Experimental Determination of Densities of Aqueous Electrolyte

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Ind. Eng. Chem. Res. 2006, 45, 6604-6613

Experimental Determination of Densities of Aqueous Electrolyte Mixtures Containing B(OH)3 or Na2B4O7 and Their Correlation with the Pitzer Model He´ ctor R. Galleguillos,* Mirsa A. Molina, Teo´ filo A. Graber, and Marı´a E. Taboada Department of Chemical Engineering, UniVersidad de Antofagasta, Antofagasta, Chile

Felipe Herna´ ndez-Luis Department of Physical Chemistry, UniVersidad de La Laguna, Tenerife, Spain

The densities of six aqueous ternary systems that contain boric acid or disodium tetraborate and different electrolytes (NaCl, Na2SO4, or K2SO4) were measured at 20, 25, and 30 °C. The experimental study of these systems were conducted for four total molality values of the mixtures: mT ≈ 0.25, 0.50, 0.75, and 1.0 mol/kg for systems that contain B(OH)3 and mT ≈ 0.10, 0.12, 0.14, and 0.17 mol/kg for systems that contain NaB4O7. The total molality is calculated as the sum of the boron compounds and the electrolyte molalities. For each total molality, the values of the molar fraction of the B(OH)3 or NaB4O7 (free of water) were y1 ≈ 0.25, 0.50, and 0.75. The parameters of the Pitzer model were fit to the experimental density values. The regression analysis was simplified by considering the boric acid or disodium tetraborate to behave as undissociated neutral species. However, it was considered that the second virial coefficients of the neutral species (λnn), were dependent on their molality. Also, using the Pitzer model, we determined the volume of mixing (∆VM), at constant total molality of the mixture (mT) and at 25 °C, for each of the six ternary systems that have been studied. 1. Introduction Experimental values for the densities of aqueous solutions that contain boron compounds are scarce. The International Critical Tables of Numerical Data, Physics, Chemistry and Technology1 list a few values for binary aqueous solutions containing boric acid and disodium tetraborate. Reports on a few other solutions, in the saturated condition, have been given by Linke and Seidell.2 Novotny´ and So¨hnel3 developed a correlation to estimate densities of binary aqueous solutions for several inorganic substances, which include B(OH)3 and NaB4O7. The experimental data of these substances were taken from So¨hnel et al.4 Galleguillos et al.5 presented experimental data on the density and refractive index of the B(OH)3 + H2O and Na2B4O7 + H2O systems at temperatures of 20, 25, and 30 °C; this reference also included a study of the ternary systems B(OH)3 + KCl + H2O and Na2B4O7 + KCl + H2O. Given the importance of density values in calculations of mass balance in crystallizers and evaporators, we thought it useful to continue experimental determinations of this property. The present study reports data on the density of six ternary systems at 20, 25, and 30 °C; these systems include B(OH)3 + NaCl + H2O, B(OH)3 + Na2SO4 + H2O, B(OH)3 + K2SO4 + H2O, Na2B4O7 + NaCl + H2O, Na2B4O7 + Na2SO4 + H2O, and Na2B4O7 + K2SO4 + H2O. Considering the presence of electrolytes in the systems, as well as the moderate solubilities of boric acid and disodium tetraborate, whose saturation molalities at 25 °C are 0.934 and 0.157 mol/kg, respectively, it is assumed that the contents of boron compounds in the systems that have been studied represent relatively concentrated solutions. Generally, modeling the experimental data of aqueous systems that contain boron compounds is no simple task, because the boron compounds easily associate, forming various polyborates. * To whom correspondence should be addressed. Tel.: 56 55 637313. Fax: 56 55 240152. E-mail: [email protected].

