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Journal of Molecular Liquids
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Investigating thermodynamic properties of the ternary systems of MCl(M=K, Rb, Cs) with aqueous mixed solvent: N,N-dimethylacetamide
Jia Lu, 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
In this work, thermodynamic properties measurement for KCl/RbCl/CsCl in N,N-dimethylacetamide (DMA)(w)+H2O (1−w) systems (where the w=0.10, 0.20, 0.30) was carried out by potentiometric methodusing ion-selective electrodes at 298.15 K. Modeling of the activity coefficients of these ternary systemswas based on the Pitzer, the modified Pitzer and the extended Debye–Hückel equations. Meanwhile, theosmotic coefficients, the standard free energy of transference from the water to the mixture have also beenreported.
There is a consensus that studying the thermodynamic properties ofelectrolyte in mixed organic+water solvents is very important whichget a widely application in industrial and environmental, especiallydesalination and purification. Up to now, a lot of studies on the electrolytein mixed water solvents have been reported by isopiestic method,potentiometric method and other measurements [1,2]. Potentiometricmethod has an advantage in the study of thermodynamic properties,such as rapidity, stability, simplicity and good selectivity. Manyresearches on thermodynamic properties of alkali metal halidesin organic solvent have been determined using potentiometricmethod. For example, Lopes et al. investigated the activity coefficientsof NaCl in ethanol+water mixtures [3]. Uspenskaya et al. determinedthe thermodynamic properties in the sodium chloride–water–1-butanol(iso-butanol) ternary systems [4]. The activity coefficients of NaBr inethylene carbonate+water mixed solvents have been obtained byHernández-Luis group [5].Moreover, the thermodynamic property inves-tigations of alkalinemetal salts in somemodel compounds of proteins likeamino acids, peptides as well as amide are of interest for researchers [6].For instance, the activity coefficients determination of KCl in theKCl+formamide+water system by potentiometric measurement wasstudied by Ghalami-Choobar group [7]. Hernández-Luis et al. reportedthe activity coefficients of NaF/NaCl/NaBr+formamide+water [8–10]and NaCl+N-methylformamide+water systems [11]. Activity coeffi-cients for NaCl in N,N-dimethylformamide+water mixed solvent have
been investigated by the group of Alfredo Maestre [12]. As one of theamides, DMA is a highly polar solvent and also versatile solvent in variousindustrial processes [13]. However, the thermodynamic properties ofelectrolyte in DMA are not reported.
As an extension of our work on the thermodynamic properties ofalkaline metal salts+organic solvent+water systems [14–17], thispaper aims to investigate the ternary systems of MCl (M=K, Rb,Cs)+N,N-dimethylacetamide+water at 298.15 K. The experimentaldata were well fitted to the Pitzer, the modified Pitzer and theextended Debye–Hückel equations. The mean activity coefficients, os-motic coefficients, and the standard free energy of transference werealso calculated herein.
2. Experimental
Potassium chloride (Sinopharm Chemical Reagent Co., Ltd,A.R. purity>99.5%), rubidium chloride and cesium chloride (A.R.purity>99.5%, Sichuan State Lithium Materials Co., Ltd.) were driedin vacuum at 393 K for the constant weight and then stockpiledin desiccators. DMA (Sinopharm Chemical Reagent Co., Ltd, A.R.purity >99.5%), were used without pretreatment which contentsvery few water in original product could be ignored. Double distilledwater was used in all experiments.
The ion-selective electrode (model 401) was obtained from JiangsuElectroanalytic Instrument Factory. The K ion-selective electrode (ISE),Rb-ISE and Cs-ISE were filled with 0.1 mol·L−1 KCl solution, RbCl solu-tion and CsCl solution relatively. Both the electrodes were of the type ofPVC membrane and activated about 2 h before use. The membranehas no chemical reaction with DMA but dissolves in tetrahydrofuran.
16 J. Lu et al. / Journal of Molecular Liquids 178 (2013) 15–19
Ag/AgCl electrode was conditioned overnight in 0.1 mol·L−1 HCl solu-tion. Prior to the experiment, the electrodes were calibrated andpresented a good Nernstian response. The potential readings wereachieved on a pH/mV meter (Orion-868, America) and taken as the
Table 2Values of average molecular mass M, dielectric constant D, density ρ, Debye–Hückel consta
final readings when they became constant for at least 5 min. The uncer-tainty of the experimental of potential is ±0.1 mV.
