308 Acta Chim. Slov. 2008, 55, 308–314 Scientific paper Thermodynamics of the Association Reaction of RbBr in Binary Mixtures of 2-Butanol and Water from 288.15 to 308.15 K Vesna Sokol,* Renato Toma{ and Ivo Tomini} Faculty of Chemistry and Technology, University of Split, N. Tesle 10, 21000 Split, Croatia. * Corresponding author: E-mail: vsokol@ktf-split.hr Received: 13-09-2007 Abstract Molar conductivities of dilute solutions of rubidium bromide in binary mixtures of 2-butanol and water were measured in the temperature range from 288.15 to 308.15 K at 5 K intervals. The limiting molar conductivity (?o) and association constant (KA) were determined by treating experimental data with the Lee-Wheaton conductivity equation. Thermody-namic quantities for the ion-association reaction were derived from the temperature dependence of KA. The obtained results provide information on ion-ion and ion-solvent interactions. Keywords: Rubidium bromide, 2-butanol + water mixtures, association to ion-pairs, thermodynamic quantities 1. Introduction In continuation of our studies on the ion-association reactions of alkali bromides in mixtures of water and 2-butanol,1,2,3 we report conductance measurements of RbBr in mixtures with the alcohol mass fraction (w) 0.70, 0.80, 0.90 and 0.95 at five temperatures from 288.15 to 308.15 K. Mixed solvents are suitable for this study because even a small change in solvent composition make a significant difference in behaviour of the dissolved electrolyte. The study on conductometric properties of alkali bromides in water + N,N-dimethyl-formamide4 and tetrahydrofuran + water5 mixtures have been made at 298.15 K. Conductivity study on electrolytes over wide temperature range provide valuble information on thermodynamic behaviour of the dissolved electrolyte. The limiting molar conductivity (?o), association constant (KA) and association distance (R) were determined using the chemical model of conductivity based on the Lee-Wheaton equation. The Walden product values (?o?), as well as the standard ther-modynamic quantities for the association reaction, were derived from the temperature dependence of ?o and KA, respectively. The influence of the cation change on ther-modynamic quantities was discussed from a comparison with the analogous data for LiBr,1 NaBr2 and KBr3 in the same mixtures. 2. Experimental 2-butanol (Merck, p.a.) was fractionally distilled in a Vigreux column, the first fraction was thrown away, and the middle fraction of the distillate, collected at a head temperature of 372.0–372.6 K, was used to prepare the solutions. Water was distilled twice, and RbBr (Merck, suprapur) was dried for six hours at 393.15 K before use. The test solutions were prepared by adding a weighed amount of the mixed solvent to a weighed amount of the RbBr stock solution. The relative error on molarity and solvent composition was about 0.1%. The values for the density and viscosity of the pure solvent were taken from our previous work,3 while the relative permittivities were obtained by interpolation of literature data,6 and presented in Ref. (3). The molar concentration of the solution is given by the relationship (1) were m is the molality (moles of electrolyte per kilogram of solvent), d is the density of solution, and M (0.16538 kg mol–1) is the molar mass of rubidium bromide. First, a small amount of the stock solution in the corresponding mixed solvent was prepared by weighing RbBr, water and 2-butanol. The solution density was determined at 293.15 K using a pycnometer. The density coefficient D was ob- Sokol at al.: Thermodynamics of the Association Reaction of RbBr in Binary Mixtures ... Acta Chim. Slov. 2008, 55, 308–314 309 tained assuming a linear change of solution density upon its molality, d = do + Dm, where do is the density of the pure mixed solvent. The density coefficient D (kg2 dm–3 mol–1) is assumed to be independent of temperature,7 and its values for 0.70, 0.80, 0.90 and 0.95 alcohol mass fraction amount to 0.099, 0.044, 0.095 and 0.101, respectively. The resistance of test solutions was measured in two parallel cells with a precision component analyser Wayne-Kerr (model 6430A) at four frequencies (f = 500, 800, 1000 and 2000 Hz) and extrapolated against f–1 to infinite frequency. Cells were immersed in a Thermo-Haake Circulator DC10-V15/B maintaining the temperature within ±0.01 K. The cell constants were determined with dilute potassium chloride solutions.8 rage relative deviation of a single cell value from the mean amounts to ±0.14%. All measured values were corrected for the conductivity of the solvent. Conductivity data processing was carried out by means of the Lee-Wheaton equation in Pethybridge and Taba version9 (LWP) and the following set of equations was used Aca =AD[\ + C, ßK + C7 {0k)1 + C3 {ßKJ ]- (2) (3) 3. Resuts and Discussion Each molar conductivity of RbBr solutions, as presented in Table 1, is the mean value of two cells. The ave- j>f =exp[-2«ç/(l+KR>], e2 (4) (5) Table 1. Molar conductivities (?) of RbBr at various molalities (m) in aqueous 2-butanol of mass fraction w at different temperatures 104 ma 104vi/S m2 mol"1 mol kg–1 TIK = 288.15 TIK = 293.15 TIK = 298.15 TIK = 303.15 TIK = 308.15 w = 0.70 2.003 16.567 19.818 23.418 27.340 31.696 6.301 16.129 19.200 22.651 26.394 30.431 10.597 15.710 18.690 22.020 25.641 29.557 14.896 15.403 18.313 21.530 25.078 28.823 19.201 15.057 17.882 21.054 24.456 28.217 23.498 14.802 17.558 20.614 23.979 27.581 27.805 14.567 17.277 20.303 23.566 27.112 32.099 14.366 17.034 20.021 23.225 26.636 36.392 14.166 16.801 19.714 22.863 26.314 40.704 13.995 16.579 19.436 22.568 25.984 45.006 13.819 16.353 19.181 22.240 25.562 49.267 13.702 16.216 18.993 22.026 25.281 53.595 13.568 16.049 18.810 21.797 25.029 57.900 13.433 15.886 18.623 21.572 24.749 61.827 13.301 15.720 18.407 21.334 24.515 w = 0.80 4.099 13.368 16.012 19.025 22.376 26.035 6.433 12.824 15.329 18.167 21.326 24.781 8.644 12.430 14.838 17.569 20.572 23.898 10.862 12.116 14.456 17.097 20.003 23.221 13.083 11.803 14.081 16.632 19.450 22.515 15.286 11.559 13.777 16.281 19.010 21.982 17.509 11.353 13.526 15.960 18.620 21.528 19.727 11.152 13.274 15.646 18.261 21.095 21.941 10.979 13.069 15.397 17.957 20.775 24.159 10.795 12.830 15.124 17.644 20.431 26.386 10.654 12.657 14.918 17.399 20.118 28.597 10.518 12.504 14.711 17.145 19.754 30.800 10.374 12.325 14.500 16.894 19.455 33.018 10.237 12.155 14.303 16.663 19.172 Sokol at al.: Thermodynamics of the Association Reaction of RbBr in Binary Mixtures ... 310 Acta Chim. Slov. 2008, 55, 308–314 104 ma 104A/S m2 mol–1 mol kg–1 T /K = 288.15 T /K = 293.15 T /K = 298.15 T /K = 303.15 T /K = 308.15 w = 0.90 2.015 11.207 13.323 15.687 18.268 21.092 3.384 10.389 12.293 14.421 16.701 19.141 4.533 9.888 11.659 13.629 15.750 18.041 5.801 9.425 11.099 12.952 14.921 17.033 7.063 9.080 10.672 12.417 14.281 16.276 8.311 8.752 10.275 11.938 13.710 15.596 9.630 8.466 9.914 11.508 13.211 15.019 10.835 8.244 9.640 11.182 12.817 14.542 12.108 8.026 9.387 10.864 12.442 14.119 13.338 7.838 9.157 10.596 12.132 13.754 14.639 7.666 8.938 10.341 11.827 13.392 15.939 7.490 8.737 10.096 11.529 13.025 17.178 7.361 8.581 9.915 11.314 12.780 18.456 7.200 8.391 9.684 11.055 12.485 19.806 7.061 8.225 9.490 10.821 12.186 w = 0.95 2.041 8.581 