This complicates the modeling process, because of a lack of knowledge of which compounds are truly present in the system. With aqueous solutions that contain boron, the degree of association is dependent on the total boron concentration. Felmy and Weare6 suggested that, at concentrations of Vφ at 20 °C > Vφ at 30 °C. Based on this observation, it was logical that the values of V h 02 for both solutes followed the preceding tendency. Table 8 also shows that the values of the parameters λ(0)V nn and λ(1)V nn of the Na2B4O7 + H2O system are greater than those

of the B(OH)3 + H2O system. This indicates that, as the concentration of the solute increases, the short-range interactions are probably more intense in the solution that contains Na2B4O7. The solid lines in Figures 1 and 2, which cross the experimental points for y1 ) 1, represent the values obtained with the Pitzer model. Note that there was good agreement between the experimental and calculated values. Considering the AAD values of Table 8, it is affirmed that the Pitzer model, including the assumptions made in this study, presents an accurate representation of the volumetric behavior of the two binary systems that have been studied.

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Figure 5. Volume of mixing of the B(OH)3 + K2SO4 + H2O system at 25 °C.

Figure 7. Volume of mixing of the Na2B4O7 + NaCl + H2O system at 25 °C.

Figure 6. Volume of mixing of the B(OH)3 + KCl + H2O system at 25 °C.

Figure 8. Volume of mixing of the Na2B4O7 + Na2SO4 + H2O system at 25 °C.

4.3. Correlation of Ternary Systems. The regressions of the experimental data from the six ternary systems in the present study were performed using the same objective function as previously noted (eq 39). Also correlated were the densities of the B(OH)3 + KCl + H2O and the Na2B4O7 + KCl + H2O systems, the data from which were previously reported.5 The (1)V V values of V h 0ca, β(0)V ca , βca , and C ca for each of the electrolytes were obtained from Krumgalz et al.;21 the Debye-Hu¨ckel constant AV was also obtained from this reference. The values (1)V of parameters V h 02 (or V h 0nn), λ(0)V for the neutral nn , and λnn species were those obtained previously and listed in Table 8. Equation 26 shows that the parameters to be obtained using the regression are the mixing parameters λVnca and ξVnca, because all the other terms are known. The regression analysis showed that it was not necessary to include parameter ξVnca in the fit, because this did not improve the AAD. Tables 9 and 10 show the values of parameter λVnca and the AAD for the eight systems

that were correlated. These tables show that the values of the parameters λVnca for the systems that contain Na2B4O7 were higher than those for systems that contained B(OH)3. This tendency was similar to that shown for parameters λ(0)V nn and λ(1)V nn . In Figures 1 and 2, the solid lines that pass through the experimental points for different values of y1 represent the values that were obtained with the Pitzer model. In both systems, very good agreement is observed between the experimental and calculated values. The overall AAD of the four Na2B4O7 + electrolyte + H2O ternary systems reached a value of 1.6 × 10-4 g/cm3, and the overall AAD of the four B(HO)3 + electrolyte + H2O ternary systems had a value of 3.4 × 10-4 g/cm3. The highest deviation occurred with the B(HO)3 + K2SO4 + H2O system at 30 °C. The latter system probably has a much more complex behavior

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Figure 9. Volume of mixing of the Na2B4O7 + K2SO4 + H2O system at 25 °C.

of the two binary mixtures, before mixing, is greater than that obtained after the mixing process. This indicates that the final ternary mixture reaches a better packing configuration, leading to a lower volume of the system. Another aspect worthy of note in observing Figures 3-10 are the relative forms of the curves presented. It can be noted that all of the systems produced parabolic curves that were relatively symmetrical near y1 ) 0.5. This was because parameter V1 of eq 35 reached values very close to zero, indicating that, in these systems, the interactions between trios of ions (associated with the parameter CVca) were practically negligible. Based on the preceding information, at a given value for mT, the sign and magnitude of ∆VM are directly related to the sign and magnitude of V0. In the particular case of these systems, which showed parabolic curves, the greater incidence in the magnitude, and the negative sign for ∆VM, arises from binary ion-ion and neutral species-neutral species interactions that are associated with parameters BVca and λVnn, respectively (the FV values in all eight systems were nonsignificant and negligible in front of others terms in eq 36). According to Desnoyer et al.,22 it is probable that the two solutes that have been mixed in these systems have the same structural ability for orienting water molecules (two structure makers or two structure breakers), thus resulting in a repulsion with a decrease in volume. The preceding refers to ionic solutes and is, therefore, not directly applicable to the systems in the present study; however, the fact that the parameter λVnn is dependent on mn implicitly supposes that the neutral species has polarity and, thus, might indeed be relevant to the preceding consideration. 5. Conclusions

