Activity Coefficients of CsCl in PEG 200–H2O and ... - ACS Publications

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Activity Coefficients of CsCl in PEG 200−H2O and PEG 600−H2O Mixtures at 298.15 K Ruifeng Guo, Shuni Li,* Quanguo Zhai, Yucheng Jiang, and Mancheng Hu* Key Laboratory of Macromolecular Science of Shaanxi Province, School of Chemistry and Chemical Engineering, Shaanxi Normal University, Xi’ an, Shaanxi 710062, P. R. China S Supporting Information *

ABSTRACT: The mean activity coefficients of the ternary systems CsCl + polyethylene glycol (PEG) (w) + H2O (1 − w) (w = 10%, 20%, 30%, 40%) determined by the potentiometric method at T = 298.15 K are reported. The molecular weights of PEG are 200 and 600, and the CsCl molality varies from 0.01 to 4.00 mol/kg. To correlate the experimental data, the Pitzer equation, extended Debye−Hückel equation, and the modified Pitzer equation have been utilized herein. As a result, a series of thermodynamic parameters were obtained and discussed in detail, including the mean ionic activity coefficients (γ±), the osmotic coefficient (Φ), the excess Gibbs free energies (GE), the standard Gibbs free energy of transference (ΔGt0) and the primary hydration number (nhydr).

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INTRODUCTION Electrolyte solutions widely exist in nature and have been applied extensively. Especially, the systems composed of inorganic salts + polymer + water have been used to form the aqueous two phase systems (ATPSs).1−6 During the past decades, ATPs were greatly developed for applications in extraction, separation, and recycling protein, antibiotics, and enzymes, etc., therefore the thermodynamic properties are very important for understanding various interactions in the solution. Polyethylene glycol (PEG) with the structure of HO−CH2− (CH2−O−CH2−)n−CH2−OH is a well-known polymer, which is miscible with water. Aqueous two-phase portioning systems composed of PEG + salt + H2O have already been widely investigated in the laboratory. 7 However, the activity coefficients and other thermodynamic properties for the electrolyte + PEG + H2O uniform systems were rarely reported. Sadeghi and Ziamajidi studied the water activity for the PEG 400 + NaCl + H2O system.8 Hernández-Luis et al. explored the mean activity coefficients of LiCl/NaCl/KCl + PEG 4000 + H2O systems in the temperature range from 288.15 to 308.15 K.9−11 In our previous work, the phase behavior of aqueous two phase systems composed of Cs2SO4 + PEG + H2O12 was investigated. Moreover, the activity coefficients of Rb+/Cs+ in amide/amino acid/polyhydroxy alcohol−water mixture solutions13,14 were also concerned. In this article, the ternary systems CsCl + PEG 200/PEG 600 + H2O at 298.15 K were investigated by the electromotive force method. The experimental data were well fitted to the extended Debye− Hückel, the Pitzer and the modified Pitzer equations. The © XXXX American Chemical Society

corresponding thermodynamic parameters were obtained and discussed in detail.

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EXPERIMENTAL SECTION The chemicals used in our experiment are given in Table 1. CsCl was oven drying in an oven at 393.15 K for 24 h until the constant weight and stored in a desiccator before use. Water used in this work was doubly distilled. Table 1. Description of Chemicals Used in This Study chemical name (CASRN)

source

mass purity

CsCl (7647-17-8) PEG 200 (25322-68-3) PEG 600 (25322-68-3)

Shanghai China Lithium Industrial Co., Ltd. Sinopharm Chemical Reagent Co., Ltd. Sinopharm Chemical Reagent Co., Ltd.