9.925 11.368 12.861 14.383 3.135 7.732 8.900 10.134 11.390 12.646 4.218 7.151 8.205 9.313 10.428 11.528 5.309 6.691 7.648 8.658 9.668 10.657 6.401 6.342 7.236 8.177 9.113 10.028 7.488 6.046 6.891 7.773 8.642 9.485 8.578 5.802 6.592 7.424 8.243 9.055 9.669 5.578 6.344 7.128 7.911 8.679 10.761 5.393 6.120 6.871 7.616 8.346 11.847 5.222 5.923 6.648 7.362 8.062 12.943 5.072 5.750 6.450 7.139 7.804 14.028 4.945 5.599 6.275 6.945 7.578 15.120 4.814 5.451 6.106 6.749 7.373 16.199 4.701 5.319 5.957 6.584 7.192 17.269 4.600 5.202 5.823 6.430 7.017 a Molality can be converted to molarity using Eq. (1) KT = \6u:N&qo. (6) In these expresions, Acg is the molar conductivity of the free ions, Ao is the molar conductivity at infinite dilution, coefficients C1-C5 are the functions of t and ln t (t = kR), R is the greatest centre-to-centre distance between the ions in the ion-pair formed, k is the Debye parameter, ß= 2q, q is the Bjerrum critical distance, and p is defined in Ref. (9). KAc, subscript c indicating the molarity scale, is the thermodynamic equilibrium constant for the association reaction Rb+ + Br~ = Rb+-Br~, ca + ca c(i-a) (7) where ca and c(1–d) are the equilibrium concentrations of the fraction of free ions and ion pairs, respectively. a is the degree of dissociation (a = A/Aca) and represents the ratio of the measured molar conductivity (A) to the molar conductivity of free ions. y± is the mean activity coefficient of the free ions, e is the proton charge, er the relative permittivity of the solvent, eo the permittivity of vacuum. The other symbols have their usual meaning. Parameters Ao, KA c and R were calculated by the computer optimization according to Beronius,10 where Ao and KAc were adjusted for each selected value of parameter R. The optimization is completed when the minimal standard deviation (8) between the calculated and experimental conductivities is obtained. The initial values of Ao and KA c for the iteration procedure are obtained by the Kraus-Bray method.11 Each system gave a unique best set of parameters at each temperature. By plotting the standard deviation data against distance parameter (R), no significant minima were observed over the whole temperature range. Therefore, it can be concluded that it is not possible to obtain a uniform value for the distance parameter by the three-parameter fit. In Sokol at al.: Thermodynamics of the Association Reaction of RbBr in Binary Mixtures ... Acta Chim. Slov. 2008, 55, 308–314 311 that case, the distance parameter must be fixed at some arbitrarily chosen value. There are two criteria for the choice of such a value. According to the chemical model of electrolyte solutions, oppositely charged ions of the cry-stallographic radii a + and a– may be either in contact R = a, where a = a+ + a–, or separated by one or more solvent molecules R = a + d, the molecular diameter d is aproxi-mated by the length of an orientated solvent molecule.7 According to Bjerrum’s physical concept of ionic association, the upper limit of integration for KA is q (Eq. (5)). This quantity was adopted in conductometry as the distance parameter, R = q, by the efforts of Justice.12 The sum of crystallographic radii of Rb + and Br– (a) equals 0.343 nm.13 Diameter d represents the length of a water molecule, d = 0.280 nm,7 that makes R = 0.623 nm, a distance parameter significantly lower than Bjerrum’s critical distance q in these media (see Table 2). In this case, according to Fuoss’ suggestion,14 R should be equal to q. The obtained values of limiting molar conductivities, ion-association constants and standard deviations with R set at q, for all mixtures at different temperatures, are given in Table 2. To avoid thermal expansion of the solvent to the reaction enthalpy, KA,c was converted to the molality scale, K = K d. A,m A,c o The thermodynamic quantities of the ion-association reaction (Eq. (7)) were derived from the data for association constant KA,m at different temperatures. The stan- dard enthalpy (?H0) was evaluated by the least-squares treatment of the following straight line: (9) The standard deviation of the enthalpy was derived from the standard deviation of the corresponding slo-pe.