Conductivity of Sodium Chloride in Water + 1,4-Dioxane Mixtures at ...

Journal of Solution Chemistry. Vol. 28. No. 9, 1999

Conductivity of Sodium Chloride in Water + 1,4Dioxane Mixtures at Temperatures from 5 to 35°C I. Dilute Solutions M. Bester-Rogac,1,2 R. Neueder,1 and J. Barthel,1,* Received December 21, 1998; revised June 8, 1999 The molar and single-ion conductivities of dilute solutions of sodium chloride (C < 0.01 mol-dm-3) in binary mixtures of 1,4-dioxane with water were measured covering a broad solvent composition range at temperatures from 5 to 35°C. Accurate viscosity and permittivity data were determined for the organic solvent system. Evaluation of the limiting molar conductivity AI, ionic conductivities XI, and AI, and the association constant AA is based on the chemical model of electrolyte solutions, including short-range forces. KEY WORDS: Electrolyte conductivity; ionic conductivities; sodium chloride; water-dioxane mixtures.

1. INTRODUCTION Water-1,4-dioxane mixtures are a favorite solvent system to study association and mobilities of ions, because the dielectric constant can be varied over a large range. Changes upon addition of dioxane to aqueous solutions are due to increasing ion-ion interaction at decreasing dielectric constant and to changes in solvent-ion and solvent-solvent interaction. Several systematic investigations on the conductivity of alkali metal halides in water-1,4-dioxane mixtures have been carried out in the last 30 years,(l,11) but only very few of them at temperatures different from 25°C.

Institut fur Physikalische and TheoretischeChemie, Universitat Regensburg D-93040, Regensburg, Germany. 2 Present address: Department of Chemistry and Chemical Technology, University of Ljubljana, ASkerCeva 5, SI-1000 Ljubljana, Slovenia. 1

1071 0095-9782/0900-1071$16.00/0 C 1999 Plenum Publishing Corporation

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BeSter-Rogac, Neueder, and Barthel

Limiting ion conductivities of KC1 solutions in water-dioxane mixtures at 25°C are known (1) as well as the temperature dependence of the limiting transference number of Na+ and Cl- in water.(2) In this paper, a systematic conductivity study of sodium chloride-water1,4-dioxane is presented covering the temperature range from 5 to 35°C, solvent composition from xD = 0 to XD = 0.65 (xD: mole fraction of dioxane), and electrolyte concentration from 0.1 X 10 -3 to 8.0 X 10 -3 mol-dm -3 . Temperature-dependent limiting ion conductivities of Na+ and Cl- are estimated by appropriate combination of our data and the above quoted literature data. A following paper will report on the conductivity at high concentrations up to the limit of salt solution. 2. EXPERIMENTAL 2.1. Materials

Sodium chloride (suprapur, Merck) was dried for 48 h under reduced pressure in the presence of P2O5 without preceding purification at 200°C and stored under dry nitrogen. 1,4-Dioxane (p.a.,Merck) with an initial water content of about 120 ppm, found by Karl Fischer titration, and 0.015% impurities, detected by gas chromatography, was used without further purification. Millipore water with a specific conductivity of less than 2X10 -7 n -1 m-1 was used after degassing by boiling under reduced pressure. 2.2. Thermostat

The high precision thermostat used in the experiments of our laboratory has been described elsewhere(13) It can be set to each temperature of a temperature program with a reproducibility of less than 0.001 K. 2.3. Permittivity Measurement

Temperature-dependent permittivity measurements on the mixed solvent system were executed with a low-frequency (1-10 kHz) capacitance bridge (General Radio, type 1616) equipped with a conductance-balancing network and a three-terminal dielectric cell designed for high-precision measurements(13) immersed in the precision thermostat. The cell constant (C0 = 11.1386 pF, 25°C) was determined from 5 to 35°C by measuring the capacitance of the cell filled with pure argon, for which temperature- and pressure-dependent data are available in the literature.(14) The temperature coefficient of the cell constant was 1.14X10 -4 pF K-1. The permittivity of the sample was calculated from the ratio of the