BI-870 Dielectric Constant Meter (Brookhaven Instruments Corpo-ration) was used to determine the relative permittivity of the mixedsolvents at 298.15±0.2 K. Calibration was performed under atmo-spheric pressure using double-distilled water (D=78.4, 298.15 K).The density of the mixture has been measured by density meter(Anton Paar DMA 4500). The uncertainty of the experimental of rela-tive permittivity and density is ±0.1 and ±0.00003 g·cm−3.
3. Results
The cells used in this work belong to the type of cell without liquidjunction with only one fluid, which as follows:
M� ISEjMClðmÞ;waterjAg=AgCl ð1Þ
M� ISEjMClðmÞ;DMAðwÞ;waterð1−wÞjAg=AgCl ð2Þwhere m stands for the molality of MCl (M=K, Rb, Cs) solution (be-tween 0.0020 and 0.9975, 0.0025 and 0.7758, and 0.0015 and 0.9930,
nts A, B and Aφ for DMA+water mixtures at 298.15 K.
Table 5Values of the molality m, potential E, mean activity coefficients γ± and osmotic coeffi-cients Ф for KCl/RbCl/CsCl in the different mass fraction of DMA+water mixtures at298.15 K.
17J. Lu et al. / Journal of Molecular Liquids 178 (2013) 15–19
respectively). w is the mass fraction of DMA in the mixtures. Cell (1)is used to calibrate the electrode pairs and Cell (2) to measure.
The experimental mean activity coefficients can be calculated bythe Nernstian equation:
E ¼ E0 þ 2klnðmγÆÞ ð3Þ
where E0 means the standard potential of cell (1) and cell (2). k=RT/F shows the Nernst slope, in which R, T and F refer to the universal gasconstant, absolute temperature and Faraday constant, respectively.γ± indicates the mean activity coefficient of the electrolyte.
For calibrating the electrode pair of K/Rb/Cs-ISE and Ag/AgCl, theexperimental potentials E of cell (1) were plotted against ln (mγ±).The values of E for KCl, RbCl, and CsCl in pure water are shown inTable 1. The mean activity coefficients of KCl/RbCl/CsCl in purewater were calculated according to the Pitzer equation adopting thePitzer parameters from reference [18]. The values of k and E0 obtainedfrom the linear regression analysis of the experimental data were25.56±0.04 and 241.6±0.1 mV, 25.42±0.06 and 137.6±0.2 mV,
Fig. 1. Plot of γ± versusm for CsCl in various mass fraction of DMA+water mixtures at298.15 K, ■, w=0.00; , w=0.10; , w=0.20; , w=0.30.
Table 6Values of the standard potential E0 in modified Pitzer equations, the standard freeenergy of transference ΔGt
0 of KCl/RbCl/CsCl from water to DMA+water mixtures at298.15 K.
18 J. Lu et al. / Journal of Molecular Liquids 178 (2013) 15–19
and 25.59±0.05 and 134.8±0.1 mV for the systems of KCl/RbCl/CsCl+water, respectively. The theoretical value k is 25.69 mV atT=298.15 K. The average linear correlation coefficients were all larg-er than 0.9998 with a standard deviation about 0.20 mV.
The Pitzer [18], the modified Pitzer [19] and extended Debye–Hückel [20,21] equations were used to describe the thermodynamicbehavior of the electrolyte in the mixed solvents.
For 1:1 type electrolyte, the Pitzer equations for activity coefficientcan be written as:
lnγ� ¼ f γ þmBγ þm2Cγ ð4Þwhere
f γ ¼ −Aφ I1=2= 1þ bI1=2� �
þ 2=bð Þln 1þ bI1=2� �h i
ð4aÞ
Bγ ¼ 2β 0ð Þ þ 2β 1ð Þ 1–exp −αI1=2� �
1þ αI1=2–1=2α2I� �h i
= α2I� �n o
ð4bÞ
Cγ ¼ 1:5Cφ: ð4cÞ
α and b are the empirical parameters with the values of 2.0 and1.2 kg1/2·mol−1/2 [18]. β(0), β(1) and Cφ are the parameters of Pitzerequation.
Fig. 2. Variation of mean activity coefficient γ± with molality of KCl/RbCl/CsCl in theDMA+water (w=0.2) systems at 298.15 K, ■, KCl; , RbCl; , CsCl.