≥99.5%

treatment of the sample

≥99.0%

dried in an oven none

≥99.0%

none

For PVC membrane Cs-ISE, 0.1 mol/L cesium chloride solution was taken as an internal liquid and activating agent. The reproducibility of the Cs+ ion sensitive electrode was determined using the following cell: Hg‐Hg 2Cl 2|KCl(stad.)|CsCl(m)|Cs‐ISE Special Issue: Memorial Issue in Honor of Ken Marsh Received: January 10, 2017 Accepted: April 10, 2017

A

DOI: 10.1021/acs.jced.7b00024 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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interactions between unlike charged ions. Cφ represents tripleionic interactions. The value of Aφ is 0.3921 kg1/2·mol−1/2 for pure water at 298.15 K, which represents the Debye−Hückel constant parameter. The osmotic coefficient (Φ) can be calculated as follows:

The evaluation of the general characteristics of the constructed electrodes was achieved by successive calibrations over a range between 10−1 and 10−6 mol·dm−3. The standard deviation is lower than ±0.3 mV. The selectivity coefficient of the cell is lower than 10−4. To activate the electrode, the Ag/AgCl reference electrode was stored in 0.1 mol·L−1 HCl solution for at least 1 day to rebalance the chloride. The cell container is a temperaturecontrolled double wall glass using circulating water to keep the constant temperature. A Mettler Toledo-AL204 electronic analytical balance was used for weighting. Voltage readings were achieved using a high resistance electrometer (Keithley, 6517B, America). The static dielectric constants (ε) of the various mixtures were acquired from the literature.15 A density meter (Anton Paar DMA 4500) was used to measure the density (ρ/g·cm−3) of the mixed solvents, which was calibrated with double distilled water and air under atmospheric pressure before all the measurements. All the experimental data for the ternary systems with different solvent mixtures were provided in Table 2.

Φ − 1 = f φ + mBφ + m2C φ

where f φ = −Aφ(I1/2/(1 + bI1/2))

w 0.00 0.10 0.20 0.30 0.40

g·mol−1

ε

CsCl + PEG 200 18.02 78.40b 19.82 74.74b 22.02 70.52b 24.78 66.02b 28.32 61.23b

ρ

M

g·cm−3

g·mol−1

+ H2O 0.99704 1.01235 1.02844 1.04456 1.06165

The excess Gibbs free energies (G ) can be expressed in this way:18 GE = 2RTI(1 − Φ + ln γ±)

(3)

The corresponding coefficients (γ±, Φ, G ) for the CsCl + PEG + H2O system with different molalities are collected in Table 3. Modified Pitzer Model. For single-component electrolyte systems, the modified Pitzer model with merely three adjustable parameters was suggested by Perez-Villasenor et al:19 E

ln γ± = −Aφ[I1/2/(1 + bMX I1/2) + (2/bMX ) ln(1 + bMX I1/2)] + 2mBMX + 3m2CMX

(4)

Φ − 1 = −AφI1/2/(1 + bMX I1/2) + mBMX + 2m2CMX

ρ g·cm−3

(5)

CsCl + PEG 600 + H2O 18.02 78.40b 0.99704 19.95 73.73b 1.01320 22.35 68.46b 1.03021 25.41 62.85b 1.04781 29.44 56.90b 1.06579

bMX means the closest approach parameter in the Debye− Hückel term. BMX is the second virial-type coefficient. CMX is the third virial-type coefficient. Extended Debye−Hü ckel Model. Based on the ion−ion electrostatic interactions, the extended Debye−Hückel equation for calculating γ± for cesium chloride in the cosolvent can be written as follows:20,21

ε

Expanded uncertainties U(ρ) = 5 × 10−5 g·cm−3; U(ε) = 0.02; U(T) = 0.1 K; U(p) = 3 kPa (0.95 level of confidence). bReference 15.

log γ± = −Am1/2 /(1 + Bam1/2) + cm + dm2

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− log(1 + 0.002mM )

THEORETICAL MODEL Pitzer Model. According to Pitzer, the activity coefficients γ± for CsCl in the electrolyte solution of 1−1 type is described as follows:16,17 ln γ± = f γ + mBγ + m2C γ

(1)

f γ = −Aφ[I1/2/(1 + bI1/2) + (2/b) ln(1 + bI1/2)]

A = 1.8247 × 106ρ1/2 /(εT )3/2 kg1/2·mol−1/2

(6a)

B = 50.2901ρ1/2 /(εT )1/2 kg1/2·mol−1/2·Å−1

(6b)