Conductivity of Sodium Chloride in Water-Dioxane Mixtures

1073

capacitance of the dielectric cell filled with the sample to that of the cell filled with dry argon, The measured data are given in Table I. 2.4. Viscosity Measurement The temperature-dependent viscosities in Table I were determined by the use of an Ubbelohde capillary viscometer placed in a Dewar flask connected to the precision thermostat via a circulating pump. (13) The sample viscosities n were evaluated from the flow time of the liquids through the capillary, which was detected by a control unit (Schott AVS/G) using photodiodes and optical fiber bundles for the transmission of the signal. Each measurement was Table I. Density, Permittivity, and Viscosity of 1,4-Dioxane- Water Mixtures"

xD

278.15

283.15

288.15

0.0000 0.0574 0.1104 0.2000 0.2979 0.4002 0.5009 0.6482

0.99997 1.02497 1.03898 1.05036 1.05407 1.05449 1.05406 1.05289

0.99970 1.02305 1.03611 1.04661 1.04984 1.04993 1.04922 1 .04774

0.99910 1.02097 1.03315 1.04282 1.04555 1.04532 1.04434 1.04256

0.0000 0.0574 0.1104 0.2000 0.2979 0.4002 0.5009 0.6482

85.897 65.797 51.846 35.395 23.801 16.038 11.045 6.605

83.945 64.083 50.519 34.370 23.098 15.579 10.746 6.466

0.0000 0.0574 0.1104 0.2000 0.2979 0.4002 0.5009 0.6482

1.5192 2.4308 3.0727 3.5632 3.4398 3.0605 2.6667 2.2183

1.3069 2.0618 2.6029 3.0271 2.9458 2.6475 2.3332 1.9651

T 293.15

298.15

303.15

308.15

d

0.99704 0.99565 0.99404 0.99821 1.01121 1.01876 1.01639 1.01387 1.03010 1.02696 1.02372 1.02039 1.03895 1.03503 1.03104 1.02698 1.04121 1.03683 1.03239 1.02789 1.02639 1.04065 1.03593 1.03119 1.03942 1.03446 1.02947 1.02445 1.03734 1.03209 1.02681 1.02150

e

"Units: T, K; d, kg-dm-3; n, Pa-s.

82.039 62.426 49.031 33.322 22.420 15.133 10.470 6.331 n X103 1.1382 1.7744 2.2280 2.5966 2.5465 2.3106 2.0568 1.7527

80.176 60.853 47.688 32.421 21.768 14.727 10.201 6.200

78.358 59.302 46.387 31.425 21.135 14.304 9.941 6.072

76.581 57.754 45.154 30.596 20.527 13.915 9.702 5.949

74.846 56.280 43.937 29.730 19.940 13.531 9.450 5.829

1.0020 1.5388 1.9303 2.2438 2.2197 2.0304 1.8264 1.5738

0.8903 1.3495 1.6848 1.9652 1.9507 1.7993 1.6317 1.4204

0.7975 1.1930 1.4869 1.7310 1.7267 1.6034 1.4663 1.2882

0.7195 1.0749 1.3243 1.5332 1.5377 1.4373 1.3241 1.1737

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BeSter-Rogai, Neueder, and Barthel

automatically repeated at least ten times and yielded a reproducibility of the flow time of less than 0.01%. 2.5. Conductivity Measurements

The conductivity measuring ensemble of our laboratory has been described elsewhere(13,15) The three-electrode measuring cell was calibrated with dilute potassium chloride solutions.(16) At the beginning of every measuring cycle, the cell was filled with a weighed amount of solvent. After measurement of the solvent conductivity at all temperatures of the program weighed amounts of a stock solution were added using a gas-tight syringe and the temperature program was repeated. From the weights and the corresponding solution densities d the molar concentrations c were determined. A linear change of d with increasing salt content was assumed, d = ds + Dm, where m is the molonity of the electrolyte (moles of electrolyte per kilogram of solution). The densities of pure solvent ds at temperature T were taken from the literature(17) and are collected in Table I. The temperature-independent density gradient D of every solution was determined by the method of Kratky et al.(18) with the Paar equipment DMA 60, DMA 601 HT. The measured conductivity data A are given in Table II as a function of the temperatureindependent molonities. They can be converted to the temperature-dependent molarities by the use of the relationship The mean errors on conductivities and concentrations were estimated to be about 0.03%. 3. DATA ANALYSIS