(15a) The standard deviation of the reaction Gibbs energy was estimated after linearization(15b) of the relationship AG" -RT In K, (10) The standard entropy of ion-pair formation is a linear combination of two variables (11) and its standard deviation can be obtained accordingly.(15b) Eyring’s enthalpy of activation of the charge trans-port16 (?H‡) can be obtained from the temperature dependence of ?o by the equation ln A + 2/3 ln d = - MH ‡/RT + C, o o (12) Table 2. Limiting molar conductivities (?), ion-association constants (KA,c, KA,m) and standard deviations (?) of experimental ?from the model LWP for RbBr in 2-butanol (w) + water mixtures with R = q T/K 104?o/S m2 mol–1 K A,c K A,m 104a/S m2 mol 1 q/nm w = 0.70 288.15 17.37 ± 0.03 64.6 ± 1.3 56.3 ± 1.1 0.047 1.094 293.15 20.77 ± 0.03 70.8 ± 1.1 61.4 ± 1.0 0.044 1.109 298.15 24.56 ± 0.03 76.3 ± 1.1 65.9 ± 0.9 0.049 1.121 303.15 28.70 ± 0.04 81.3 ± 1.1 69.8 ± 0.9 0.057 1.134 308.15 33.23 ± 0.03 86.9 ± 0.8 74.2 ± 0.7 0.045 1.154 w = 0.80 288.15 14.97 ± 0.03 259.8 ± 3.1 221.1 ± 2.6 0.027 1.368 293.15 18.00 ± 0.04 278.6 ± 3.3 235.9 ± 2.8 0.034 1.383 298.15 21.48 ± 0.05 301.5 ± 3.7 254.0 ± 3.1 0.043 1.401 303.15 25.38 ± 0.07 325.6 ± 4.7 272.9 ± 3.9 0.061 1.420 308.15 29.71 ± 0.08 353.4 ± 4.9 294.6 ± 4.1 0.071 1.442 w = 0.90 288.15 13.44 ± 0.02 1269 ± 7 1054 ± 6 0.017 1.629 293.15 16.20 ± 0.03 1436 ± 9 1186 ± 7 0.021 1.657 298.15 19.37 ± 0.04 1628 ± 9 1338 ± 7 0.025 1.688 303.15 22.92 ± 0.05 1843 ± 11 1506 ± 9 0.030 1.722 308.15 26.96 ± 0.06 2112 ± 13 1717 ± 11 0.036 1.760 w = 0.95 288.15 12.47 ± 0.03 4055 ± 21 3327 ± 17 0.012 1.695 293.15 14.93 ± 0.04 4762 ± 24 3885 ± 20 0.014 1.738 298.15 17.78 ± 0.04 5644 ± 28 4579 ± 23 0.014 1.785 303.15 21.01 ± 0.06 6747 ± 38 5446 ± 31 0.018 1.825 308.15 24.67 ± 0.09 8146 ± 57 6544 ± 46 0.025 1.870 Sokol at al.: Thermodynamics of the Association Reaction of RbBr in Binary Mixtures ... 312 Acta Chim. Slov. 2008, 55, 308–314 were do is the density of solvent. The values of the standard thermodynamic quantities at 298.15 K, along with their standard deviations, are given in Table 3. Table 3. Standard thermodynamic quantities for the ion-association reaction (Eq. (7)) calculated from KA,m in 2-butanol (w) + water mixtures at 298.15 K w ?Ho/J mol–1 ?Go/J mol–1 ?So/J K–1 mol–1 0.70 10059 ± 390 -10382 ± 34 68.6 ± 1.3 0.80 10620 ± 280 -13727 ± 30 81.7 ± 1.0 0.90 17920 ± 390 -17845 ± 13 120.0 ± 1.3 0.95 24940 ± 760 -20895 ± 12 153.7 ± 2.6 Figure 1 shows the concentration dependence of the experimental molar conductivity of RbBr at five temperatures in 2-butanol (w = 0.95) + water. Full line represents the results of the chemical model of conductivity (Eqs. (2 – 6)). The graphs for analogous data in the other three mixtures are similar. Figure 1. Molar conductivity of RbBr in aqueous 2-butanol of mass fraction 0.95 from 288.15 K to 308.15 K in steps of 5 K; O, experimental data; full line, calculated values. The limiting molar conductivity increases with temperature and decreases with the alcohol addition to a mixture. Such a behaviour of ?o is in agreement with the solvent viscosity. The Walden