Activity coefficients of CsF in (Urea + H2O) or (N-methylformamide + H2O) mixed solvents at 298.2 K

Journal of Molecular Liquids 220 (2016) 829–835

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Activity coefficients of CsF in (Urea + H2O) or (N-methylformamide + H2O) mixed solvents at 298.2 K Xiuhua Hao, 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

Article history: Received 17 March 2016 Received in revised form 9 May 2016 Accepted 10 May 2016 Available online xxxx Keywords: Activity coefficient CsF Urea N-methylformamide Potentiometric method

a b s t r a c t This paper reports the thermodynamic properties of CsF in (Urea + H2O) or (N-methylformamide + H2O) mixed solvents by potentiometric method at 298.2 K. The experimental data are fitted using the Pitzer, modified Pitzer and extended Debye-Hückel equation. The mean activity coefficients, osmotic coefficient and excess Gibbs free energies are obtained and the corresponding derived parameters are reported at the same time. The standard free energy of transference and the primary hydration number are also obtained. © 2016 Elsevier B.V. All rights reserved.

1. Introduction Electrolyte solution and the thermodynamic properties of the system are of great interest in industry and researchers for the exploitation and utilization of the resources. The thermodynamic properties of alkali metals in aqueous, aqueous-organic mixtures and aqueous electrolyte solutions [1–3] have received considerable attention in consideration of their importance in chemical engineering, purification and so on. Accurate descriptions of the thermodynamic properties and phase behavior of the electrolyte containing chemical systems are important for the process modeling and construction of chemical plants for the purpose of the cost optimization. Hernández-Luis et al. determined the thermodynamic properties of the alkaline halides (NaF, NaCl, NaBr) in organic – water mixtures with both ε-decreasing co-solvent (methanol-water, ethanol-water) [4–6] and ε-increasing co-solvent (ethylene carbonate-water, formamide-water, N-methylformamide-water) [7–9]. Moreover, thermodynamic properties of the mixed electrolyte systems, such as NaCl + Na2SO4 + H2O [10] and KBr-K2SO4-H2O [11] was investigated to discuss the ion–ion and other interactions in the solution. In the past decade, our research group reported the thermodynamic properties of the alkali metal, Rb and Cs salts in amide/amino acid water mixtures or in mixed electrolyte solutions [12–14]. As an extension of our series work, we present herein the thermodynamics properties of the ternary systems CsF + urea + water and CsF + Nmethylformamide + water at 298.2 K. The Pitzer, modified Pitzer and the extended Debye-Hückel equations were used to process the ⁎ Corresponding authors. E-mail addresses: [email protected] (S. Li), [email protected] (M. Hu).

http://dx.doi.org/10.1016/j.molliq.2016.05.030 0167-7322/© 2016 Elsevier B.V. All rights reserved.

experimental data. The mean activity coefficients (γ±), osmotic coefficients (Ф), excess Gibbs free energies (GE), the standard free energy of transference (ΔG0t ) and the primary hydration number of the electrolyte (nhydr) for CsF in amides - water mixtures with mass fraction of amide in the solvent mixtures varied from 0.00 to 0.40 are presented. Finally, the corresponding conclusions obtained which are useful for the further research and application. 2. Experimental Chemicals employed in this research are listed in Table 1. Urea was utilized after 12 h drying at T = 383.2 K till constant weight. CsF and N-methylformamide were used without further purification. Doubledistilled water was used throughout the whole experiment in the preparation of working solutions. Values of the relative permittivity and density were taken from the reference [9,15] and presented in Table S1. The Cs ion-selective electrode (Cs-ISE) and the F-ISE were obtained from Jiangsu Electroanalytical Instrument Co. Cs-ISE was a PVC membrane type based on valinomycin and was filled with 0.10 mol·L−1 CsF as the internal liquid in K ion-selective electrode (model 401), F-ISE (model 201) was a kind of crystal membrane electrode. Both the electrodes need to be calibrated before the experiment and show a reasonable Nernst response. Both the solvents and electrodes were maintained in a sealed double-walled glass to prevent contamination and to keep the temperature at T = 298.2 K (within an uncertainty of 0.2 K) with circulating water. Accurate weighing was performed on an analytical balance (Mettler Toledo-AL 204, Switzerland) with accuracy 0.0001 g. All potentiometric measurements were made using a pH/mV meter (Orion-868, America) with

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X. Hao et al. / Journal of Molecular Liquids 220 (2016) 829–835

3.2. Modified Pitzer equation

Table 1 Chemical samples employed in this study.