The analysis of conductivity data in the framework of a low concentration chemical model(19) proceeds by means of the following set of equations

A and A°° are molar conductivities at molarity c and infinite dilution, respectively, (1 — a) is the fraction of oppositely charged ions acting as ion pairs, and KA is the equilibrium constant in terms of ion and ion-pair concentrations. y'± is the mean activity coefficient of the free ions. The Debye parameter K is given by


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Table II. Molar Conductivities of NaCl in 1,4-Dioxane- Water Mixtures" mX103

278.15

283.15

0.17780 0.33593 0.56955 0.86453 1.20662 1.50431 1.95181 2.53912

76.999 76.806 76.534 76.265 75.938 75.740 75.470 75.147

88.287 88.035 87.746 87.409 87.030 86.791 86.466 86.093

0.34494 0.58986 0.79859 1.02130 1.31483 1.75751 2.25825 2.91802 3.84269 5.18981

49.474 49.111 48.910 48.769 48.668 48.358 48.085 47.811 47.437 47.047

57.548 57.135 56.879 56.735 56.604 56.247 55.915 55.578 55.152 54.692

0.53360 0.79006 1.06466 1.31736 1.65694 2.04842 2.55784 3.18626 4.18682

36.719 36.525 36.336 36.180 35.978 35.771 35.552 35.331 35.009

42.901 42.680 42.453 42.269 42.037 41.768 41.512 41.267 40.867

0.29801 0.58664 0.89097 1.17417 1.72908 2.29308 3.03461 3.83012 5.14526

28.948 28.550 28.229 27.980 27.512 27.126 26.691 26.311 25.770

33.795 33.318 32.924 32.634 32.074 31.613 31.089 30.645 30.016

0.25232 0.43245

24.659 24.073

28.678 27.855

288.15

T 293.15

xD:0.0, D = 0.041 100.139 112.511 99.819 112.079 99.460 111.721 99.080 111.251 98.659 110.829 98.397 1 110.465 98.013 1 10.036 97.590 109.591 xD:0.0574,D = 0.041 66.192 75.354 65.718 74.799 65.407 74.445 65.262 74.287 65.085 74.074 64.686 73.593 64.318 73.168 63.912 72.688 63.390 72.137 62.861 71.509 XD:0.1104, D = 0.041 49.577 56.708 49.308 56.393 49.039 56.081 48.834 55.850 48.549 55.508 48.238 55.156 47.946 54.778 47.658 54.469 47.186 53.926 XD:0.2000,D = 0.041 39.047 44.6% 38.472 44.005 38.012 43.462 37.669 43.039 36.991 42.258 36.461 41.650 35.850 40.941 35.324 40.329 34.580 39.458 xD:0.2979, D = 0.038 32.755 37.234 31.928 36.271

298.15

303.15

308.15

125.348 124.888 124.428 123.928 123.456 123.093 122.591 122.081

138.609 138.096 137.587 137.031 136.454 136.077 135.539 134.943

152.287 151.727 151.166 150.563 149.913 149.490 148.894 148.256

85.057 84.418 84.046 83.802 83.568 83.046 82.546 82.020 81.358 80.642

95.187 94.474 94.065 93.767 93.515 92.907 92.341 91.748 91.014 90.195

105.795 104.988 104.509 104.186 103.862 103.201 102.575 101.915 101.123 100.161

64.325 63.950 63.603 63.315 62.936 62.551 62.128 61.735 61.103

72.327 71.914 71.517 71.186 70.761 70.311 69.829 69.358 68.651

80.757 80.283 79.807 79.449 78.961 78.465 77.923 77.375 76.570

50.733 49.912 49.262 48.794 47.907 47.184 46.356 45.653 44.646

57.110 56.145 55.418 54.867 53.842 53.015 52.074 51.265 50.109

63.842 62.718 61.896 61.266 60.094 59.155 58.089 57.155 55.838

42.023 40.890

47.049 45.749

52.335 50.841

BeSter-Rogai, Neueder, and Barthel

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Table II. Continued.

