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Authors requiring further information regarding Elsevier’s archiving and manuscript policies are encouraged to visit: http://www.elsevier.com/copyright Author's personal copy 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].