Wilczek-Vera, J.H. Vera, J. Chem. Eng. Data 54 (2009)

345–350.

or ethyl) mixtures. The experimental data were fitted satisfacto-

[8] F. Deyhimi, M. Abedi, J. Chem. Eng. Data 57 (2012) 324–329.

rily to Pitzer, extended Debye–Hückel and Pitzer–Simonson–Clegg

[9] F. Deyhimi, R. Salamat-Ahangari, J. Chem. Eng. Data 54 (2009) 227–231.

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the Gibbs energies of transfer were obtained along with the cor-

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responding parameters for these three models.

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[12] S. Feng, J. Tang, S.N. Li, Q.G. Zhai, Y.C. Jiang, M.C. Hu, J. Chem. Eng. Data 56 (2011)

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