The modified Pitzer equation is convenient to use with just three adjustable parameters [19]:

Chemical name (the CAS code)

Source

CsF (13400-13-0)

Shanghai China Lithium Industrial Co., ≥99.5% Ltd. Sinopharm Chemical Reagent Co., Ltd. ≥99.5%

N-methylformamide (123-39-7) Urea (57-13-6)

Mass purity

Sinopharm Chemical Reagent Co., Ltd.

h

i ln γ
¼ −Aφ I 1=2 = 1 þ bMX I1=2 þ ð2=bMX Þ ln 1 þ bMX I 1=2 þ 2mBMX þ 3m2 C MX

≥99.5%

ð4Þ


 Ф−1 ¼ −Aφ I 1=2 = 1 þ bMX I 1=2 þ mBMX þ 2m2 C MX :

ð5Þ

resolution 0.1 mV. The whole experiment process should be accomplished within 1.5 h. 3.3. Extended Debye-Hückel equation 3. Correlation of activity coefficient data According to the extended Debye-Hückel equation, the mean activity coefficient γ± for CsF in the mixtures may be written as [20,21]:

3.1. The Pitzer equation According to Pitzer, the mean activity coefficients γ± for 1–1 type electrolytes were calculated on the basis of the following relation [16, 17]: γ

2 γ

γ

lnγ
¼ f þ mB þ m C

ð1Þ

where γ


 logγ
¼ −Am1=2 = 1 þ Bam1=2 þ cm þ dm2 − logð1 þ 0:002mM Þ ð6Þ With a the ion size parameter, c and d the ion-interaction parameters, M stands for the average molecular mass of co-solvent. A and B are the Debye-Hückel constants with the following forms: 1=2

f ¼ −Aφ

h



i I1=2 = 1 þ bI1=2 þ ð2=bÞ ln 1 þ bI1=2 1=2

Aφ ¼ 1:4006  106 ρ1=2 ðεTÞ3=2 kg

 mol

−1=2

A ¼ 1:8247  106 ρ1=2 =ðεTÞ3=2 kg ð1aÞ ð1bÞ

with Bγ ¼ 2βð0Þ þ 2βð1Þ

nh

 i  o

1− exp −αI1=2 1 þ αI1=2 −α 2 I=2 = α 2 I ð1cÞ

and

1=2

B ¼ 50:2901ρ1=2 =ðεTÞ1=2 kg

 mol

 mol

−1=2

−1=2

−1

Å

ð6aÞ ð6bÞ

The tunable parameters of Pitzer, modified Pitzer and extended Debye-Hückel equations, apparent standard potential difference E0, together with the corresponding standard deviation obtained are shown in Tables 3–4. 4. Results and discussion 4.1. Calibration of the electrode pair

C γ ¼ 1:5C φ

ð1dÞ

where β(0), β(1) and Cφ, which depend on temperature and pressure, are the Pitzer's ion-interaction parameters. Here we assumed Cφ = 0 since the low concentrations of the electrolyte, it applies similarly to the term d in extended Debye-Hückel equation introduced below. Aφ is the Debye-Hückel constant for the osmotic coefficient. I represents the ionic strength. The values of the constants are as follows: α = 2.0 kg1/ 2 ·mol− 1/2, b = 1.2 kg1/2·mol−1/2. The osmotic coefficient (Φ) can be expressed as: φ

Ф−1 ¼ f þ mBφ þ m2 C φ

ð2Þ

Cs−ISE jCsF ðmÞ; H2 O j F−ISE

ðIÞ

Cs−ISE jCsF ðmÞ; urea=NMF ðwÞ; H2 O ð1−wÞ j F−ISE

ðIIÞ

where, m is the molality of CsF in pure water or in urea/NMF + H2O mixtures, w (w = 0.00, 0.10, 0.20, 0.30, 0.40) is the mass fraction of urea/NMF in mixed solvent. The relation between activity coefficient γ± and potential E of the cell is given by the Nernst equation: E ¼ E0 þ 2k ln ðmγ
Þ:

with

 φ 1=2 f ¼ −Aφ I1=2 = 1 þ bI

ð2aÞ


 Bφ ¼ βð0Þ þ βð1Þ exp −αI1=2 :

ð2bÞ

The excess Gibbs free energies (GE) are given by [18]: GE ¼ 2RTI ð1−Ф þ ln γ
Þ

The experimental cells without liquid junction can be represented as:

ð3Þ

Values for Aφ and Debye-Hückel constants A, B are given in Table S1. The mean activity coefficient (γ±), osmotic coefficient (Φ) and the excess Gibbs free energies (GE) for the studied systems are summarized in Table 2. All the symbols have their common meaning.