product is almost independent of temperature, see Table 4, as found for LiBr, NaBr and KBr in the same mixtures. The variation of the Walden product ?o? with the solvent composition gives information on ion-solvent interactions. The Walden product decreases with increasing mass fraction of alcohol, which can be explained by presolvation of ions by alcohol molecules. This presolvation of ions leads to an increase of the hydrodyna-mic radii of ions and decrease of their mobility. By comparing ?o?of RbBr with the same quantity for other alkali bromides in the same mixtures, the influence of the nature of cation can be discussed. From Figure 2 it can be observed that the dependencies of the Walden product for LiBr, NaBr, KBr and RbBr on the solvent composition at 298.15 K are similar. The values of ?o? retain the order ?o?(Li+) < ?o?(Na+) < ?o?(K+) < ?o?(Rb+) in the whole range of composition. The increase of the Walden product with increasing crystallographic radii of alkali ions indicates that the effective radius of cations follows the order: Li+ > Na+ > K+ > Rb+. This is the result of the stronger solvation of smaller ions which leads to their larger hydrodynamic radii. The differences in sol-vation of the mentioned electrolytes decrease with alcohol addition to the mixture. The similar behaviour of the Wal-den product was found for Li+, Na+, K+ and Cs+ in DMF + water mixtures.4 The association constant KA,c increases with increasing temperature. KA,c is low in aqueous 2-butanol of mass Figure 2. Variation of Ao7) with Lr in 2-butanol + water mixtures at 298.15 K for: LiBr (^), Ref. (1);NaBr (O), Ref. (2); KBr (T), Ref. (3); RbBr (V), this work. Table 4. Walden product of RbBr in 2-butanol (w) + water mixtures at different temperatures 107Aorj/S m2 mol 1 Pa s w T/K = 288.15 T/K = 293.15 T/K = 298.15 T/K = 303.15 T/K = 308.15 0.70 85.30 83.77 82.10 80.25 78.95 0.80 68.01 67.21 66.57 66.17 65.78 0.90 54.69 54.48 54.45 54.39 54.65 0.95 48.97 48.82 48.56 48.66 48.50 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 Sokol at al.: Thermodynamics of the Association Reaction of RbBr in Binary Mixtures ... Acta Chim. Slov. 2008, 55, 308–314 313 fractions 0.70 and 0.80, while it is considerably higher for w = 0.90 and 0.95. This increase can be explained by the lower relative permittivity of the mixed solvent. Figure 3 shows the variation of ln KA,m for alkali bromides with the inversed relative permittivity of the solvent at 298.15 K. The values of the association constant retain the order Rb-Br > KBr > NaBr > LiBr in the whole temperature range. Figure 3. Variation of ln KA m with L–1 in 2-butanol + water mixtures at 298.15 K for: LiBr (O), Ref. (1); NaBr (D), Ref. (2); KBr (A), Ref. (3); RbBr (V), this work. From Table 3 it can be concluded that the association of Rb+ and Br– ions is an endothermic reaction which results in an entropy increase. Both, ?Ho and ?So values increase with increasing 2-butanol content in the mixture. The similar behaviour show other mentioned alkali bromides, see Figure 4. The Gibbs energy for the association reaction is negative at all temperatures and becomes more negative with the increasing alcohol content. That indicates a greater degree of association at lower relative permittivity. From Figure 4 it can be observed that entropy term (T?So) dominates over association making an endothermic reaction spontaneous. This behaviour is due to considerable structural effects, probably brought by two main processes: breaking of the solvation layers and building-up of the bulk solvent. Figure 5 shows the dependence of the association Gibbs energy for alkali bromides on the