Pitzer, Modified Pitzer, and Extended Debye–Hückel Modeling

Article pubs.acs.org/jced

Pitzer, Modified Pitzer, and Extended Debye−Hückel Modeling Approaches: Ternary RbF or CsF + Glycine + Water Electrolyte Systems at 298.15 K Lei Ma, 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 ABSTRACT: This article deals with the mean activity coefficients of RbF or CsF in the glycine + water mixed systems. The Pitzer, the modified Pitzer, and the extended Debye−Hückel equations are used to describe the nonideal behavior of the electrolyte. The osmotic coefficients, the excess Gibbs free energy, and the standard Gibbs energies of transfer were calculated with the corresponding parameters.

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INTRODUCTION An accurate description of the thermodynamic properties of electrolyte solutions is not only required for the investigation of the phase equilibria, but also for applications in many industrial processes.1 There have been a series of studies providing thermodynamic data on electrolytes in mixed solvents or mixed electrolyte systems, and alkaline metal salts are often the most studied electrolyte. Deyhimi et al. have carried out many studies on the thermodynamic properties of chlorides in a mixed system of different solvents.2−4 Hernandez-Luis et al. investigated the thermodynamic behavior of NaCl in ethylene carbonate + water systems and KCl in poly(ethylene glycol) (PEG) 4000 + water systems.5,6 The mean activity coefficients of KCl in (formamide or glucose + water) systems were determined by Ghalami-Choobar’s group.7,8 However, only a few studies describe the thermodynamic behavior of alkaline metal fluoride in organic solvents. Jones et al. reported the thermodynamic data of LiF dissolution in alkylcarbonate.9 The mean activity coefficients of NaF in methanol−water, ethanol− water, formamide−water, glucose−water, and sucrose−water mixtures have been obtained by Hernandez-Luis and coworkers.10−12 Furthermore, the presence of electrolyte solutions is encountered in separation processes for amino acids; thus, there is a need for a more profound understanding of the thermodynamic behavior of electrolyte + amino acid systems.13 Ghalami-Choobar et al. measured the mean activity coefficients for KCl in the proline + water system.13 Zhuo et al. determined the thermodynamic properties for CaCl2 in (glycine, alanine, serine, or proline + water) mixtures at T = 298.15 K.14,15 In our previous work, we obtained the mean activity coefficients of RbCl and CsCl in glycine + water mixtures and RbF and CsF in ethylene glycol + water.16,17 As an extension of our series of works on the thermodynamic properties of unusual alkali metal salts in the mixed solvent system,16,17 this paper investigated the ternary systems RbF or © XXXX American Chemical Society

CsF + glycine + H2O. The mean activity coefficients, the osmotic coefficients, the excess Gibbs free energy, and the standard Gibbs energies of transfer of the systems were reported.

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EXPERIMENTAL SECTION Analytical reagent rubidium fluoride and cesium fluoride (purity > 0.9950) were purchased from Shanghai China Lithium Industrial Co., Ltd., and used without further purification. glycine (Sinopharm Chemical Reagent Co., Ltd., A.R. purity > 99.5 %) dried in vacuum at 393 K for the constant weight before use. Water used in experiment was doubly distilled water, and the specific conductance was approximately (1.0 to 1.2)·10−4 S·m−1. Details of the potentiometric measurements and general techniques were the same as previously described in our previous work.16,17 The Rb ion-selective electrode (Rb-ISE) and Cs ion-selective electrode (Cs-ISE) were a PVC membrane type based on valinomycin and were filled with 0.10 mol·L−1 RbF or CsF as the internal liquid in K ion-selective electrode. Both the membrane electrode and the F-ISE (model 201) were obtained from Jiangsu Electroanalytical Instrument Co., and the electrodes were calibrated before the experiment and showed a good Nernstian response. The cells used in this work are given as follows: Rb‐ISE|RbF(m), glycine(mA ), water|F‐ISE

(A)

Cs‐ISE|CsF(m), glycine(mA ), water|F‐ISE

(B)

Here m is the molalities of RbF or CsF, and mA is the glycine molalities of (0.10, 0.20, 0.30, and 0.40) mol·kg−1. The uncertainties in the electrolyte molalities, glycine molalities, Received: September 12, 2012 Accepted: November 13, 2012

A

dx.doi.org/10.1021/je300995q | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Experimental Electromotive Force E, Mean Activity Coefficients γ±, Osmotic Coefficients Φ, and Excess Gibbs Free Energy GE at Different RbF or CsF and Glycine Molalities in the Glycine + H2O Mixture at 298.15 K m

E

mol·kg−1

mV

0.0032 0.0062 0.0092 0.0123 0.0156 0.0222 0.0290 0.0361 0.0428 0.0530 0.0633 0.0732 0.0893 0.1059 0.1323 0.1574 0.1949 0.2350 0.2792 0.3214 0.3762 0.4288 0.4932 0.5553