The fitting values of E , parameters in Debye−Hückel equation and standard deviations of the fitting process were summarized in Tables 4 and 5. 0

(1a)

Aφ = 1.4006 × 106ρ1/2 (εT )3/2 kg1/2·mol−1/2

(6)

in which a represents the ion radius parameter in Å, c and d are characterized as the ion-interaction parameters, M means the average molecular weight. The Debye−Hückel parameters A and B are defined as

where

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(1b)

RESULTS Electrode Calibration. The mean activity coefficients of CsCl in PEG−H2O systems were investigated at 298.15 K on the galvanic cells without transference:

Bγ = 2β (0) + 2β (1){[1 − exp(−aI1/2)(1 + aI1/2

C γ = 1.5C φ

(2b) E

a

− a 2I /2)]/(a 2I )}

(2a)

Bφ = β (0) + β (1) exp( −aI1/2)

Table 2. Values of Mass Fractions (w), Average Molecular Mass (M), Density (ρ), Relative Permittivity (ε) for Different PEG 200/600 + Water Mixtures at 298.15 K and p = 0.1 MPaa M

(2)

(1c) (1d)

Cs‐ISE|CsCl(m), H 2O|Ag‐AgCl

In these equations, the values of a and b are 2.0 and 1.2 kg1/2· mol−1/2, respectively. I represents the summation of ionic strength, which is equal to m in molalitiy scale for the 1−1 type electrolytes. Variable parameters in the Pitzer equation are expressed as β(0), β(1), and Cφ. β(0) is identified as the interaction between like and unlike charged ions. β(1) is the

(I)

Cs‐ISE|CsCl(m), PEG200/600(w), H 2O(1 − w)|Ag‐AgCl (II)

in which, w is the mass fraction of PEG, and m is the molality of CsCl in mixed solvent (w = 10%, 20%, 30%, and 40%). B

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Table 3. Experimental Cell Potential E, Mean Activity Coefficients γ±, Osmotic Coefficients Φ and Excess Gibbs Free Energies GE for CsCl in PEG 200/600−H2O mixed solvents at T = 298.15 K and p = 0.1 MPaa m

E

mol·kg−1

mV

γ±

Φ

GE/RT

m

E

mol·kg−1

mV

CsCl + PEG 200 + H2O

γ±

Φ

GE/RT

CsCl + PEG 600 + H2O w = 0.00

0.0085 0.0280 0.0574 0.0969 0.1937 0.3873 0.6802 1.0730 1.5605 2.1523 2.9473 3.9436

−117.63 −61.28 −27.98 −3.95 26.49 56.39 80.25 99.41 115.36 129.60 143.84 157.51

0.9052 0.8434 0.7943 0.7528 0.6923 0.6283 0.5769 0.5383 0.5104 0.4908 0.4772 0.4716

0.9682 0.9473 0.9308 0.9170 0.8974 0.8782 0.8654 0.8591 0.8589 0.8643 0.8771 0.8982

−0.0011 −0.0066 −0.0185 −0.0389 −0.1027 −0.2657 −0.5651 −1.0266 −1.6584 −2.4796 −3.6365 −5.1259

0.0305 0.0608 0.1000 0.2118 0.4333 0.7446 1.1681 1.6897 2.3162 3.1456 4.0728

−44.52 −13.46 8.66 41.91 71.80 94.37 112.89 128.04 141.73 155.27 167.51

0.8273 0.7765 0.7348 0.6655 0.5953 0.5423 0.5006 0.4697 0.4477 0.4324 0.4270

0.9417 0.9244 0.9103 0.8871 0.8646 0.8490 0.8392 0.8358 0.8391 0.8520 0.8750

−0.0080 −0.0216 −0.0437 −0.1246 −0.3321 −0.6864 −1.2410 −1.9986 −2.9780 −4.3437 −5.9137