ð7Þ

Here E0 is the apparent standard potential difference of the cell (I) or cell (II). The Nernst theoretical slope (k) is combination with the universal gas constant R, absolute temperature T and Faraday constant F, is expressed as k = RT / F. m is the molality of CsF in pure water or mixtures. A good linear relationship obtained when E is plotted against lna. Fig. S1 shows the Nernst response results of Cs-ISE and F-ISE electrode pair for CsF in water at 298.2 K. E0 and k can be evaluated by a least-squares analysis, the values are 86.0 mV and 25.60 for CsF + urea + H2O, 125.5 mV and 25.05 for CsF + NMF + H2O. The linear correlation coefficients (R2) for the studied amide - water systems are both 0.9999.The standard deviation (SD) for the relevant systems is 0.37 (CsF + urea + H2O) and 0.18 (CsF + NMF + H2O) respectively. According to calibration results, we can get the conclusion that the electrode pairs have a reasonable Nernst response in this work.

X. Hao et al. / Journal of Molecular Liquids 220 (2016) 829–835

831

Table 2 Experimental potential difference E, mean activity coefficients γ±, osmotic coefficients Ф and excess Gibbs free energies GE for CsF in urea/NMF + H2O mixtures at T = 298.2 K and p = 0.1 MPa. m mol·kg

E −1

of mixed solvent

γ±

Ф

GE/RT

mV

m mol·kg

E −1

of mixed solvent

γ±

Ф

GE/RT

mV

CsF + Urea + H2O w = 0.00 0.0024 0.0047 0.0071 0.0095 0.0144 0.0194 0.0246 0.0325 0.0406 0.0536 0.0665

−226.7 −192.4 −172.2 −158.2 −137.3 −122.8 −111.2 −97.7 −86.9 −73.6 −63.3

0.9481 0.9295 0.9159 0.9051 0.8876 0.8740 0.8623 0.8478 0.8356 0.8200 0.8077

0.9828 0.9768 0.9725 0.9691 0.9636 0.9595 0.9561 0.9520 0.9486 0.9446 0.9417

−0.0002 −0.0005 −0.0009 −0.0013 −0.0024 −0.0036 −0.0051 −0.0076 −0.0104 −0.0153 −0.0206