T 293.15

mx103

278.15

283.15

288.15

0.58613 0.82373 1.05722 1.42358 1.89514 2.50849 3.40923 5.01391 7.63307

23.639 23.145 22.696 22.122 21.505 20.870 20.141 19.166 18.082

27.332 26.748 26.217 25.541 24.811 24.064 23.212 22.054 20.789

0.25978 0.53566 0.81287 1.10351 1.48993 1.99488 2.64761 3.42813 4.56775

19.817 18.144 17.018 16.152 15.288 14.438 13.628 12.908 12.130

22.667 20.692 19.371 18.362 17.360 16.375 15.437 14.605 13.705

0.09524 0.18411 0.28109 0.40794 0.57081 0.75025 0.92367 1.18813 1.85416 3.16064

15.623 13.522 12.191 11.052 10.078 9.323 8.775 8.141 7.119 6.067

17.589 15.154 13.624 12.323 11.212 10.357 9.737 9.023 7.874 6.697

0.05154 0.10350 0.15792 0.22477 0.29069 0.37231 0.48674 0.64434 0.89642 1.22748

3.541 2.646 2.210 1.900 1.706 1.536 1.372 1.218 1.065 0.938

3.781 2.761 2.347 2.017 1.803 1.626 1.451 1.290 1.124 0.989

31.314 35.561 30.628 34.744 29.998 34.015 29.208 33.096 28.352 32.102 31.089 27.477 29.924 26.470 28.387 25.135 26.694 23.665 XD:0.4002,D = 0.041 25.696 28.888 23.385 26.203 21.839 24.433 20.686 23.100 21.784 19.530 18.400 20.500 17.327 19.280 16.384 18.208 15.371 17.073 XD:0.5009,D = 0.038 19.621 21.712 16.826 18.529 15.084 16.563 14.912 13.612 12.359 13.514 11.400 12.447 10.706 11.677 10.800 9.909 8.631 9.389 7.326 7.950 XD:0.6482, D = 0.037 3.996 4.195 2.968 3.105 2.584 2.472 2.123 2.216 .898 1.981 1.781 .708 .523 1.587 1.408 .352 1.225 .178 1.077 .036

298.15

303.15

308.15

40.072 39.110 38.283 37.211 36.072 34.907 33.574 31.812 29.873

44.809 43.710 42.740 41.525 40.222 38.887 37.364 35.370 33.183

49.766 48.513 47.407 46.021 44.549 43.036 41.294 39.059 36.599

32.239 29.145 27.144 25.611 24.117 22.666 21.296 20.092 18.824

35.712 32.181 29.911 28.181 26.504 24.876 23.344 22.003 20.583

39.312 35.305 32.749 30.811 28.937 27.124 25.423 23.940 22.372

23.841 20.250 18.049 16.213 14.663 13.486 12.638 11.673 10.126 8.563

25.986 21.966 19.522 17.497 15.795 14.504 13.580 12.525 10.846 9.154

28.137 23.669 20.978 18.758 16.902 15.500 14.494 13.353 11.544 9.723

4.367 3.228 2.683 2.299 2.055 1.845 1.643 1.457 1.267 1.112

4.520 3.335 2.768 2.371 2.117 1.900 1.691 1.498 1.302 1.142

4,651 3.424 2.840 2.430 2.169 1.946 1.731 1.533 1.331 1.166

1 ; A, aUnits: T, K; K; m, m, mol mol-- kgkg-1; A,SS-cm2-mol-1 cm2-mol-1 DD, kg2-dm-3-mol-1. D,mol kg2-1-dnm . -3-mol-1mol-1.