0.0263 0.0537 0.0975 0.1952 0.3974 0.6984 1.0992 1.5948 2.1931 2.9919 3.9970

−42.51 −10.32 15.70 45.63 76.03 99.35 117.96 133.05 147.31 161.17 174.98

0.8227 0.7684 0.7163 0.6500 0.5794 0.5250 0.4847 0.4558 0.4356 0.4218 0.4166

0.9397 0.9210 0.9031 0.8809 0.8586 0.8440 0.8368 0.8364 0.8425 0.8572 0.8826

−0.0071 −0.0198 −0.0462 −0.1217 −0.3214 −0.6822 −1.2335 −1.9843 −2.9539 −4.3105 −6.0623

0.0284 0.0590 0.0991 0.1945 0.3960 0.6942 1.0926 1.5885 2.1849 2.9826 3.9657

−24.78 7.70 29.91 58.82 88.35 110.75 129.23 144.46 157.84 170.73 182.65

0.8008 0.7407 0.6926 0.6256 0.5526 0.4961 0.4532 0.4209 0.3968 0.3774 0.3646

0.9320 0.9110 0.8944 0.8715 0.8474 0.8302 0.8193 0.8141 0.8144 0.8213 0.8358

−0.0088 −0.0249 −0.0519 −0.1324 −0.3489 −0.7374 −1.3347 −2.1588 −3.2287 −4.7469 −6.7006

0.0575 0.0979 0.1995 0.3962 0.6936 1.0885 1.5891

20.04 42.67 72.73 101.48 123.44 141.07 155.40

0.7272 0.6785 0.6090 0.5389 0.4797 0.4313 0.3914

0.9080 0.8919 0.8689 0.8447 0.8216 0.8003 0.7823

−0.0260 −0.0548 −0.1456 −0.3668 −0.7716 −1.3962 −2.2895

0.0100 0.0297 0.0706 0.1497 0.2985 0.5981 0.9033 1.5039 2.1055 3.0078 4.0015

−110.05 −58.06 −17.49 16.74 46.88 77.24 94.27 116.85 131.54 147.78 162.25

0.8980 0.8398 0.7784 0.7154 0.6525 0.5884 0.5524 0.5130 0.4920 0.4765 0.4715

0.9657 0.9461 0.9254 0.9047 0.8852 0.8679 0.8608 0.8587 0.8638 0.8782 0.8996

−0.0015 −0.0072 −0.0248 −0.0718 −0.1864 −0.4764 −0.8207 −1.5825 −2.4132 −3.7261 −5.2129

0.0128 0.0321 0.0694 0.1502 0.3022 0.6017 0.9077 1.5007 2.1075 3.0105 4.0086

−85.68 −42.78 −7.43 26.67 56.01 85.35 102.94 124.22 139.15 155.60 168.48

0.8729 0.8138 0.7504 0.6761 0.6039 0.5352 0.4987 0.4614 0.4415 0.4245 0.4116

0.9564 0.9355 0.9126 0.8859 0.8615 0.8431 0.8381 0.8414 0.8499 0.8621 0.8696

−0.0024 −0.0091 −0.0277 −0.0833 −0.2211 −0.5633 −0.9692 −1.8457 −2.8134 −4.3283 −6.0701