0.0869 0.1119 0.1435 0.1769 0.2073 0.2752 0.3523 0.4659 0.5530 0.6129

−50.5 −38.6 −26.9 −17.0 −9.5 4.0 15.8 29.3 37.6 42.7

0.7921 0.7775 0.7636 0.7524 0.7443 0.7313 0.7220 0.7144 0.7117 0.7111

0.9383 0.9357 0.9338 0.9330 0.9329 0.9342 0.9372 0.9434 0.9489 0.9531

−0.0298 −0.0419 −0.0584 −0.0769 −0.0946 −0.1360 −0.1853 −0.2607 −0.3196 −0.3604

w = 0.10 0.0045 0.0090 0.0138 0.0190 0.0286 0.0382 0.0480 0.0626 0.0779 0.1033

−179.1 −144.3 −123.4 −108.1 −88.0 −73.9 −63.1 −50.3 −39.8 −26.3

0.9367 0.9151 0.8990 0.8857 0.8670 0.8528 0.8411 0.8271 0.8154 0.8001

0.9793 0.9725 0.9676 0.9636 0.9583 0.9544 0.9514 0.9480 0.9453 0.9423

−0.0004 −0.0011 −0.0020 −0.0032 −0.0058 −0.0087 −0.0119 −0.0172 −0.0233 −0.0341

0.1280 0.1706 0.2054 0.2556 0.3055 0.3560 0.4160 0.4680 0.5344 0.6242

−16.0 −2.4 6.5 16.9 25.4 32.7 40.2 46.3 52.6 60.5

0.7885 0.7733 0.7638 0.7531 0.7450 0.7385 0.7324 0.7283 0.7241 0.7200

0.9403 0.9383 0.9375 0.9372 0.9375 0.9382 0.9395 0.9408 0.9428 0.9458

−0.0456 −0.0666 −0.0850 −0.1128 −0.1417 −0.1719 −0.2087 −0.2414 −0.2839 −0.3424

0.0020 0.0040 0.0060 0.0082 0.0132 0.0182 0.0233 0.0308 0.0384 0.0509 0.0634

−217.0 −181.7 −161.0 −145.8 −122.1 −106.1 −94.1 −80.4 −69.7 −56.1 −45.4

0.9590 0.9438 0.9329 0.9236 0.9072 0.8949 0.8849 0.8728 0.8629 0.8498 0.8392

0.9865 0.9817 0.9783 0.9754 0.9705 0.9669 0.9641 0.9609 0.9583 0.9552 0.9528

w = 0.20 −0.0001 0.0861 −0.0003 0.1085 −0.0006 0.1486 −0.0009 0.1819 0.2143 −0.0018 −0.0028 0.2875 −0.0040 0.3454 −0.0060 0.4314 −0.0081 0.5162 −0.0120 0.5925 −0.0162 0.6423

−30.7 −19.6 −4.6 5.1 13.0 27.2 36.2 47.1 56.1 63.0 67.2

0.8244 0.8132 0.7984 0.7892 0.7820 0.7702 0.7636 0.7566 0.7519 0.7491 0.7478

0.9499 0.9481 0.9463 0.9456 0.9455 0.9462 0.9473 0.9496 0.9522 0.9549 0.9567

−0.0246 −0.0336 −0.0510 −0.0663 −0.0820 −0.1192 −0.1499 −0.1972 −0.2450 −0.2889 −0.3178

0.0021 0.0042 0.0065 0.0088 0.0138 0.0188 0.0238 0.0312 0.0387 0.0513 0.0639

−199.1 −164.6 −143.6 −128.9 −106.5 −91.2 −79.6 −66.3 −55.9 −42.2 −31.7

0.9595 0.9448 0.9332 0.9242 0.9087 0.8970 0.8875 0.8758 0.8662 0.8532 0.8428

0.9867 0.9820 0.9783 0.9755 0.9708 0.9674 0.9647 0.9615 0.9590 0.9558 0.9535

w = 0.30 −0.0001 0.0846 −0.0003 0.1041 −0.0006 0.1453 −0.0010 0.1785 −0.0018 0.2100 −0.0029 0.2887 −0.0040 0.3522 −0.0059 0.4432 −0.0080 0.5282 −0.0118 0.5946 −0.0159 0.6551

−18.1 −8.0 8.1 18.2 26.1 41.7 51.6 63.1 72.0 78.1 83.2

0.8294 0.8196 0.8045 0.7959 0.7896 0.7792 0.7745 0.7714 0.7712 0.7723 0.7741

0.9509 0.9494 0.9480 0.9479 0.9484 0.9512 0.9546 0.9604 0.9665 0.9716 0.9764

−0.0233 −0.0309 −0.0481 −0.0629 −0.0775 −0.1159 −0.1480 −0.1949 −0.2391 −0.2735 −0.3046

0.0020 0.0040 0.0061 0.0086 0.0138 0.0190 0.0241 0.0318 0.0395 0.0522 0.0647

−187.5 −152.7 −131.7 −114.6 −91.5 −75.8 −64.0 −50.5 −39.9 −26.2 −15.8

0.9631 0.9491 0.9388 0.9292 0.9143 0.9030 0.8939 0.8829 0.8739 0.8619 0.8525

0.9879 0.9834 0.9802 0.9772 0.9728 0.9696 0.9670 0.9641 0.9619 0.9591 0.9572

w = 0.40 −0.0001 0.0847 −0.0003 0.1069 −0.0005 0.1425 −0.0009 0.1774 −0.0017 0.2151 −0.0027 0.2831 −0.0038 0.3447 −0.0056 0.4317 −0.0076 0.5129 −0.0112 0.5822 −0.0151 0.6402