1077

where e is the proton charge, e is the relative permittivity of the solvent, and e0 is the permittivity of vacuum. The other coefficients have their usual meaning. The coefficients of Eq. (2) are given in Refs. 19 and 20. The limiting slope S and the parameter E are completely calculable when the solvent data are available. The coefficients J1 and J2 are functions of the distance parameter R, representing the distance to which oppositely charged ions can approach as freely moving particles in the solution and, therefore, is, on the other hand, the upper limit of the ion association to ion pairs represented by the distance parameter of the mean activity coefficient y'± (Eq. 3). We used three-parameter fits (19-2l) for the data analysis, which set the coefficients S, E, J1 of Eq.(2) to their calculated values(19,20) to obtain the limiting values of molar conductivity AI, the association constant KA and the coefficient J2 by nonlinear least-squares iterations. The input data for the calculation of the coefficients are the solvent properties given in Table I and the distance parameter R. From extended investigations on electrolyte solutions in amphiprotic hydroxylic solvents, such as water and alcohols, it is known that solvation effects yield upper limits of association, which include the formation of solvent-separated ion pairs

where a = a+ + a- is the sum of the crystallographic radii, here a = 0.279 nm for NaCl(19) and s is the length of an OH group, s = 0.28 nm. In this investigation we fixed the distance parameter R at R = a + 2s. As an example, Fig. 1 shows the three-parameter fits at various temperatures at mole fraction XD = 0.4002 with R = 0.839 nm.

4. RESULTS AND DISCUSSION The limiting conductivities AI and the association constants KA are given in Table III. Coefficients J2 are not quoted. They confirm the R parameters, but give no independent information. A temptative fit based on R = a + s, which is reasonable for NaCl in pure water where association is negligible, shows limiting molar conductivities A°° equal to those of (a + 2s) fits in the water-rich solutions (XD < 0.1). Only slight differences occur at increasing dioxane concentrations, where a perturbation by triple-ion formation must be expected at very high dioxane content. The association constants show that NaCl is almost completely dissociated

1078

Be$ter-Rogac, Neueder, and Barthel

Fig. 1. Molar conductivities of NaCl in dioxane-water mixtures (XD = 0.4) at 308.15 (1), 303.15 (2), 298.15 (3), 293.15 (4), 288.15 (5), 283.15 (6), and 278.15 K (7).

in the water-rich mixtures. At increasing dioxane content, chemical evidence suggests the discussion based on the results obtained with R = a + 2s. 4.1. Limiting Electrolyte Conductivities The limiting molar conductivity decreases with increasing mole fraction of 1,4-dioxane at each temperature (Fig. 2). The comparison with data from the literature is only possible at 25°C,(3) where the limiting conductivites were redetermined from the original measuring data with our solvent data and coefficients and, therefore, differ slightly from those given by the authors. The temperature dependence of the limiting conductivity yields Eyring's enthalpy of activation of the charge transport(22)

where ds is the density of the solvent (Fig. 3). The enthalpy AH depends only on the solvent properties. It shows a maximum in the range 0.1 < XD < 0.2. The same pattern as for conductivities is observed for the solvent viscositites. The slope d(In T ) / d ( 1 / T ) of the electrolyte-free solvent mixture in Fig. 3 shows this feature.

1079

Conductivity of Sodium Chloride in Water-Dioxane Mixtures Table III.

Limiting Equivalent Conductivities and Association Constants of NaCI Solutions in 1,4-dioxane- water Mixturesa

XD T

0.0

0.0574

0.1104

0.2000

278.15 283.15 288.15 293.15 298.15 303.15 308.15

77.71 89.12 101.09 113.57 126.54 139.95 153.78

50.16 58.38 67.15 76.48 86.34 96.67 107.43

37.74 44.11 50.99 58.37 66.21 74.48 83.18

29.94 34.98 40.45 46.32 52.61 59.25 66.28

278.15 283.15 288.15 293.15 298.15 303.15 308.15

0.59 0.97 1.82 2.50 2.38 2.64 2.60

4.47 4.77 4.39 5.01 5.07 5.38 5.49

7.40 7.45 7.75 8.45 7.87 7.82 8.14

18.04 19.68 20.84 22.61 23.71 25.04 26.14

0.2979

0.4002

0.5009

0.6482

26.29 30.57 35.04 39.90 45.11 50.61 56.41

23.46 26.99 30.81 34.87 39.20 43.74 48.52

21.46 24.57 27.89 31.44 35.21 39.17 43.35

15.81 18.25 20.31 22.96 24.88 27.27 29.67

A"

KA 95.7 105.2 106.5 112.7 119.4 126.5 134.0

536.9 575.8 623.7 673.0 725.5 780.3 841.8

5026.4 5541.6 6117.7 6755.6 7472.7 8266.3 9153.0

344700 412900 465100 549970 602600 685700 776600

"Units: T, K; AI, S-cm2-mor-1 ;K A , dm 3 -mol -1 .