0.0283 0.0642 0.1449 0.3031 0.5969 0.8958 1.4904 2.0941 2.9947 3.9906

−35.36 2.06 36.51 67.33 95.65 112.60 133.34 148.45 164.75 177.01

0.8026 0.7306 0.6467 0.5660 0.4958 0.4591 0.4213 0.4015 0.3839 0.3687

0.9308 0.9041 0.8727 0.8441 0.8246 0.8200 0.8250 0.8349 0.8468 0.8499

−0.0085 −0.0280 −0.0894 −0.2506 −0.6281 −1.0723 −2.0551 −3.1303 −4.8170 −6.7642

0.0279 0.0672 0.1471 0.3068 0.6039 0.9047 1.5095 2.1234 3.0245 4.0325

−23.86 15.40 48.04 77.92 105.91 122.83 143.65 159.01 173.66 184.72

0.7801 0.6963 0.6109 0.5288 0.4600 0.4254 0.3902 0.3708 0.3496 0.3244

0.9222 0.8905 0.8580 0.8290 0.8119 0.8103 0.8192 0.8285 0.8296 0.8063

−0.0095 −0.0339 −0.1032 −0.2860 −0.7109 −1.2035 −2.2958 −3.4845 −5.3260 −7.5167

0.0259 0.0673 0.1490 0.3057 0.6072 0.9114 1.5067

−14.45 26.97 60.57 89.86 117.96 135.05 155.62

0.7637 0.6712 0.5858 0.5086 0.4419 0.4081 0.3734

0.9171 0.8831 0.8521 0.8267 0.8111 0.8088 0.8150

−0.0097 −0.0379 −0.1153 −0.3074 −0.7622 −1.2852 −2.4108

w = 0.10

w = 0.20

w = 0.30

w = 0.40

C

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Table 3. continued m

E

mol·kg−1

mV

γ±

Φ

GE/RT

0.3605 0.3348 0.3191

0.7709 0.7692 0.7857

−3.4499 −5.1428 −7.3770

m

E

mol·kg−1

mV

γ±

Φ

GE/RT

0.3542 0.3346 0.3148

0.8232 0.8283 0.8175

−3.6387 −5.5732 −7.8336

w = 0.40 2.1803 2.9787 3.9745

166.66 178.33 190.88

2.1126 3.0188 4.0237

170.04 185.36 197.03

a w is the mass fraction of PEG in mixed solvent; m is the molality of CsCl in pure water or mixtures. The expanded uncertainties are U(m) = 0.0002 mol·kg−1; U(E) = 0.02 mV; U(γ) = 0.02; U(T) = 0.1 K; U(p) = 3 kPa (0.95 level of confidence).

Table 4. Summary of Both Standard Potential E0 and the Parameter Value Obtained from the Pitzer and the Modified Pitzer Equations of CsCl in PEG 200/600−H2O Mixtures at T = 298.15 K and p = 0.1 MPa Pitzer

w

Modified Pitzer

β(0)

β(1)

Cφ

E0

kg·mol−1

kg·mol−1

kg2·mol−2

mV

0.10 0.20 0.30 0.40

0.0178 0.0343 0.0320 0.0000

0.1048 0.1074 0.1829 0.4755

0.0027 0.0007 0.0000 0.0060

0.10 0.20 0.30 0.40

0.0555 0.0692 −0.1001 −0.0994

−0.1138 −0.1443 −0.1407 0.1485

−0.0056 −0.0081 −0.0159 −0.0129

SD

bMX

BMX

CMX

E0

kg1/2·mol−1/2

kg·mol−1

kg2·mol−2

mV

SD

0.0051 0.0219 0.0378 −0.0410

0.0019 0.0008 −0.0018 0.0044

139.77 149.42 164.86 178.36

0.17 0.23 0.15 0.30

0.0755 0.0955 0.1236 0.0819

−0.0037 −0.0052 −0.0090 −0.0057

142.99 157.40 170.95 184.89

0.17 0.29 0.29 0.26

CsCl + PEG 200 + H2O 139.80 0.17 1.5404 149.44 0.23 1.5085 164.55 0.27 1.4497 178.82 0.28 2.5692 CsCl + PEG 600 + H2O 142.99 0.17 0.8765 157.41 0.28 0.8370 170.97 0.29 0.8959 184.93 0.25 1.5056

Table 5. Standard Potential E0 and the Debye−Hückel Parameters of CsCl in PEG 200/600−H2O Mixtures at T = 298.15 K and p = 0.1 MPa w 0.10 0.20 0.30 0.40

a

c

d

E0

Å

kg· mol−1

kg2·mol−2

mV

2.8977 2.7580 2.5524 3.9870

CsCl + PEG 200 + H2O 0.0030 0.0034 0.0167 0.0022 0.0309 −0.0013 −0.0370 0.0073

SD

139.88 149.52 164.97 178.69

0.17 0.22 0.15 0.02

a

c

d

E0

Å

kg· mol−1

kg2·mol−2

mV

SD

143.02 157.44 171.00 185.03

0.17 0.29 0.28 0.23

1.7536 1.6013 1.6186 2.4319

CsCl + PEG 600 + H2O 0.0644 −0.0041 0.0822 −0.0062 0.1058 −0.0109 0.0665 −0.0660

Figure 1. Mean activity coefficients γ± versus the molality m of CsCl in PEG 200/600−H2O mixtures at T = 298.15 K.