−2.7 8.7 22.7 33.4 42.9 56.4 66.3 77.7 86.6 93.1 98.2

0.8408 0.8308 0.8192 0.8110 0.8047 0.7974 0.7939 0.7922 0.7930 0.7951 0.7975

0.9551 0.9538 0.9531 0.9534 0.9544 0.9575 0.9611 0.9671 0.9733 0.9789 0.9838

−0.0218 −0.0298 −0.0435 −0.0578 −0.0739 −0.1041 −0.1323 −0.1727 −0.2105 −0.2424 −0.2689

−19.7

0.8066

0.9414

−0.0212

CsF + NMF + H2O

0.0023

−181.1

0.9484

0.9830

w = 0.00 −0.0002 0.0677

(continued on next page)

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X. Hao et al. / Journal of Molecular Liquids 220 (2016) 829–835

Table 2 (continued) m mol·kg

E −1

of mixed solvent

γ±

Ф

GE/RT

mV

m mol·kg

E −1

of mixed solvent

γ±

Ф

GE/RT

mV

0.0049 0.0074 0.0096 0.0119 0.0169 0.0216 0.0273 0.0338 0.0420 0.0549

−144.8 −125.1 −112.2 −102.3 −85.4 −73.5 −62.6 −52.5 −42.2 −29.6

0.9282 0.9146 0.9047 0.8958 0.8802 0.8686 0.8568 0.8456 0.8337 0.8186

0.9764 0.9721 0.9689 0.9662 0.9614 0.9579 0.9545 0.9514 0.9481 0.9443

−0.0005 −0.0009 −0.0013 −0.0018 −0.0030 −0.0043 −0.0060 −0.0080 −0.0109 −0.0159

0.0868 0.1074 0.1388 0.1698 0.2111 0.2558 0.3093 0.3943 0.4776 0.5703

−8.4 1.3 13.2 22.6 32.7 41.7 50.6 62.2 71.4 80.2

0.7922 0.7799 0.7654 0.7545 0.7434 0.7345 0.7266 0.7185 0.7139 0.7115

0.9383 0.9361 0.9340 0.9331 0.9329 0.9336 0.9353 0.9393 0.9441 0.9501

−0.0297 −0.0397 −0.0559 −0.0729 −0.0968 −0.1239 −0.1575 −0.2129 −0.2685 −0.3314

0.0020 0.0041 0.0063 0.0111 0.0131 0.0169 0.0219 0.0266 0.0344 0.0422 0.0549

−170.6 −134.8 −114.6 −87.3 −79.1 −66.9 −54.4 −45.0 −33.2 −23.4 −11.0

0.9544 0.9368 0.9248 0.9053 0.8990 0.8885 0.8776 0.8689 0.8570 0.8470 0.8341

0.9851 0.9795 0.9757 0.9699 0.9680 0.9650 0.9620 0.9596 0.9566 0.9541 0.9512

w = 0.10 −0.0001 0.0675 −0.0004 0.0877 −0.0007 0.1077 0.1398 −0.0015 −0.0019 0.1736 −0.0028 0.2170 −0.0040 0.3028 −0.0053 0.3634 −0.0076 0.4639 −0.0101 0.5550 −0.0145

−1.4 10.9 20.6 33.0 43.1 53.6 69.0 77.6 89.2 97.6

0.8237 0.8104 0.8000 0.7868 0.7760 0.7650 0.7490 0.7403 0.7288 0.7205

0.9490 0.9464 0.9447 0.9427 0.9414 0.9404 0.9392 0.9387 0.9382 0.9377

−0.0193 −0.0275 −0.0361 −0.0510 −0.0677 −0.0904 −0.1383 −0.1740 −0.2361 −0.2948

w = 0.20 0.0015 0.0033 0.0048 0.0079 0.0131 0.0177 0.0226 0.0268 0.0337 0.0423 0.0553

−161.1 −121.2 −102.7 −78.4 −53.8 −39.5 −27.5 −19.5 −8.5 2.3 15.1

0.9622 0.9459 0.9365 0.9219 0.9049 0.8936 0.8838 0.8769 0.8672 0.8573 0.8453

0.9876 0.9825 0.9796 0.9752 0.9703 0.9672 0.9647 0.9629 0.9606 0.9583 0.9557

−0.0001 −0.0002 −0.0004 −0.0009 −0.0018 −0.0028 −0.0040 −0.0051 −0.0069 −0.0095 −0.0137