Fig. 2. Limiting molar conductivities of NaCI in dioxane-water mixtures at 308.15 (1), 298.15 (2), 288.15 (3), and 278.15 K (4); a, recalculated data from Ref. 3.


1080

Fig. 3. Curve (1) activation energy AH of the ionic movement; and curve (2) temperature dependence of the solvent viscosity d In r\d(1/T).

Only weak (in water rich solutions) or no (in dioxane rich solutions) temperature dependence of the Walden product A°°n is observed (see Table IV). A weak maximum of the Walden product exists in the range 0 < xD < 0.1 at every temperature; at dioxane composition greater than 0.1, it decreases strongly, suggesting increasing hydrodynamic radii of the ions. 4.2. Limiting Ion Conductivities Temperature-dependent limiting ion conductivities were determined by the following procedure. In a first step, the limiting ion conductivity of the Table IV. Walden Product of NaCI Solutions in 1,4-Dioxane-Water Mixtures" xc

T 278.15 283.15 288.15 293.15 298.15 303.15 308.15 a

0.0 118.06 116.47 115.06 113.80 112.66 111.61 110.64

0.0574

0.1104

121.93 120.37 119.15 1 17.69 1 16.52 115.33 115.49

A I T)X10 3 106.72 115.96 105.92 114.81 113.62 105.06 103.98 112.67 103.41 111.55 1 10.74 102.60 110.17 101.65

Units: T, K; A°°T|, S-cm2-mol-1 Pa-s.

0.2000

0.2979

0.4002

0.5009

0.6482

90.60 90.20 89.38 88.72 88.15 87.56 86.91

72.17 71.83 71.58 71.21 70.96 70.57 70.18

57.76 57.86 57.94 58.01 58.04 58.04 58.00

35.74 36.57 36.26 36.78 35.96 35.75 35.42


1081

chloride ion at 25°C was obtained up to a mole fraction of dioxane XD = 0.43 from the transference numbers, tI (Cl - ) given in Ref. 23 and the limiting equivalent conductivities AI (KC1)(2) of potassium chloride in dioxane-water mixtures. At low dioxane concentrations, additional limiting ion conductivities of the chloride ion (l) support these data. The upper curve of Fig. 4 shows the literature data for XI (Cl - ) together with a fitting function, which allows interpolations. From our limiting equivalent conductivities AI (NaCI) of Table III and the interpolated XI (Cl - )-values at 25°C of Fig. 4, which also are quoted in Table V, the cationic limiting conductivities XI (Na+) were calculated [XI (Na+) = AI (NaCI) - XI (Cl-)]. They are given in Table V and in the lower curve of Fig. 4 and are the base for the calculation of the transference numbers of cation and anion at 25°C in the solvent mixtures up to a dioxane mole fraction of XD = 0.5. The limiting ion conductivities at different temperatures were evaluated in a second step. Because of the very weak temperature dependence of transference numbers, which occurs at the same order of magnitude for various solvents,(24,32) the temperature dependence of the Na+ ion in pure water may also be used for the solvent mixtures, [ d t I ( x D = 0 ) / d T ] =3.6X 10 -4 K -1 , (12) to yield temperature-dependent transference numbers of the sodium ion in water-dioxane mixtures up to XD = 0.5 according to

Fig. 4. Limiting ion conductivities at 298.15 K. •, X I (Cl - ) from Ref.I; a, XI (Cl - ) calculated from Ref. 4 and Ref. 23; o, XI (Na+) calculated from AI (NaCI) and XI (Cl - ).