defined as RT/F. The theoretical Nernst slope is 51.38 mV at 298.15 K. T represents the thermodynamic temperature. F means Faraday constant, and R denotes the standard gas constant. γ± is the mean ionic activity coefficient of CsCl in pure water, which can be obtained from the Pitzer and Nernst

The Nernst equation for the cell is 0

E = E + 2k ln(mγ±)

(7)

where E is the value of cell potential for the electrode pair. E0 stands for the apparent standard potential difference. k is D

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equations. To check the Nernst response of the electrode pair, the relationship between E and ln(mγ±) at 298.15 K is depicted in Supporting Information, Figure S1. E0 and k can be calculated through a linear regression method. The values are 126.8 mV and 25.06 for the CsCl + PEG 200 + H2O system, and 130.0 mV and 25.45 for the CsCl + PEG 600 + H2O system, respectively. The linear correlation coefficients (R2) of two systems are both of 0.9999. The activity coefficients of CsCl in pure water in this work are compared with the data reported by Hamer,22 which showed a good agreement. The results are depicted in Figure S2. It indicates that our electrode pairs have a good Nernst response and can be well used for the further experiments. When considering the effect of the composition changes on the calibration curve, the estimated experimental deviation for the measured cell potential values was ±0.10 mV when m < 2.0 mol·kg−1 and ±0.20 mV when 2.0 < m < 4.0 mol·kg−1.

Figure 2. Comparison of the mean activity coefficients γ± of CsCl in PEG 200/600−H2O (w = 10%) mixed solvent at T = 298.15 K.

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DISCUSSION Figure 1 presents the γ± vs m for CsCl in PEG 200/PEG 600 + H2O cosolvent systems at 298.15 K. It was clear that γ± decreases with increasing m of CsCl for a fixed solvent. The reason for this tendency is that the ion−ion (association) interactions are the dominant factor for the ε-decreasing cosolvent.23,24 When the concentration of CsCl was given, γ± decreased with the increasing content of PEG 200 or PEG 600 in the mixed solvent. This phenomenon is the same as in the some other systems, such as alcohol−water, amino acid−water, amide−water and so on.25,26 The increase of PEG in the cosolvent system will decrease the dielectric constant. Usually, low dielectric constant results in stronger interaction between ion−ion and relatively lower concentration for solvation free ions. Thus, the mean activity coefficients decreased. For CsCl in the aqueous system, the association degree can be evaluated by considering the following equilibrium:27

PEG600, respectively. The result showed that the increasing polymerization degree increased the hydration number of PEG. That is, for PEG with low molecular weight, only firmly bound water can be kept together with the PEG chain. Thus, more water can be accessed for the hydration of CsCl which resulted in the larger activity coefficients of the electrolyte in the solution. The excess Gibbs free energies GE have the same tendency as plotted in Figure S3 and Figure S4. The standard Gibbs free energy of transference ΔGt0 is used to express the migration energy from water to nonaqueous solvent of solute. It can be calculated according to the following form:31,32 ΔGt 0 = F(Em 0 − Ew 0) + 2RT ln(ρw /ρm )

The standard solubility product is one of the major factors to evaluate equilibrium state of the electrolyte solubility, which can be deduced from ΔGt0 on the basis of the following relation:33

CsCl ↔ Cs+ + Cl− (1 − α)

K=

mα

mα

ΔGt 0 = RT ln(K 0 sp,w /K 0 sp,m)

α 2mγ±′ 2 1−α

(9)