For 1:1 type electrolyte, the modified Pitzer equations are simpleand convenient which only have three characteristic parametersand expressed as following:
lnγ� ¼ −Aφ I1=2= 1þ bI1=2� �
þ 2=bð Þln 1þ bI1=2� �h i
þ 2mBMX þ 3m2CMX:
ð5Þ
In Eq. (5) b, BMX, and CMX are the fitting parameters.Aφ is the Debye–Hückel coefficient for the osmotic coefficient. The
definition of Aφ is
Aφ ¼ 1:4006 � 106ρ1=2 DTð Þ3=2: ð6Þ
The density (ρ/g·cm−3) and relative permittivity (D) of the mixedsolvents were measured and given in Table 2.
The extended Debye–Hückel equations may be written as follows:
logγ� ¼ −Am1=2= 1þ Bam1=2� �
þ cmþ dm2–log 1þ 0:002 mMð Þ þ Ext
ð7Þ
where a is the ion size parameter, c and d are ion-interaction param-eters,M represents the averagemolecular mass of mixed solvents andExt contributes to the extended terms. A and B indicate the Debye–Hückel constants which can be written as
A ¼ 1:8247 � 106ρ1=2= DTð Þ3=2kg1=2 �mol−1=2 ð7aÞ
B ¼ 50:2901ρ1=2= DTð Þ1=2kg1=2 �mol−1=2 � Å−1
: ð7bÞ
All the parameters in Eq. (7) have their usual meaning.To combine Eqs. (3) and (4), (3) and (5) or (3) and (7), the E0
obtained fromPitzer, modified Pitzer and extendedDebye–Hückel equa-tions gets a good agreement with each other. Tables 3 and 4 showed thevalues of E0 with the fitting standard deviation and the correspondingparameters.
4. Discussion
The mean activity coefficients and the osmotic coefficientsobtained from the fitting of the experimental data E by the Pitzermodel are shown in Table 5. The mean activity coefficient versusthe molality of CsCl in different mass fraction of DMA+watermixtures was shown in Fig. 1. It can be observed that γ± decreaseswith the increase of the concentration of the electrolyte, and in-creases with the decrease of the DMA mass percentages in themixed solvents. This may be caused by the structural interactionsand electrostatic interaction models. The values of the mean activitycoefficients of KCl/RbCl have the same trend as those of the meanactivity coefficients of CsCl in mixtures.
For the different electrolyte, Fig. 2 indicates that γ± decreaseswith the increase of the cationic radius [22]. It may be interpretedthat the smaller cationic radius is, the smaller the hydration number[23]. So the mean activity coefficients decrease with orderKCl>RbCl>CsCl. Meanwhile, the corresponding osmotic coefficients
Fig. 3. Plot of the standard free energy of transference, ΔGt0 vs the weight percentage of
DMA for KCl/RbCl/CsCl at 298.15 K, ■, KCl; , RbCl; , CsCl.
19J. Lu et al. / Journal of Molecular Liquids 178 (2013) 15–19
were calculated using the equation of Pitzer in Eq. (5) and listed inTable 5.
The standard free energy of transference, ΔGt0, one of the most
useful thermodynamic properties of solution can be calculated fromthe expression [24]:
ΔGt0 ¼ F Em
0–Ew
0� �
þ 2RTln ρw=ρmð Þ ð8Þ
The subscripts m and w stand for the mixtures and pure water,respectively. Other symbols have their usual meaning. The values ofΔGt
0 were presented in Table 6 and plotted versus the mass fractionof DMA in Fig. 3.
It can be seen that ΔGt0 are all positive, which means that the
transfer of the electrolyte from water to DMA+water mixtures isnot spontaneous. On the other hand, the ΔGt
0 goes to more positivealong with the increasing percentage of the DMA, indicating thatthe solvation power of K+, Rb+ or Cs+ decreases when the mass frac-tion of DMA in the mixed solvents increased [25].
5. Conclusion
The results in this study present that the thermodynamic proper-ties of KCl/RbCl/CsCl in DMA+H2O mixed solvents were researchedby potentiometric measurement at 298.15 K. The Pitzer, the modifiedPitzer and the extended Debye–Hückel model were used to describethe thermodynamic behavior of the electrolyte in the mixed solvent.The activity coefficients, osmotic coefficients and the standard freeenergy of transference, and the parameters for the Pitzer (β(0), β(1)
and Cφ), the modified Pitzer (b, BMX and CMX), and the extended
Debye–Hückel (a, c and d) were also obtained. This work providedthe basic thermodynamic reference data for deep research.
Acknowledgment
This project was supported by the National Natural Science Foun-dation of China (No: 21171111) and the Fundamental Research Fundsfor the Central Universities (Program No: GK201001006).
References
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[3] A. Lopes, F. Farelo, M.I.A. Ferral, Journal of Solution Chemistry 30 (9) (2001)757–770.