BeJter-Rogac, Neueder, and Barthel

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Table V. Single-Ion Conductivities in 1,4-Dioxane- Water Mixtures"

XD

T

0.0

0.0574

0.1104

0.2000

0.2979

0.4002

0.5009

10.99 12.83 14.77 16.90 19.18 21.61 24.19

9.95 11.49 13.17 14.97 16.90 18.94 21.10

9.22 10.60 12.09 13.68 15.39 17.19 19.10

15.30 17.74 20.27 23.00 25.93 29.00 32.22

13.51 15.50 17.64 19.90 22.30 24.80 27.42

12.24 13.97 15.80 17.76 19.82 21.98 24.24

X" (Na+) 278.15 283.15 288.15 293.15 298.15 303.15 308.15

30.29 34.90 39.77 44.88 50.24 55.81 61.60

20.27 23.70 27.38 31.32 35.51 39.94 44.58

278.15 283.15 288.15 293.15 298.15 303.15 308.15

47.42 54.22 61.32 68.69 76.30 84.14 92.18

29.89 34.68 39.77 45.16 50.83 56.73 62.85

a

15.37 12.35 14.49 18.04 20.95 16.83 24.08 19.35 22.07 27.44 31.00 24.97 28.05 34.77 V (CI-) 17.59 22.37 26.07 20.49 30.04 23.62 26.97 34.29 30.54 38.77 43.48 34.28 48.41 38.23

Units: T, K; XI, S-cm2-mol-1.

These transference numbers are combined with the A°°-values of Table III to obtain the limiting single-ion conductivities of Na+ and Cl- at all temperatures of the program given in Table V. 4.3. Concentration Dependence of Single-Ion Conductivities The knowledge of the distance parameters R and the association constants KA, from the analysis of the electrolyte conductivity data by using Eq.(2), and the additional information on the limiting ionic conductivities obtained from the combination of limiting electrolyte conductivities and transference numbers permits us the separate representation of the concentration dependence of the cation and anion conductivities at all temperatures and solvent compositions of the program with the help of the following equations(33)


1083

Reference 33 contains the expressions of all coefficients that occur in Eq. (8). As an example, Fig. 5 shows the ion conductivities of Na + (1) and Cl - (2) at XD = 0.4 and a temperature of 298.15 K. The circles are the experimental conductivity data of the electrolyte and curve (3) is the sum of curve (1) and (2). 4.3. Association Constants The association constants in Table III are very small in water-rich solutions and increase significantly at increasing dioxane content. In the temperature range investigated, 278.15 < T/K < 308.15, the temperature coefficient dKddT of the association constant is positive, as usually found for alkali salt solutions. The Gibbs' energy of ion-pair formation is given by the relationship

Figure 6 shows that AG0 is linearly dependent on the temperature at all

Fig. 5. Concentration dependence of the ionic conductivity of NaCl in dioxane-water mixtures ( x D = 0.4). (I) Na+; (2) Cl - ; (3) summation curve and experimental data for A°°.

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Fig. 6. Gibbs energy of association of NaCI in dioxane-water mixtures at compositions ;xD:0.0 (1), 0.0574 (2), 0.1104 (3), 0.2000 (4), 0.2979 (5), 0.4002 (6), 0.5009 (7), 0.6482 (8).

Fig. 7. Thermodynamic functions of association of NaCI in dioxane-water mixtures. (1) Gibbs energy; (2) enthalpy; (3) entropy.


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solvent compositions. The entropy and enthalpy of ion-pair formation are known from the temperature dependence of AG0