K0sp

ln K

(8)

where K is the equilibrium constant, m is the molality of CsCl, α is the dissociation degree of the solute, and γ′± is the mean activity coefficient of a completely dissociated 1:1 electrolyte. γ′± and α can be calculated according to the literature method27 using the reported data28,29 (Table S1). The dissociation degree α decreases with the increase of mCsCl. That is, the ion-pair interaction increased with the increasing m of CsCl. The association degree in the PEG−H2O mixture is bigger than that in pure water, which indicates that the association of CsCl enhances when PEG is added to water. Figure 2 shows the comparison of γ± for CsCl + PEG 200/ PEG 600 + H2O systems at wPEG = 10%. At a fixed m of CsCl, γ± in the PEG 600 system is always lower than that in PEG 200. This could be attributed to the lower relative permittivity of PEG 600−H2O than that of PEG 200−H2O. The hydroxyl groups and oxygen atom of the PEG can participate in forming intermolecular and intramolecular hydrogen bonding in the pure state. While, when PEG was added in aqueous solution, the hydration effect of PEG with different molecular weights can change the properties of the solution. The hydration number of PEG was determined by Migliardo and co-workers30 with the values of 7.4 and 31.2 at 25 °C for PEG200 and

K0sp,w

0 sp,m

= ln K

0

(10)

0

sp,w

− ΔGt /RT

(11)

K0sp,m

and represent the electrolyte standard solubility product in pure water and in the PEG-H2O mixed solvent, respectively. The subscript “m” and “w” means the mixtures and pure water. The value of ln K0sp,w can be calculated from the literature.34 The values of E0*, ΔGt0, and ln K0sp,m have been summarized in Table 6. E0* is the average values obtained using the Pitzer, Table 6. Average Values of Standard Potential E0*, the Standard Free Energy of Transference ΔGt0 and the Standard Solubility Product lnK0sp, m of CsCl from Water to the Mixtures at T = 298.15 K and p = 0.1 MPa E0* w 0.00 0.10 0.20 0.30 0.40 E

mV

ΔGt0 kJ·mol

−1

0

ln K

sp,m

CsCl + PEG 200 + H2O 126.88 0.0000 1.9323 139.81 1.1726 1.4592 149.46 2.0255 1.1152 164.80 3.4280 0.5494 178.62 4.6819 0.0436

E0*

ΔGt0

mV

kJ·mol−1

ln K0sp,m

CsCl + PEG 600 + H2O 130.05 0.0000 1.9323 143.00 1.1699 1.4603 157.42 2.4789 0.9323 170.98 3.7036 0.4382 184.95 4.9677 −0.0718 DOI: 10.1021/acs.jced.7b00024 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Figure 3. Relationship of the standard free energy of transference ΔGt0 and the standard solubility product ln K0sp,m for CsCl vs the mass fraction w of PEG 200/600−H2O mixtures at T = 298.15 K.

Figure 4. Variation of ΔEc0 vs a function of water volume fraction (RT/F) ln φw in the PEG 200/600−H2O mixtures at 298.15 K.

modified Pitzer, and the extended Debye−Hückel equations. The relationship of ΔGt0 and ln K0sp,m vs the mass fraction w of PEG 200/600 in the mixtures is plotted in Figure 3. In all cases, ΔGt0 is positive, which implies that the transferring of CsCl from H2O into the PEG−H2O mixed solvent systems is not a thermodynamically beneficial process. Moreover, ΔGt0 increased when increasing the PEG content in the mixed solvent. This is due to the weakening of the hydrogen bond between the water and chloride ion.35 The standard solubility product ln K0sp,m has an opposite tendency as that of ΔGt0 also shown in Figure 3. When evaluating the free energy interaction parameters, the standard transfer Gibbs energy ΔG0t m(M) (mol per kilogram of the mixed solvent) and ΔG0t m(W) (mol per kilogram of pure water) can be converted to each other as follows:11 ΔGt0m(W) = ΔGt0m(M) − νRT ln(1 + 0.001mNMN)