−106.6 −73.2 −53.7 −39.9 −28.4 −11.3 1.6 11.9 20.0 30.1 38.4 45.2 54.6 62.6 73.0 81.2 91.2 100.0 108.0 114.6 122.1 128.3 135.4 140.8

0.0110 0.0158 0.0205 0.0281 0.0355 0.0426 0.0501 0.0601 0.0701 0.0797 0.0943 0.1092 0.1318 0.1543 0.1870 0.2200 0.2611 0.3091 0.3547 0.4008 0.4678 0.5241 0.5704

−47.4 −29.8 −17.4 −2.2 8.8 17.4 25.2 33.7 40.8 47.1 55.0 62.0 70.8 78.3 87.3 94.9 102.9 111.1 117.5 123.4 130.9 136.5 140.6

0.0044 0.0090 0.0130 0.0177 0.0247

−98.9 −64.0 −45.8 −31.0 −15.0

γ±

Φ

RbF + Glycine + Water RbF + Pure Water 0.9409 0.9805 0.9205 0.9740 0.9064 0.9695 0.8945 0.9658 0.8841 0.9626 0.8676 0.9577 0.8539 0.9537 0.8423 0.9505 0.8329 0.9479 0.8208 0.9448 0.8106 0.9423 0.8021 0.9403 0.7905 0.9378 0.7806 0.9359 0.7677 0.9338 0.7578 0.9325 0.7462 0.9316 0.7366 0.9314 0.7282 0.9318 0.7219 0.9327 0.7155 0.9343 0.7108 0.9361 0.7064 0.9387 0.7033 0.9414 0.10 mol·kg−1 Glycine 0.9031 0.9686 0.8880 0.9640 0.8765 0.9605 0.8611 0.9561 0.8490 0.9527 0.8394 0.9501 0.8305 0.9478 0.8204 0.9452 0.8117 0.9432 0.8044 0.9415 0.7948 0.9395 0.7864 0.9379 0.7758 0.9361 0.7670 0.9349 0.7566 0.9339 0.7481 0.9334 0.7397 0.9334 0.7319 0.9341 0.7261 0.9351 0.7213 0.9364 0.7161 0.9387 0.7128 0.9410 0.7107 0.9430

0.20 mol·kg−1 Glycine 0.9373 0.9154 0.9017 0.8894 0.8751

0.9796 0.9728 0.9687 0.9651 0.9611

GE/RT

m

E

mol·kg−1

mV

−0.0003 −0.0007 −0.0012 −0.0019 −0.0027 −0.0044 −0.0065 −0.0088 −0.0112 −0.0151 −0.0193 −0.0235 −0.0309 −0.0389 −0.0524 −0.0661 −0.0874 −0.1115 −0.1390 −0.1661 −0.2024 −0.2380 −0.2823 −0.3258

0.0032 0.0074 0.0109 0.0146 0.0182 0.0255 0.0328 0.0403 0.0475 0.0589 0.0703 0.0812 0.0993 0.1179 0.1474 0.1756 0.2178 0.2598 0.3144 0.3510 0.4138 0.4870 0.5655

−141.6 −101.0 −82.0 −67.7 −56.9 −40.6 −28.6 −18.7 −11.0 −0.8 7.6 14.5 24.0 32.1 42.7 51.0 61.2 69.4 78.6 83.9 91.9 100.0 107.5

−0.0016 −0.0026 −0.0038 −0.0059 −0.0083 −0.0107 −0.0134 −0.0172 −0.0213 −0.0254 −0.0319 −0.0389 −0.0501 −0.0618 −0.0796 −0.0984 −0.1227 −0.1522 −0.1810 −0.2109 −0.2551 −0.2930 −0.3245

0.0031 0.0060 0.0091 0.0117 0.0145 0.0209 0.0271 0.0328 0.0384 0.0473 0.0534 0.0628 0.0786 0.0948 0.1202 0.1452 0.1827 0.2213 0.2676 0.3153 0.3766 0.4354 0.4960 0.5703 0.6306

−146.7 −113.9 −93.6 −81.1 −70.6 −52.9 −40.4 −31.2 −23.7 −13.6 −7.8 −0.1 10.6 19.6 30.9 39.8 50.8 59.9 69.1 76.9 85.3 92.3 98.7 105.4 110.3