0.0693 0.0840 0.1032 0.1318 0.1661 0.2180 0.2990 0.3700 0.4606 0.5531

25.7 34.8 44.4 56.0 66.7 79.6 94.3 104.4 114.3 122.5

0.8350 0.8261 0.8165 0.8049 0.7937 0.7801 0.7633 0.7509 0.7368 0.7236

0.9537 0.9520 0.9504 0.9484 0.9466 0.9442 0.9405 0.9371 0.9324 0.9272

−0.0186 −0.0241 −0.0316 −0.0436 −0.0590 −0.0839 −0.1260 −0.1655 −0.2192 −0.2774

w = 0.30 0.0015 0.0031 0.0047 0.0066 0.0100 0.0152 0.0208 0.0259 0.0331 0.0387 0.0523

−138.1 −104.1 −83.2 −66.5 −47.1 −26.7 −12.0 −1.4 10.4 17.9 32.4

0.9629 0.9495 0.9396 0.9303 0.9176 0.9034 0.8917 0.8830 0.8730 0.8664 0.8535

0.9879 0.9837 0.9806 0.9778 0.9741 0.9700 0.9669 0.9647 0.9622 0.9607 0.9579

−0.0001 −0.0002 −0.0004 −0.0007 −0.0012 −0.0022 −0.0034 −0.0046 −0.0065 −0.0081 −0.0122

0.0663 0.0835 0.1081 0.1331 0.1667 0.2176 0.2912 0.3845 0.4615 0.5414

43.6 54.6 67.0 76.8 87.4 99.9 113.5 126.5 135.2 142.5

0.8430 0.8327 0.8211 0.8117 0.8015 0.7893 0.7755 0.7616 0.7518 0.7425

0.9558 0.9539 0.9520 0.9507 0.9493 0.9476 0.9456 0.9429 0.9406 0.9379

−0.0168 −0.0229 −0.0323 −0.0424 −0.0569 −0.0802 −0.1164 −0.1656 −0.2085 −0.2551

w = 0.40 0.0017 0.0033 0.0052 0.0069 0.0082 0.0115 0.0151 0.0203 0.0270 0.0371 0.0519

−123.4 −90.1 −68.7 −54.8 −46.4 −29.8 −17.6 −3.0 11.4 26.1 42.2

0.9633 0.9509 0.9404 0.9331 0.9282 0.9179 0.9091 0.8988 0.8882 0.8758 0.8621

0.9880 0.9842 0.9810 0.9788 0.9773 0.9744 0.9719 0.9692 0.9665 0.9636 0.9607

−0.0001 −0.0002 −0.0004 −0.0007 −0.0009 −0.0014 −0.0020 −0.0031 −0.0046 −0.0071 −0.0113

0.0737 0.0942 0.1237 0.1605 0.1998 0.2392 0.2935 0.3747 0.4615 0.5526

59.0 70.7 83.7 96.0 106.2 114.8 124.5 135.9 145.9 154.0

0.8476 0.8372 0.8257 0.8145 0.8050 0.7970 0.7877 0.7758 0.7649 0.7545

0.9579 0.9562 0.9544 0.9529 0.9516 0.9505 0.9489 0.9465 0.9437 0.9405

−0.0182 −0.0252 −0.0361 −0.0507 −0.0674 −0.0849 −0.1101 −0.1501 −0.1955 −0.2456

w is the mass fraction of urea/NMF in mixed solvent. m is the molality of CsF in pure water or mixtures. u(m) = 0.0001 mol·kg−1; u(E) = 0.1 mV; u(γ±) = 0.01; u(T) = 0.2 K; u(P) = 3 kPa.

4.2. Activity coefficients and excess Gibbs free energies The mean activity coefficients of CsF γ± against the molality m in CsF + urea/NMF + H2O system at 298.2 K was shown in Fig. 1 and Fig. S2. It was clear that the mean activity coefficient γ± decreases

with the increasing m of CsF at a fixed w of mixtures which is due to the association between the ions [21,22]. Moreover, for ε-increasing co-solvent systems (Table S1), γ± increases with the increasing of w in the mixed solvent. The result suggests that the high dielectric constant of the mixed solvents weakens the ion–ion interactions in the