alcohol content at 298.15 K. The order of the ?Go curves, Li+ > Na+ > K+ > Rb+, suggests that ion-pair formation is weaker with more strongly solvated ions. Figure 5. Values of AGo for the ion-pair formation as a function of the 2-butanol content (w) in 2-butanol + water mixtures at 298.15 K for: LiBr (•), Ref. (1); NaBr (O), Ref. (2); KBr (T), Ref. (3); RbBr (V), this work. Eyring’s enthalpy of activation of the charge transport (?H‡) relates to the mean of the temperature range (298.15 K). Figure 6 shows the dependence of ln ?o + 2/3 Figure 4. Thermodynamic quantities ?Ho and ?So for the ion-pair formation for different electrolytes in aqueous 2-butanol of mass fraction w at 298.15 K; LiBr, NaBr and KBr from Refs. (1–3), respectively. Figure 6. Dependences of (ln ?o + 2/3ln do) on 1/T for RbBr in aqueous 2-butanol of mass fractions 0.70, 0.80, 0.90 and 0.95. The activation energy of the transport process ?H‡ was determined according to Eq. (12). Sokol at al.: Thermodynamics of the Association Reaction of RbBr in Binary Mixtures ... 314 Acta Chim. Slov. 2008, 55, 308–314 ln do upon 1/T for RbBr in all investigated mixtures. The activation energy of the ionic movement is obtained from the slope of the straight lines. Thus, ?H‡/kJ mol–1 for Rb-Br in aqueous 2-butanol of the mass fraction 0.70, 0.80, 0.90 and 0.95 amounted to 23.45, 24.81, 25.15 and 24.69, respectively. Corresponding values in Ref. (3) for LiBr, NaBr and KBr are very close: for example in the mixture with w = 0.95 they are 24.59, 24.85, 24.30, respectively. 4. Acknowledgment This work is supported by a grant from the Ministry of Science, Education and Sports of the Republic of Croatia. 5. References 1. V. Sokol, I. Tomini}, R. Toma{, M. Vi{i}, Croat. Chem. Acta 2005, 78, 43–47. 2. I. Tomini}, V. Sokol, I. Mekjavi}, Croat. Chem. Acta 1998, 71, 705–714. 3. V. Sokol, R. Toma{, M. Vi{i}, I. Tomini}, J. Solution Chem. 2006, 35, 1687–1698. 4. A. Szejgis, A. Bald, J. Gregorowicz, C. M. Kinart, Phys. Chem. Liq. 1997, 34, 189–199. 5. M. N. Roy, D. Nandi, D. K. Hazra, J. Indian Chem. Soc. 1993, 70, 121–124. 6. A. Bald, J. Gregorowicz, A. Szejgis, J. Electroanal. Chem. 1992, 340, 153–167. 7. M. Be{ter-Roga~, R. Neueder, J. Barthel, J. Solution Chem. 1999, 28, 1071–1086. 8. J. Barthel, F. Feuerlein, R. Neueder, R. Wachter, J. Solution Chem. 1980, 9, 209–219. 9. A. D. Pethybridge, S. S. Taba, J. Chem. Soc. Faraday Trans. I 1980, 76, 368–376. 10. P. Beronius, Acta. Chem. Scand. A 1974, 28, 77–82. 11. C. A. Kraus, W. C. Bray, J. Amer. Chem. Soc. 1913, 35, 1315–1434. 12. J. C. Justice, Electrochim. Acta 1971, 16, 701–712. 13. J. M. G. Barthel, H. Krienke, W. Kunz, Physical Chemistry of Electrolyte Solutions-Modern Aspects, Steinkopff/Darm-stadt, Springer/New York, 1998. 14. R. M. Fuoss, J. Phys. Chem. 1978, 82, 2427–2440. 15. B. Carnahan, H. A. Luther, J. O. Wilkes, Applied Numerical Methods, John Wiley and Sons/New York, a) p. 572, b) p. 534, 1969. 16. S. B. Brummer, G. J. Hills, J. Chem. Soc. Faraday Trans. 1961, 57, 1816–1837. Povzetek Izmerili smo molske prevodnosti razred~enih raztopin rubidijevega bromida v binarnih me{anicah 2-butanola in vode v tempraturnem obmo~ju med 288.15 in 308.15 K v intervalih po 5 K. Dobljene podatke smo analizirali z Lee-Wheatonovo ena~bo za prevodnost elektrolitov ter dolo~ili molske prevodnosti pri neskon~nem razred~enju (?o) ter konstante asociacije ionov (KA). Iz temperaturne odvisnosti KA smo izpeljali termodinamske koli~ine za opis asociacije ionov, ki nam dajejo informacije o ion-ion ter ion-topilo interakcijah v raztopinah. Sokol at al.: Thermodynamics of the Association Reaction of RbBr in Binary Mixtures ...