−0.0004 −0.0011 −0.0019 −0.0029 −0.0047

0.0031 0.0061 0.0089 0.0119 0.0151

−154.6 −121.2 −102.0 −87.9 −76.2

B

γ±

Φ

CsF + Glycine + Water CsF + Pure Water 0.9402 0.9803 0.9144 0.9720 0.8995 0.9673 0.8870 0.9635 0.8770 0.9604 0.8603 0.9555 0.8473 0.9518 0.8360 0.9487 0.8269 0.9463 0.8147 0.9433 0.8044 0.9409 0.7961 0.9391 0.7844 0.9369 0.7746 0.9352 0.7621 0.9337 0.7528 0.9330 0.7419 0.9330 0.7338 0.9337 0.7260 0.9355 0.7221 0.9371 0.7171 0.9403 0.7135 0.9447 0.7115 0.9498 0.10 mol·kg−1 Glycine 0.9446 0.9257 0.9120 0.9025 0.8940 0.8784 0.8666 0.8574 0.8497 0.8391 0.8329 0.8245 0.8127 0.8027 0.7903 0.7804 0.7687 0.7592 0.7501 0.7426 0.7348 0.7288 0.7237 0.7186 0.7151 0.20 mol·kg−1 Glycine 0.9465 0.9286 0.9162 0.9061 0.8971

GE/RT

−0.0003 −0.0009 −0.0016 −0.0024 −0.0033 −0.0054 −0.0077 −0.0103 −0.0130 −0.0175 −0.0223 −0.0271 −0.0357 −0.0450 −0.0605 −0.0762 −0.1008 −0.1264 −0.1608 −0.1845 −0.2258 −0.2749 −0.3281

0.9819 0.9759 0.9717 0.9688 0.9663 0.9618 0.9585 0.9561 0.9541 0.9515 0.9500 0.9481 0.9456 0.9437 0.9416 0.9403 0.9390 0.9384 0.9381 0.9381 0.9386 0.9392 0.9401 0.9412 0.9423

−0.0002 −0.0006 −0.0012 −0.0017 −0.0023 −0.0038 −0.0055 −0.0072 −0.0090 −0.0120 −0.0142 −0.0177 −0.0240 −0.0310 −0.0425 −0.0546 −0.0738 −0.0946 −0.1207 −0.1486 −0.1858 −0.2225 −0.2613 −0.3099 −0.3501

0.9825 0.9770 0.9732 0.9702 0.9676

−0.0002 −0.0006 −0.0011 −0.0016 −0.0023

dx.doi.org/10.1021/je300995q | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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Table 1. continued m

E

mol·kg−1

mV

γ±

Φ

GE/RT

m

E

mol·kg−1

mV

−1

0.0317 0.0382 0.0452 0.0546 0.0637 0.0729 0.0877 0.0998 0.1222 0.1434 0.1693 0.1959 0.2372 0.2644 0.3212 0.3768 0.4318 0.4924 0.5384

0.0023 0.0045 0.0071 0.0096 0.0122 0.0174 0.0226 0.0278 0.0354 0.0458 0.0563 0.0667 0.0823 0.0978 0.1210 0.1464 0.1784 0.2168 0.2679 0.3062 0.3536 0.4059 0.4622 0.5021 0.5481 0.0027 0.0055 0.0082 0.0109 0.0139 0.0194 0.0252 0.0308 0.0364 0.0450 0.0536

−2.9 5.9 14.0 23.0 30.3 36.9 45.6 51.7 61.3 68.9 76.9 83.8 93.0 98.3 107.5 115.2 121.8 128.3 132.7

−133.4 −99.9 −77.7 −63.2 −51.6 −34.5 −21.8 −12.1 −0.4 11.8 21.5 29.7 39.8 48.0 58.0 67.1 76.5 85.8 95.9 102.2 109.1 115.8 122.2 126.0 130.1 −131.5 −95.9 −76.9 −62.5 −50.9 −34.7 −22.0 −12.3 −4.2 6.0 14.4

0.20 mol·kg Glycine 0.8635 0.8547 0.8465 0.8372 0.8294 0.8226 0.8132 0.8067 0.7966 0.7888 0.7809 0.7742 0.7658 0.7613 0.7537 0.7481 0.7439 0.7403 0.7382 0.30 mol·kg−1 Glycine 0.9544 0.9386 0.9258 0.9163 0.9081 0.8948 0.8842 0.8756 0.8649 0.8534 0.8439 0.8360 0.8261 0.8181 0.8082 0.7996 0.7908 0.7824 0.7737 0.7683 0.7628 0.7577 0.7530 0.7501 0.7472 0.40 mol·kg−1 Glycine 0.9526 0.9354 0.9241 0.9148 0.9065 0.8942 0.8838 0.8756 0.8685 0.8594 0.8517

γ±

Φ

GE/RT

−1

0.9638 0.9608 0.9578 0.9560 0.9539 0.9522 0.9508 0.9491 0.9476 0.9464 0.9454 0.9447 0.9445 0.9447 0.9451 0.9459 0.9470 0.9483 0.9496 0.9517

−0.0037 −0.0053 −0.0077 −0.0095 −0.0124 −0.0157 −0.0189 −0.0248 −0.0317 −0.0409 −0.0527 −0.0702 −0.0882 −0.1140 −0.1394 −0.1714 −0.2140 −0.2549 −0.2965 −0.3640