Figure 10. Volume of mixing of the Na2B4O7 + KCl + H2O system at 25 °C.

than the other systems analyzed. However, it can be assumed that the modified Pitzer model was adequate to represent the volumetric behavior of the eight ternary systems presently analyzed. 4.4. Volume of Mixing. We determined the values for the mixture volumes of the eight systems correlated with the Pitzer model at 25 °C using eqs 35-38. Figures 3-10 present the values of ∆VM versus y1 for each of these ternary systems. Each graph of these figures contains the individual curve that represents the different values of total molality (mT) of each ternary mixture. It can be observed in the figures that the ternary systems generally show negative values for the volume of mixing ∆VM over the entire y1 interval. It is also observed that most of the ternary solutions have ∆VM values that become increasingly negative with increases in mT. The fact that the ∆VM value may be negative indicates that the excess volume

This work provides reliable density data for six ternary systems that contain B(OH)3 or Na2B4O7 and electrolytes such as NaCl, Na2SO4, and K2SO4. This information is important in engineering calculations such as material balance in evaporation and crystallization processes. The reliability of the data obtained in this work was validated by comparison with experimental results for NaCl solutions from other authors. The experimental data were correlated with the Pitzer model, supposing that the B(OH)3 and Na2B4O7 are undissociated neutral species. However, in the analysis, the second virial coefficient of these compounds was considered to be dependent on its molality. This implied that a small modification to the thermodynamic model should be made. Despite the drastic assumed simplification, the results obtained in the data correlation are satisfactory and appropriate for engineering calculations. Acknowledgment The authors are grateful for financing provided by CONICYT, through Fondecyt Project No. 1040299. Literature Cited (1) International Critical Tables of Numerical Data, Physics, Chemistry and Technology; McGraw-Hill: New York, 1928. (2) Linke, W. F.; Seidell, A. Solubilities of Inorganic and Metal Organic Compounds; American Chemical Society: Washington, DC, 1958. (3) Novotny´, P.; So¨hnel, O. J. Chem. Eng. Data 1988, 33, 49-55. (4) So¨hnel, O.; Novotny´, P.; Wurzelova´, J. Chem. Listy 1982, 76, 979. (5) Galleguillos, H. R.; Flores, E. K.; Aguirre, C. E. J. Chem. Eng. Data 2001, 46, 1632-1634. (6) Felmy, A. R.; Weare, J. H. Geochim. Cosmochim. Acta 1986, 50, 2771-2783.

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(17) Krumgalz, B. S.; Pogorelsky, R.; Pitzer, K. S. J. Solution Chem. 1995, 24, 1025-1038. (18) Connaughton, L. M.; Millero, F. J.; Pitzer, K. S. J. Solution Chem. 1989, 18, 1007-1017. (19) Chen-Tung, A. C.; Hwa, J. H. J. Chem. Eng. Data 1980, 25, 307310. (20) Lo Surdo, A.; Alzola, E.; Millero, F. J. Chem. Eng. Data 1982, 27, 649-662. (21) Krumgalz, B. S.; Pogorelskii, R.; Sokolov, A. Pitzer, K. S. J. Phys. Chem. Ref. Data 2000, 29, 1123-1139. (22) Desnoyer, J. E.; Arel, M.; Perron, G.; Jolicouer, C. J. Phys. Chem. 1969, 73, 3346-3351.

ReceiVed for reView March 10, 2006 ReVised manuscript receiVed June 22, 2006 Accepted July 13, 2006 IE060294I