ΔGt0m(W)(W → W + N ) = 2νgENmN + 6νgEENmN mE + 3ν 2gENNmE2 (13)

where gEN and gEEN are pair and triple Gibbs energy interaction parameters. The salting coefficient ks can be obtained with the pair interaction parameter gEN by RTks = 2vgEN. The values of 2vgEN are 1.4 and 4.2 for PEG200 and PEG600, respectively. And the calculated values of ks are 0.6 and 1.7 for PEG200 and PEG600. The positive ks suggested that CsCl is the salted-out electrolyte for PEG in the solution.37,38 The interaction between PEG200/600 and CsCl can be described as R−Cs+, R−Cl− (R represents the alkyl groups in PEG), O−Cl− and O−Cs+ (O represents −O− or −OH group in PEG) as indicted for amino acid and amide systems.39,40 The structural interactions between the R group and Cl− or Cs+ generate a positive contribution to gEN. The electrostatic repulsive interaction between O and Cl− also has a positive contribution to gEN, whereas, the electrostatic attractive interaction of O−Cs+ contributes a negative value to gEN. For the CsCl−PEG200/600−H2O systems, the positive values of gEN indicate that the interactions are mainly decided by the O− Cl−. Moreover, the interaction between PEG and CsCl is also

(12)

where mN is the molality of the PEG 200/600 (in mol/kg water) and MN is the molecular mass of the PEG 200/600. On the basis of the McMillan-Mayer theory,36 ΔG0t m(W) could be explained: F

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ORCID

discussed through the variation of viscosity in different PEG mixtures.41 The primary hydration number nhydr means the number of water molecules firmly bounded by a mole of electrolyte. It can be calculated and estimated based on the standard electromotive force in molal concentration and the mass fraction of water according to the expression of Feakins and French:42,43

Shuni Li: 0000-0002-6614-9241 Quanguo Zhai: 0000-0003-1117-4017 Mancheng Hu: 0000-0003-2920-0439 Funding

This work was supported by the National Natural Science Foundation of China (Nos. 21571120, U1607116), the Fundamental Research Funds for the Central Universities (GK201701003).

(ΔGt 0)c /F = ΔEc 0 = Ecs 0 − Ecw 0 = nhydr(RT /F ) ln φw (14) 0

0

Ec = Em + 2k log ds

(14a)

φw = (ww /d w )/(ww /d w + wpoly /d poly )

(14b)

Notes

The authors declare no competing financial interest.

■

The subscript “s” and “w” denoted the mixed solvent and water. Em0 can be expressed as E0 in molal scale. Density was represented by d, and mass fraction was defined as w. The volume fraction of water in the mixtures was depicted by φw. Figure 4 showed the relationship between ΔEc0 and (RT/F) ln φw. The nhydr values, 4.4 (r = 0.9974) in the PEG 200−H2O system and 4.9 (r = 0.9925) in the PEG 600-H2O system, were calculated from the linear regression. Clearly, the nhydr value is smaller for PEG 200. This behavior may be related to the difference of the dipole moment of both cosolvents (minor effect) and the molecule volume of two solvents (main effect). PEG 200 molecules are smaller than PEG 600, they would easily replace water molecules from the solvation layer.

■

CONCLUSION We presented the thermodynamic properties for CsCl + PEG 200/PEG 600 + H2O ternary systems at 298.15 K. The extended Debye−Hückel, modified Pitzer and Pitzer models were used to correlate the experimental data. Because of the different dielectric constant and molecular weight, the excess Gibbs free energy GE and the mean activity coefficient γ± of CsCl in the PEG 200−H2O system was larger than that in PEG 600−H2O. Moreover, the association constant of CsCl was calculated by the osmotic coefficient data. The values of kS and gEN both are positive, which indicates that PEG molecules were salted-out by CsCl in water. In addition, the primary hydration number (nhydr) in CsCl−PEG 200−H2O is smaller than that in CsCl−PEG 600−H2O system.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b00024. Ion-pair dissociation constant K and the dissociation degree α of CsCl in PEG 200/600−H2O mixtures; response of the Cs-ISE and Ag/AgCl electrode pair at 298.15 K; comparison of mean activity coefficients of CsCl in water at T = 298.15 K; the excess Gibbs free energy GE versus the molality m of CsCl in PEG 200/ 600−H2O mixtures at T = 298.15 K; comparison of the excess Gibbs free energy GE of CsCl in PEG 200/600− H2O (w = 10%) mixed solvent at T = 298.15 K (PDF)

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