−160.7 −125.3 −106.6 −82.5 −65.6 −52.2 −37.7 −26.1 −16.9 −6.9 −0.9 6.4 14.1 20.7 29.7 37.4 47.1 54.5 63.2 71.4 79.6 86.0 93.6 101.6

0.20 mol·kg Glycine 0.8834 0.8723 0.8606 0.8533 0.8441 0.8358 0.8292 0.8195 0.8106 0.8013 0.7923 0.7821 0.7743 0.7658 0.7594 0.7531 0.7467 0.7420 0.7383 0.7336 0.30 mol·kg−1 Glycine 0.9496 0.9315 0.9199 0.9030 0.8897 0.8785 0.8656 0.8550 0.8465 0.8370 0.8313 0.8243 0.8171 0.8110 0.8027 0.7958 0.7874 0.7813 0.7742 0.7679 0.7617 0.7571 0.7520 0.7468

0.9836 0.9780 0.9745 0.9696 0.9659 0.9630 0.9598 0.9574 0.9556 0.9538 0.9528 0.9517 0.9507 0.9499 0.9491 0.9487 0.9484 0.9484 0.9486 0.9490 0.9496 0.9502 0.9510 0.9520

−0.0002 −0.0006 −0.0010 −0.0020 −0.0033 −0.0049 −0.0074 −0.0103 −0.0134 −0.0177 −0.0210 −0.0258 −0.0318 −0.0381 −0.0486 −0.0598 −0.0773 −0.0937 −0.1178 −0.1450 −0.1794 −0.2103 −0.2536 −0.3093

−170.5 −137.7 −116.4 −101.1 −90.6 −73.7 −61.3 −51.7 −44.0 −33.0 −24.7

0.40 mol·kg−1 Glycine 0.9525 0.9367 0.9243 0.9143 0.9069 0.8941 0.8841 0.8760 0.8693 0.8596 0.8520

0.9845 0.9796 0.9759 0.9729 0.9708 0.9673 0.9647 0.9626 0.9610 0.9588 0.9573

−0.0002 −0.0005 −0.0009 −0.0014 −0.0019 −0.0031 −0.0044 −0.0057 −0.0072 −0.0098 −0.0124

0.9580 0.9557 0.9537 0.9515 0.9498 0.9485 0.9467 0.9456 0.9442 0.9433 0.9427 0.9425 0.9426 0.9429 0.9440 0.9454 0.9470 0.9490 0.9506

−0.0066 −0.0086 −0.0109 −0.0141 −0.0175 −0.0209 −0.0269 −0.0320 −0.0419 −0.0518 −0.0644 −0.0778 −0.0993 −0.1140 −0.1456 −0.1775 −0.2097 −0.2459 −0.2737

0.0211 0.0273 0.0354 0.0414 0.0503 0.0597 0.0685 0.0836 0.1005 0.1219 0.1478 0.1844 0.2203 0.2694 0.3163 0.3736 0.4476 0.5168 0.5859 0.6959

−59.8 −47.4 −34.8 −27.2 −17.8 −9.5 −2.9 6.8 15.6 25.2 34.3 44.9 53.3 63.3 71.1 79.2 88.0 95.0 101.2 109.7

0.9851 0.9802 0.9762 0.9734 0.9710 0.9672 0.9643 0.9621 0.9594 0.9567 0.9547 0.9531 0.9513 0.9500 0.9487 0.9478 0.9472 0.9468 0.9468 0.9470 0.9474 0.9479 0.9484 0.9489 0.9494

−0.0001 −0.0004 −0.0008 −0.0012 −0.0016 −0.0027 −0.0040 −0.0053 −0.0074 −0.0106 −0.0140 −0.0176 −0.0234 −0.0295 −0.0391 −0.0502 −0.0649 −0.0833 −0.1090 −0.1289 −0.1543 −0.1830 −0.2146 −0.2374 −0.2640

0.0029 0.0059 0.0087 0.0142 0.0200 0.0264 0.0356 0.0453 0.0547 0.0673 0.0762 0.0889 0.1041 0.1195 0.1440 0.1689 0.2064 0.2401 0.2880 0.3403 0.4043 0.4605 0.5373 0.6338

−0.0002 −0.0005 −0.0009 −0.0014 −0.0019 −0.0031 −0.0044 −0.0059 −0.0074 −0.0099 −0.0126

0.0027 0.0052 0.0081 0.0110 0.0136 0.0193 0.0248 0.0302 0.0354 0.0445 0.0529

0.9846 0.9793 0.9758 0.9731 0.9708 0.9673 0.9646 0.9626 0.9609 0.9588 0.9572

C

dx.doi.org/10.1021/je300995q | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. continued m

