Ind. Eng. Chem. Res. 1999, 38, 4137-4138
4137
Reply to “Comments on ‘Surface Tension Model for Concentrated Electrolyte Solutions by the Pitzer Equation’” Yi-Gui Li Department of Chemical Engineering, Tsinghua University, Beijing 100084, People’s Republic of China
Sir: In our previous paper1 the relation between the surface tensions and the osmotic coefficients of electrolyte solutions which are calculated by the Pitzer equation is established. I agree with Dr. Anil Kumar’s idea that an accurate thermodynamic model and its parameters of the osmotic coefficient of an electrolyte solution is required to arrive at correct surface tension data. Because the concentrations of many systems listed in Table 1 in our previous paper1 exceed the applicable concentration range (0-6 m) of the Pitzer equations, the modified Pitzer parameters evaluated by Kim and Frederich2 are used instead of the original Pitzer parameters.3 For some systems the correlation deviations of surface tension are larger, particularly in lowconcentration ranges. In this reply, I try to use the original Pitzer parameters3 with limited maximum concentration ranges, used to re-fit the surface tension data for 10 single electrolyte aqueous systems. The correlation results are listed in Table 1 and some of them are shown in Figures 1-4. From Table 1 it can be seen that among these 10 systems, only for HCl and MnCl2 aqueous systems the accuracies of the correlated surface tension values by use of the original Pitzer parameters are better than those of the modified Pitzer parameters (compared with Table 1 in our previous paper1). From these figures there are still some deviations in low-concentration ranges. So if one needs more accurate correlation results in low-concentration ranges, you should re-fit the Pitzer parameters in a specific concentration range first and then to re-fit the interface parameter g again. But, in this case, your application ranges for your regressed interface parameters must be very narrow, although the correlation accuracy of surface tension data will be increased. As for mixed electrolyte solutions, in our previous paper,1 we predicted the surface tension data for binary and ternary electrolyte systems without mixing param-
Figure 1. Correlated surface tension values for a HCl aqueous solution (T ) 293.15 K).
Figure 2. Correlated surface tension values for a NaCl aqueous solution (T ) 293.15 K).
Figure 3. Correlated surface tension values for a MnCl2 aqueous solution (T ) 291.15 K).
eters. In this reply I used the mixing parameters θ and ψ4 and θ(0), θ(1), and ψ5, respectively, to some binary and ternary electrolyte systems with original Pitzer parameters and compared the predicted results with those without mixing parameters. The predicted results are listed in Table 2 and some of them are shown in Figures 5-7. From Table 2, it can be seen that the predicted results by use of the original Pitzer parameters without mixing parameters only for the KBr-KCl system (see Figure 5) are better than those by use of the modified Pitzer parameters. The predicted results with the mixing parameters only for KBr-NaBr and LiCl-KCl systems (see Figure 6) seem better than those without mixing parameters. The results from two sets of mixing parameters are nearly the same. Sometimes, the consideration of mixing parameters may decrease the prediction accuracy (see Table 2). If we re-regress the Pitzer parameters of the osmotic coefficient for single-electro-
10.1021/ie991069m CCC: $18.00 © 1999 American Chemical Society Published on Web 09/11/1999
4138
Ind. Eng. Chem. Res., Vol. 38, No. 10, 1999
Figure 4. Correlated surface tension values for a SrCl2 aqueous solution (T ) 293.15 K).
Figure 5. Predicted surface tension values for a KBr(1)-KCl(2) aqueous solution (T ) 291.15 K; m1/m2 ) 1).
Table 1. Correlation Results of Surface Tension and Parameters for Single-Electrolyte Aqueous Solutions by Use of Original Pitzer Parameters3
system
T (K)
parameter, g
AAD (%)
HCl NaCl KCl LiCl NaBr LiBr KBr MnCl2(82) SrCl2 Sr(NO3)2
293.15 293.15 293.15 298.15 293.15 293.15 293.15 291.15 293.15 291.15
1.04606 0.1165 0.06275 0.1910 0.1185 0.9215 0 0.3905 0 0
0.25 0.53 0.095 0.63 0.21 5.22 0.32 0.76 0.64 0.76
maximum concentration (m) for regressing φ σ 6 6 4.8 6 4 2.5 5.5 4 4 2
14.98 6.0 4.39 3.82 2.90 17.27 2.245 5.62 2.81 3.12
Table 2. Predicted Results of Surface Tension for Mixed Electrolyte Solutions with and without Mixing Parameters by Use of the Original Pitzer Parameters
Figure 6. Predicted surface tension values for a LiCl(1)-KCl(2) aqueous solution (T ) 298.15 K; m1/m2 ) 1).
deviations (%)
system
T (K)
KBr-KCl KBr-NaBr
291.15 283.15 303.15 323.15 LiCl-KCl 298.15 NaCl-KCl 298.15 LiCl-NaCl 298.15 LiCl-NaCl-KCl 298.15
this work previous work1 with with θ(0), Imax θ(1), ψ (m) θ ) ψ ) 0 θ ) ψ ) 0 θ, ψ 0.405 0.915 1.242 1.429 0.588 0.415 0.232 0.340
0.257 1.115 1.437 1.488 0.589 0.457 0.241 0.322
1.000 1.274 1.306 0.475 0.478 0.243 0.360
0.250 1.002 1.271 1.308 0.478 0.481 0.260 0.349
4.90 5.82 5.82 5.82 4.47 3.23 3.21 3.28
lyte solutions in the narrow concentration ranges, we should re-regress the mixing parameters also in the same narrow concentration ranges of electrolyte solutions to obtain the accurate prediction results of the surface tension data. I do not recommend such a complicated computation. Acknowledgment We thank Dr. Anil Kumar for his interest in our published paper. Literature Cited (1) Li, Z.-B.; Li, Y.-G.; Lu, J.-F. Surface Tension Model for Concentrated Electrolyte Aqueous Solutions by the Pitzer Equation. Ind. Eng. Chem. Res. 1999, 38, 1133. (2) Kim, H. T.; Frederick, W. J. Evaluation of Pitzer Ion Interaction Parameters of Aqueous Electrolytes at 25 °C. 1. Single Salt Parameters. J. Chem. Eng. Data 1988, 33, 177.
Figure 7. Predicted surface tension values for a LiCl(1)-NaCl(2)-KCl(3) aqueous solution (T ) 298.15 K; m1:m2:m3 ) 1:1:1). (3) (a) Pitzer, K. S. Thermodynamics of Electrolytes I. Theoretical Basis and General Equations. J. Phys. Chem. 1973, 77, 268. (b) Pitzer, K. S. Ion Interaction Approach: Theory and Data Correlation. In Activity Coefficients in Electrolyte Solutions, 2nd ed.; Pitzer, K. S., Ed.; CRC Press: Boston, 1991; Chapter 3. (4) Pitzer, K. S.; Kim, J. J. Thermodynamics of Electrolytes IV. Activity and Osmotic Coefficients for Mixed Electrolytes. J. Am. Chem. Soc. 1974, 96, 5701. (5) Yang, J.-Z.; Pitzer, K. S. Thermodynamics of Electrolyte Mixtures. Activity and Osmotic Coefficients Consistent with the Higher-Order Limiting Law for Symmetrical Mixing. J. Sol. Chem. 1988, 17, 909.
IE991069M