X. Hao et al. / Journal of Molecular Liquids 220 (2016) 829–835

833

Table 3 Summary of both standard potential E0 and the parameter values obtained from the Pitzer and modified Pitzer equations for CsF + urea/NMF + H2O systems at T = 298.2 K and p = 0.1 MPa. w

Pitzer

Modified Pitzer

(0)

(1)

β

kg·mol

0

β −1

kg·mol

E −1

SD

bMX

mV

kg

BMX

1/2

·mol

−1/2

kg·mol

E0

CMX −1

2

kg ·mol

−2

SD

mV

CsF + Urea + H2O 0.10 0.0817 0.20 0.0778 0.30 0.1250 0.40 0.1262

0.3143 0.3474 0.2048 0.2057

101.3 104.6 118.0 132.6

0.16 0.15 0.26 0.27

2.9733 3.5746 1.1881 1.3486

0.0155 −0.0096 0.2379 0.2149

0.0312 0.0461 −0.0592 −0.0492

101.1 104.3 118.1 132.7

0.14 0.06 0.25 0.26

CsF + NMF + H2O 0.10 0.0352 0.20 −0.0303 0.30 −0.0046 0.40 −0.0099

0.5348 0.6927 0.6070 0.5925

143.5 168.4 188.2 197.9

0.12 0.12 0.20 0.26

3.0409 3.6313 2.8183 3.3201

0.0648 0.0451 0.1125 0.0659

−0.0179 −0.0394 −0.0715 −0.0429

143.4 168.3 188.2 197.8

0.12 0.10 0.21 0.26

solution. That is, it is unfavorable to form ion-pairs in such solution. The activity coefficients of CsF in urea - water and NMF - water systems at w = 0.20 is depicted in Fig. 1 for comparison. It shows that the difference of γ± in urea - water and NMF - water is clear only at the concentration of CsF larger than 0.30 mol·kg−1. This may be interpreted that the distinction of the solvation effect is more obvious (weaken the ion-ion interactions) when increasing the electrolyte concentration. Similar tendency can be observed for the excess Gibbs free energies GE as depicted in Fig. 2 and Fig. S3. The results of activity coefficients and the excess Gibbs free energies suggest that the properties of the solvent affect the ion-ion and ion-solvation interactions in the electrolyte solution.

4.4. The primary hydration number Feakins and French [24,25] derived an equation to roughly estimate the primary hydration numbers nhydr of electrolyte in solutions. Hernandez-Luis et al. calculated the primary hydration numbers of alkali halide in different aqueous - organic co-solvents [9,26–28]. nhydr can be calculated on the basis of the following equations [29,30]: 

 ΔGt 0 c =F ¼ ΔEc 0 ¼ Ecs 0 −Ecw 0 ¼ nhydr ðRT=F Þ ln φw

with φw ¼ ðww =dw Þ=ðww =dw þ wamide =damide Þ

4.3. The standard free energy of transference

ð9Þ

ð10Þ

The standard free energy of transference Δ G0t is a measure of the change in total energy of the solute when it is transferred from one solvent (usually water) to another at infinite dilution, and can be calculated according to the form of expression [9,23]:
 ΔG0t ¼ F E0m −E0w þ 2RT ln ðρw ρw =ρm Þ

ð8Þ

The obtained ΔG0t for CsF + urea + H2O and CsF + NMF + H2O systems are presented in Table 5. The average values E0⁎ in Table 5 were calculated considering the three models aforementioned. As shown in Fig. 3, the values of Δ G0t in CsF + NMF + H2O system is larger than that in CsF + urea + H2O system, and the values of ΔG0t for the two systems are both positive, indicating the non-spontaneous process of ion transfer in this case. Moreover, we can see that the changing of ΔG0t is exactly opposite with that of the dielectric constant. This phenomenon indicates that CsF is more easily solvated in the mixed solvents because of the larger dielectric constant of the co-solvent. Moreover, the solvation ability of CsF is stronger in urea - H2O mixtures than that in NMF - H2O. Table 4 Standard potential E0 and the Debye-Hückel parameters of CsF + urea/NMF + H2O systems at T = 298.2 K and p = 0.1 MPa. w

a

c

E0

Å

kg·mol−1

mV

SD

CsF + Urea + H2O 0.10 0.20 0.30 0.40

4.8317 5.3567 4.1735 4.3293

0.0542 0.0546 0.1003 0.1047

a

c

E0

Å

kg·mol−1

mV

SD

CsF + NMF + H2O 101.2 104.5 118.0 132.6

0.16 0.13 0.26 0.27

6.2557 7.9327 7.3437 7.8222

0.0247 −0.0134 0.0083 0.0050

143.4 168.3 188.1 197.8

0.12 0.11 0.22 0.26

Fig. 1. The mean activity coefficients γ± versus the molality m of CsF in urea + H2O system and the comparison of mean activity coefficients of CsF in urea + H2O and NMF + H2O mixtures (w = 0.20) at T = 298.2 K.