E

mol·kg−1

mV

γ±

Φ

GE/RT

m

E

mol·kg−1

mV

−1

0.0621 0.0762 0.0901 0.1040 0.1257 0.1602 0.1913 0.2314 0.2729 0.3286 0.3858 0.4460 0.5122

21.5 31.4 39.4 46.3 55.4 67.0 75.7 84.8 92.7 101.7 109.7 116.6 123.4

0.40 mol·kg Glycine 0.8452 0.8362 0.8288 0.8226 0.8145 0.8044 0.7973 0.7900 0.7840 0.7776 0.7725 0.7681 0.7643

Φ

GE/RT

0.9560 0.9539 0.9529 0.9521 0.9516 0.9517 0.9522 0.9532 0.9552 0.9574 0.9599 0.9632 0.9661

−0.0153 −0.0224 −0.0286 −0.0372 −0.0488 −0.0658 −0.0818 −0.1054 −0.1411 −0.1767 −0.2160 −0.2679 −0.3121

−1

0.9560 0.9544 0.9533 0.9525 0.9517 0.9510 0.9509 0.9510 0.9514 0.9522 0.9532 0.9543 0.9555

−0.0154 −0.0203 −0.0254 −0.0307 −0.0394 −0.0540 −0.0679 −0.0864 −0.1063 −0.1339 −0.1631 −0.1945 −0.2298

−17.2 −3.7 5.3 15.1 25.1 36.3 44.7 54.6 66.3 75.5 83.9 92.9 99.7

0.0617 0.0818 0.0983 0.1201 0.1479 0.1867 0.2217 0.2716 0.3441 0.4145 0.4906 0.5896 0.6729

0.40 mol·kg Glycine 0.8452 0.8329 0.8249 0.8164 0.8079 0.7989 0.7927 0.7859 0.7790 0.7743 0.7709 0.7680 0.7666

deviation were 154.0 mV, (25.50 ± 0.02) mV, 1, and 0.13, respectively. As the experimental data had shown a good Nernst response, the electrode pair is satisfactory enough for our study.

and potential are ± 0.0001, ± 0.01, and ± 0.1, respectively. Each molality of the solutions in experiment was prepared by weighing the materials using an analytical balance with a precision of ± 0.1 mg. The electromotive force reached a stable value with a fluctuation of 0.1 mV after 5−10 min at all ionic strengths.

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METHODS The mean activity coefficients of RbF or CsF in glycine + water mixed solvent were calculated by the Pitzer model,18,19 the modified Pitzer equation,20 and the extended Debye−Hückel model21,22 were used to extract the information on the ionic interactions. The Pitzer Model. The Pitzer model is used widely to describe the thermodynamics of electrolyte solution. For 1−1 type electrolyte RbF or CsF, the mean activity coefficients (γ±) is given as follows:18

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RESULTS AND DISCUSSION Calibration of Electrode Pair of Rb/Cs-ISE and F-ISE. The response of the electrodes was evaluated in pure RbF or CsF aqueous solution by using cells A and B. The Nernstian equation can be expressed by: E = E 0 + 2k ln(mγ±)

γ±

(1)

E represents the standard potential of the cells A and B, and γ± is the mean activity coefficient of RbF or CsF. The Nernst slope k = RT/F, where R represents the universal gas constant, T is the thermodynamic temperature, and F indicates the Faraday constant. The values of E for RbF or CsF in the pure water are listed in Table 1. The mean activity coefficients of RbF or CsF in water were calculated by using the Pitzer model at 298.15 K.18 The Pitzer parameters of RbF and CsF in water were taken from ref 19. In Figure 1, when the measured potentials E were plotted against the ln a, a good linear correlation is obtained with the values of E0, k, and a correlation coefficient (R2) at 298.15 K. The values of E0, k, R2, and the standard deviation for the RbF system were 188.8 mV, (25.35 ± 0.03) mV (theoretical Nernst slope: 25.69 mV at 298.15 K), 0.99999, and 0.20, respectively. For the CsF system, the values of E0, k, R2, and the standard 0

ln γ± = f γ + mBγ + m2C γ

(2)

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

(3)

Bγ = 2β (0) + 2β (1){[1 − exp(−αI1/2)(1 + αI1/2 − 1/2α 2I )]/(α 2I )}

(4)

C γ = 1.5C φ

(5)

the osmotic coefficient (Φ) is given by: Φ − 1 = f φ + mBφ + m2C φ

(6)

f φ = −Aφ(I1/2/(1 + bI1/2))

(7)

Bφ = β (0) + β (1)exp( −αI1/2)

(8)

E

the excess Gibbs free energy (G ) can be written as: GE = 2RTI(1 − Φ + ln γ±)

(9) −1

Here m are the molalities of electrolyte (mol·kg ), I represents the ionic strength, and α and b are empirical parameters with values of (2.0 and 1.2) kg1/2·mol−1/2 , respectively. β (0) (kg·mol−1), β(1)(kg·mol−1), and Cφ (kg·mol−1)2 are the Pitzer parameters of solute. Aφ is the Debye−Hückel constant for the osmotic coefficient defined by eq 10: Figure 1. Response of the Rb-ISE (a) or Cs-ISE (b) and F-ISE electrode pair in the mixture at 298.15 K.