Data analysis yields temperature-independent entropies AS0 and only slightly temperature-dependent values of AH° at all solvent compositions. Figure 7 shows the dependence on the solvent composition of the enthalpies AH° and entropies AS0 of ion-pair formation together with the AG° values at 25°C. ACKNOWLEDGMENT M. Be§ter-Rogac is grateful to the Alexander von Humboldt Foundation for a grant enabling her to perform this investigation at the Institut of Physical and Theoretical Chemistry at the University of Regensburg. REFERENCES 1. R. L. Kay and T. L. Broadwater, Electrochim. Acta 16, 667 (1971). 2. J. E. Lind and R. M. Fuoss, J. Phys. Chem. 65, 999, 1414 (1961); J. Phys. Chem. 66, 1727 (1962). 3. R. W. Kunze and R. M. Fuoss, J Phys. Chem. 67, 911, 914 (1963). 4. T. M. Fabry and R. M. Fuoss, J. Phys. Chem. 68, 971 (1963). 5. J. C. Justice and R. M. Fuoss, J. Phys. Chem. 67, 1707 (1963). 6. C. F. Mattina and R. M. Fuoss, J. Phys. Chem. 79, 1604 (1975). 7. A. D'Aprano, F. Accasina, and R. M. Fuoss, J. Solution Chem. 19, 65 (1990). 8. M. C. Justice, J. C. Justice, and R. L. Kay J. Solution Chem. 19, 1211 (1990). 9. B. Das, Thermochim. Acta 44, 379 (1981). 10. L. A. Dunn and W. L. Marshall, J. Phys. Chem. 73, 2619 (1969). 11. E. Rousset, J. Barthel, and J. C. Justice, J. Solution Chem. 22, 571 (1993). 12. R. A. Robinson and R. H. Stokes, Electrolyte solutions, 2nd edn. (Butterworths, London, 1970). 13. J. Barthel, R. Wachter, and H.-J. Gores, in "Modern Aspects of Electrochemistry" Vol. 13, B. E. Conway and J. O'M. Bockris, eds. (Plenum Press, New York, 1979). 14. D. E. Gray, American Institut of Physics and Handbook, 3rd edn. (McGraw-Hill, New York, 1972). 15. R. Wachter and J. Barthel, Ber. Bunsenges. Phys. Chem. 83 634 (1979). 16. J. Barthel, F. Feuerlein, R. Neueder, and R. Wachter, J. Solution Chem. 9, 209 (1980). 17. M. Sakurai, J. Chem. Eng. Data 37, 492 (1992). 18. O. Kratky, H. Leopold, and H. Stabinger, Z Angew. Phys. 27, 273 (1969). 19. J. Barthel, H. Krienke, and W. Kunz, Physical Chemistry of Electrolyte Solutions-Modern Aspects (Steinkoppf/Darmstadt, and Springer, New York, 1998). 20. J. Barthel and R. Neueder, in Electrolyte Data Collection, Part 1, R. Eckermann and G. Kreysa, eds., (DECHEMA Chem. Data Ser, Vol VII, Frankfurt, 1992).

21. J. Barthel, J. C. Justice, and R. Wachter, Z. Phys. Chem. NF 84, 100 (1973). 22. S. B. Brummer and G. 1. Hills, J. Chem. Soc. Faraday Trans. 57, 1816 (1961).

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23. A. Fratiello and R. L. Kay, J. Solution Chemistry 3, 857 (1974). 24. J. Barthel, U. StrOder, L. Iberl, and H. Hammer, Ber. Bunsenges. Phys. Chem. 86,636 (1982). 25. T. Erdey-Gruz, E. Kugler, I. Nagy-Czako, and K. Balthazar-Vass, Rev. Roum. Chim. 17, 137 (1972). 26. H. S. Harned and E. C. Dreby, J. Amer. Chem. Soc. 61, 3113 (1939). 27. J. E. Smith and E. B. Dismukes, J. Phys. Chem. 68, 1603 (1964). 28. R. Gopal and O. N. Bhatnagar, J. Phys. Chem. 71, 3007 (1967). 29. M. Ueno, S. I and K. Shimizu, Bull. Chem. Soc. Jpn. 58, 1225 (1985). 30. J. S. Banait and G. S. Bhatti, J. Chem. Eng. Data 36, 121 (1991). 31. R. Gopal and J. S. Jha, Indian J. Chem. Sect. A 15, 80 (1977). 32. V. Vitagliano, Gau.. Chim. Ital. 90, 1847 (1960). 33. J. Perie, M. Perie, and J. C. Justice, J. Solution Chem. 9, 395 (1980).