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X. Hao et al. / Journal of Molecular Liquids 220 (2016) 829–835

Fig. 2. The excess Gibbs free energies GE versus the molality m of CsF in urea + H2O system and comparison of GE of CsF in urea + H2O and NMF + H2O mixtures (w = 0.20) at T = 298.2 K.

Fig. 3. The relationship of the standard free energy of transference ΔG0t for CsF vs the dielectric constant ε of urea/NMF + H2O mixtures at T = 298.2 K.

number because of the interaction of the organic solvent with water and electrolyte. Ec 0 ¼ Em 0 þ 2k logds

ð11Þ 5. Conclusion

where the subscripts ‘s’ and ‘w’ mean mixed solvent and water respectively. φw symbolizes the volume fraction of water in co-solvent. w and d are the mass fraction and density of water or amides (urea and NMF). E0c is the standard potential difference expressed in molar concentration scale. E0m is the standard potential difference in molality (usually simplified to E0). The rest of the symbols have their common meaning. Fig. S4 shows the relationships ΔE0c vs. (RT / F) lnφw. The ion hydration number nhydr of CsF in the urea + H2O and NMF + H2O co-solvent are approximately 4.8 and 5.9, respectively. The value of nhydr is lower in urea than that in NMF. Urea-H2O has higher dielectric constant than that of NMFH2O, therefore, it is more easily for urea to displace water from the primary hydration shell and thus possibly deduce the hydration number of the electrolyte in the solution. Moreover, different properties of the solvent, such as dipole moment (μurea = 4.2 D and μNMF = 3.86 D) and molecule volume also attribute to the difference of the hydration

Table 5 The average values of standard potential E0⁎ and the standard free energy of transference ΔG0t of CsF from water to the urea + H2O or NMF + H2O mixture at T = 298.2 K and p = 0.1 MPa. w

E0⁎ mV

0.00 0.10 0.20 0.30 0.40

ΔG0t −1

kJ·mol

E0⁎

ΔG0t

mV

kJ·mol−1

CsF + Urea + H2O

CsF + NMF + H2O

86.0 101.2 104.5 118.1 132.6

125.5 143.4 168.3 188.1 197.8

0.0000 1.3120 1.5135 2.7020 3.9418

0.0000 1.6558 3.9909 5.8358 6.7087

This paper presents data on thermodynamic properties of CsF + urea / N-methylformamide + water systems by potentiometric method at T = 298.2 K. The experimental data were analyzed with three thermodynamic models including the Pitzer, modified Pitzer and the extended Debye-Hückel equations. Systematic trend in the values of the mean activity coefficients, the excess Gibbs free energies, the standard free energy of transference, etc. for the systems studied has been observed and discussed. In addition, the primary CsF hydration number obtained concurrently. Funding This work was supported by the National Natural Science Foundation of China (nos. 21571120 and 21301114). Appendix A. Supplementary data Values of average molecular mass M, dielectric constant ε, density ρ, Debye-Hückel constants A, B and Pitzer constant Aφ for urea/NMF–H2O mixtures at T = 298.2 K and p = 0.1 MPa; the Nernst response of Cs-ISE and F-ISE electrode pair in the water for CsF + urea/NMF + H2O systems at T = 298.2 K; the mean activity coefficients γ± versus the molality m of CsF in NMF + H2O system at T = 298.2 K; the excess Gibbs free energies GE versus the molality m of CsF in NMF + H2O system at T = 298.2 K; plots of ΔE0c vs a function of water volume fraction (RT / F) lnφw in urea/NMF + H2O mixtures at T = 298.2 K. Supplementary data associated with this article can be found in the online version, at http://dx.doi.org/10.1016/j.molliq.2016.05.030.

X. Hao et al. / Journal of Molecular Liquids 220 (2016) 829–835

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