Aφ = (1/3)[(2πNAρ)/1000]1/2 [e 2 /(εkT )]3/2 D

(10)

dx.doi.org/10.1021/je300995q | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 2. Values of Average Molecular Mass M, Dielectric Constant ε, Density ρ, Debye−Hückel Constants A and B, and Pitzer Constants Aφ for Different Glycine + H2O Mixtures at 298.15 K mglycine mol·kg

ρ

M

−1

−1

ε

g·mol

0.00 0.10 0.20 0.30 0.40

18.02 18.12 18.22 18.32 18.42

A kg ·mol

0.9970 1.0002 1.0033 1.0064 1.0095

0.5100 0.4899 0.4721 0.4594 0.4457

1/2

g·cm

78.40 80.60 82.70 84.30 86.10

B

−3

−1/2

kg ·mol 1/2

Aφ

−1/2

−1

kg ·mol−1/2

·Å

1/2

0.3285 0.3244 0.3208 0.3182 0.3154

0.3921 0.3760 0.3623 0.3526 0.3421

Table 3. Standard Potential E0 and Parameter Values Obtained from the Pitzer and Modified Pitzer Equations, for Different Glycine + H2O Mixtures at 298.15 K Pitzer

Modified Pitzer

mglycine

β(0)

β(1)

Cφ

E0

mol·kg−1

kg·mol−1

kg·mol−1

kg2·mol−2

mV

0.10 0.20 0.30 0.40

0.0980 0.0821 0.0497 0.0549

0.2875 0.3849 0.4847 0.4826

0.0000 0.0000 0.0000 0.0000

0.10 0.20 0.30 0.40

0.0615 0.0599 0.0475 0.0721

0.4376 0.4658 0.5078 0.4525

0.0000 0.0000 0.0000 0.0000

SD

bMX

BMX

CMX

E0

kg1/2·mol−1/2

kg·mol−1

kg2·mol−2

mV

SD

0.1075 0.1164 0.0931 0.1094

−0.0125 −0.0258 −0.0284 −0.0354

186.3 179.4 175.1 170.9

0.09 0.06 0.10 0.06

0.0959 0.1028 0.0994 0.1091

−0.0243 −0.0274 −0.0321 −0.0240

150.8 144.1 139.7 133.4

0.12 0.09 0.05 0.06

RbF + Glycine + H2O 186.4 0.09 2.0875 179.4 0.06 2.3577 175.2 0.10 2.8171 170.9 0.06 2.7666 CsF + Glycine + H2O 150.9 0.11 2.5297 144.2 0.08 2.6533 139.8 0.05 2.8531 133.4 0.06 2.7618

Table 4. Values of Standard Potential E0 and the Debye−Hückel Parameters for RbF and CsF in the Different Glycine + H2O Mixtures at 298.15 K mglycine

a

c

d

E0

mol·kg−1

Å

kg·mol−1

kg2·mol−2

mV

0.10 0.20 0.30 0.40

4.46 5.32 6.30 6.41

0.0663 0.0578 0.0368 0.0446

RbF + Glycine + H2O 0.0000 0.0000 0.0000 0.0000

186.3 179.4 175.1 170.9

a

c

d

E0

SD

Å

kg·mol−1

kg2·mol−2

mV

SD

0.09 0.06 0.10 0.06

5.58 6.05 6.58 6.27

0.0392 0.0403 0.0348 0.0534

CsF + Glycine + H2O 0.0000 0.0000 0.0000 0.0000

150.8 144.1 139.7 133.3

0.12 0.09 0.06 0.06

where the constants NA, ρ, ε, and k represent the Avogadro constant, density of the solvent, vacuum permittivity, and Boltzmann constant, respectively. The values of Aφ in pure water is 0.3921 kg1/2·mol−1/2 at 298.15 K. The experimental results, including E values, the mean activity coefficients, the osmotic coefficients, and the excess Gibbs free energy for the Pitzer equation are shown in Table 1. Modified Pitzer Model. Pérez-Villaseñor et al. proposed a modified Pitzer model considering the closest approach parameter in the Debye−Hückel term as an adjusting parameter and determined various interaction terms.23 This modification, which contains only three adjusting parameters improves the correlative capacity of the equation, is convenient to use. The modified Pitzer model has been shown in eq 11, where the bMX, BMX, and CMX are three fitting parameters.

log γ± = −Am1/2 /(1 + Bam1/2) + cm + dm2 − log(1 + 0.002mM ) + Ext

where a is the ion size parameter, c and d indicate the ioninteraction parameters, M represents the average molecular mass of mixed solvent, and Ext is the contribution of the extended terms. The Debye−Hückel constants A and B are given by eqs 13 and 14. A = 1.8247·106ρ1/2 /(εT )3/2 kg1/2·mol−1/2

(13)

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

(14)

The values of relative permittivity and density for the mixed solvents are get from the literature14 and are listed in Table 2 together with the values for M, A, B, and Aφ. By combining eqs 1 and 2, 1 and 11, or 1 and 12, the values of E0 can be optimized, as well as the characteristic interaction parameters of each model. In Tables 3 and 4, these values are presented along with the corresponding standard deviation of the fit. Calculation of Thermodynamic Properties. The mean activity coefficients, osmotic coefficients, and excess Gibbs free energy calculated by the Pitzer equations are listed in Table 1. Figure 2 shows the plot of the mean activity coefficients against

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

(12)

(11)

Extended Debye−Hückel Equation. The mean activity coefficients of RbF or CsF were calculated from extended Debye−Hückel equation are often used to test the accuracy of the experimental data. The extended Debye−Hückel equation for mean activity coefficients has the following form in eq 12, E

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Table 5. Average Values of Standard Potential E0* for the Three Equations and Standard Gibbs Energy of Transfer, ΔGt0, for the Systems RbF or CsF + Glycine + H2O Mixtures at 298.15 K mglycine mol·kg 0.00 0.10 0.20 0.30 0.40

Figure 2. Mean activity coefficients for RbF (a) and CsF (b) versus total ionic strength of electrolyte in various glycine/water mixed solvent systems containing (0.00, 0.10, 0.20, 0.30, and 0.40) mol·kg−1 molalities of glycine at 298.15 K.

−1

E0* mV

ΔGt0 −1

kJ·mol

RbF + Glycine + H2O 188.8 0.0000 186.3 −0.2564 179.4 −0.9402 175.1 −1.3684 170.9 −1.7920

E0*

ΔGt0

mV

kJ·mol−1

CsF + Glycine + H2O 154.0 0.0000 150.9 −0.3228 144.1 −0.9897 139.7 −1.4296 133.4 −2.0567

required to charge a hard sphere (ion) of radius r in a dielectric continuum (solvent) of relative permittivity ε.28 For RbF or CsF systems, it should be expressed by the following equation:

the total ionic strength. The mean activity coefficients decrease with the increase of the ionic strength at the fixed glycine molality and increase with the increasing of glycine molalities. This phenomenon may be explained by the increase in density and dielectric constant of the mixed solvent. The electrostatic attraction between the electrolyte ions is enhanced with the increase of the electrolyte molalities. In addition, the interaction of amino acids and ions reduces the interaction between the electrolyte ions. The excess Gibbs free energy (GE) can be calculated from the osmotic and the mean activity coefficients. The GE represents the nonideality in the behavior of the studied systems and informs us about fundamental interactions between solute and solvent.24,25 In Figure 3, the excess Gibbs

ΔGt 0 = 69.25(1/εm − 1/εw )(1/r+ + 1/r −)

(16)

where εm and εw stand for the relative permittivity of the mixed solvent and water, and r+ and r− are the radius of cation and anion. Figure 4 shows the standard Gibbs energy of transfer for

Figure 4. Standard Gibbs energy of transfer for RbF and CsF in different molalities of glycine.

RbF and CsF in different molalities of glycine at 298.15 K. The ΔGt0 are negative, obviously, indicating that the transference of RbF or CsF from water to the glycine + water mixture of solvent is spontaneous; on the other hand, ΔGt0 becomes more negative with an increase of the amino acid molalities. In conclusion, Tables 3 and 4 show that the values of E0 obtained from the Pitzer equation, the modified Pitzer equation, and the extended Debye−Hückel equation are in satisfactory agreement with each other, and the standard deviations of the adjustments are also comparable.

Figure 3. Variation of excess Gibbs free energy with the total ionic strength of RbF(a) and CsF(b) in various glycine/water mixed solvent systems containing (0.00, 0.10, 0.20, 0.30, and 0.40) mol·kg−1 molalities of glycine at 298.15 K.

free energy increases as the glycine molalities increases. There are the polar groups in glycine + water mixed solvents that can interact with the anion and cation. The larger molalities of the glycine in mixed solvents, the higher the excess Gibbs free energy. The standard Gibbs energy of transfer is used to measure the change in the total energy of the solute when it is transferred from one solvent to another. It can be defined as the difference between the standard Gibbs free energy per electrolyte mole in a pure solvent, usually water, and another pure solvent or mixed solvents.6 The expression is as follows:26,27 ΔGt 0 = F(Em 0 − Ew 0) + 2RT ln(d w /dm)

Ew0

■

CONCLUSION The results concerning the modeling of the ternary RbF or CsF + glycine + water electrolyte system with the Pitzer, the modified Pitzer, and the extended Debye−Hückel equations are reported. Both models are in good agreement with each other and give satisfactory results. The mean activity coefficients, osmotic coefficients, excess Gibbs free energy, and the Gibbs energies of transfer were obtained along with the corresponding parameters for the models. The γ±, Φ, and GE values increase as the total ionic strength decreases and the molalities of glycine increase. The ΔGt0 are all negative obviously, which indicates that the transference of RbF or CsF from water to the glycine + water mixed solvent is spontaneous. The information collected above is expected to be used by biophysical chemists who are examining the mixed ion effects on the behavior of the biomolecules.

(15)

Em0

where and represent the standard of potential of RbF or CsF in pure water and in mixed solvents, and dw and dm indicate the relative density of water and mixture of solvents, respectively. The values of ΔGt0 calculated from eq 15 are given in Table 5. The Born model also can calculate the energy F

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(16) Jiang, Y. C.; Yang, Q.; Hu, M. C. Thermodynamic Properties of L-Alanine in (RbCl or CsCl) + Water from 298.15 to 313.15 K. J. Chem. Eng. Data 2005, 50, 1608−1612. (17) Wang, L.; Li, S. N.; Zhai, Q. G.; Jiang, Y. C.; Hu, M. C. Activity Coefficients of RbF or CsF in the Ethene Glycol + Water System by Potentiometric Measurements at 298.15 K. J. Chem. Eng. Data 2011, 56, 4416−4421. (18) Pitzer, K. S. Thermodynamics of Electrolytes. I. Theoretical Basis and General Equations. J. Phys. Chem. 1973, 77, 268−277. (19) Pitzer, K. S.; Mayorga, G. Thermodynamics of Electrolytes. II. Activity and Osmotic Coefficients for Strong Electrolytes with One or Both Ions Univalent. J. Phys. Chem. 1973, 77, 2300−2308. (20) Pérez-Villaseñor, F.; Iglesias-Silva, G. A. Osmotic and Activity Coefficients Using a Modified Pitzer Equation for Strong Electrolytes 1:1 and 1:2 at 298.15 K. Ind. Eng. Chem. Res. 2002, 41, 1031−1037. (21) Robinson, R. A.; Stokes, R. H. Electrolyte Solutions; Butterworth: London, 1959. (22) Harned, H. S.; Owen, B. B. The Physical Chemistry of Electrolytic Solutions, Reinhold: New York, 1958. (23) Pérez-Villaseñor, F.; Carro-Sánchez, S. Comparison among Pitzer-type Models for the Osmotic and Activity Coefficients of Strong Electrolyte Solutions at 298.15 K. Ind. Eng. Chem. Res. 2011, 50, 10894−10901. (24) Calvar, N.; Gómez, E.; Domínguez, Á .; Macedo, E. A. Study of the influence of the structure of the alcohol on vapor pressures and osmotic coefficients of binary mixtures alcohol + 1-hexyl-3methylimidazolium bis(trifluoromethylsulfonyl)imide at T = 323.15 K. Fluid Phase Equilib. 2012, 313, 38−45. (25) Domańska, U.; Królikowski, M.; Acree, W. E., Jr. Thermodynamics and activity coefficients at infinite dilution measurements for organic solutes and water in the ionic liquid 1-butyl-1-methylpyrrolidinium tetracyanoborate. J. Chem. Thermodyn. 2011, 43, 1810−1817. (26) Feakins, D.; Voice, P. J. Studies in Ion Solvation in Nonaqueous Solvents and Their Aqueous Mixtures: Part 14. Free Energies of Transfer of the Alkali-metal Chlorides from Water to 10−99% (w/ w) Methanol + Water Mixtures at 25 °C. J. Chem. Soc., Faraday Trans. 1972, 168, 1390−1405. (27) Kalidas, C.; Hefter, G.; Marcus, Y. Gibbs Energies of Transfer of Cations from Water to Mixed Aqueous Organic Solvents. Chem. Rev. 2000, 100 (3), 820−852. (28) Senanayake1, G.; Hefter, G. Gibbs Energies of Transfer of Fluoride Salts from Water to Aqueous Alcohol Mixtures. Monatsh. Chem. 2003, 134, 669−677.

AUTHOR INFORMATION

Corresponding Author

*Tel.: +86-29-81530767. Fax: +86-29-81530727. E-mail: [email protected]; [email protected]. Funding

Project supported by the National Natural Science Foundation of China (No. 21171111) and the Fundamental Research Funds for the Central Universities (Program No. GK201001006). Notes

The authors declare no competing financial interest.

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