Ind. Eng. Chem. Res. 1999, 38, 4135-4136
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Comments on “Surface Tension Model for Concentrated Electrolyte Solutions by the Pitzer Equation Anil Kumar† Physical Chemistry Division, National Chemical Laboratory, Pune 411 008, India
Sir: Very recently, Li et al.1 have proposed a model for predicting the surface tension of aqueous electrolyte solutions with good accuracy. Their model is shown to be applicable to high electrolyte concentrations and temperatures up to 353 K. Though the equations involved in the model are simple, I wish to raise a word of caution for the users who are involved in the type of work described in the paper. The authors have employed the standard thermodynamic expressions together with the Butler equation2 to arrive at their main equation (their eq 11) to calculate the surface tension of electrolyte solution, σsolu, as given below:
σsolu ) RTν(mBφB - mSφS)/Aw55.51 where m and φ are the molality and osmotic coefficients of the electrolyte solution, respectively. The superscripts B and S refer to bulk and surface phases, respectively. Aw is the molar surface area of pure water, while ν indicates the number of particles in an electrolyte. R and T have their usual significance. It is clear from the above equation that accurate knowledge of the osmotic coefficient (the osmotic coefficient of an electrolyte solution is directly related to the activity of water, aw, by ln aw ) -νmφ/55.51) of an electrolyte solution is required to arrive at correct the surface tension. It is, therefore, a problem in which how accurate one can compute the φ of the electrolyte solutions, particularly at very high concentrations. If the computed values of φ are of lower accuracy, these values will reflect in the predictions of the surface tension of the solution. Thus, the surface tension model after their eq 11 is solely dependent on the prediction of osmotic coefficients. The authors have employed the specific interaction theory of Pitzer3 for inserting the values of osmotic coefficients of the electrolyte solutions via adjustable Pitzer coefficients. The Pitzer equations combine the long- and short-range interaction forces with the help of the Debye-Huckel term and three or four virial coefficients. Though the authors have used a modified set of the Pitzer coefficients, these coefficients are not universal values for an electrolyte system. Let us take a simple example of aqueous MnCl2, for which the authors have shown (their Figure 4) the calculated surface tension values as compared to the experimental ones. An examination of this drawing clearly shows that their equation overestimates the surface tension in a systematic fashion, all the way up to m ≈ 4 mol kg-1. The line indicating the calculated surface tensions does not clearly predict the slope, (∂σi/∂mi), as can be witnessed from the contrast shown in their Figure 4. The calculated σ values do not show any tapering with the molality, which is an expected trend of the physicochemical properties. Analogous differences of the ex†
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perimental and the calculated σ values are also seen in the cases of aqueous NaCl and SrCl2. This serious limitation in their model arises out of the Pitzer coefficients, as they are vital input parameters. For testing this, we fitted the osmotic coefficient data of aqueous MnCl2 up to m ) 2 mol kg-1 from the extensive tabulation of Robinson and Stokes4 by employing the Pitzer equations. These newly computed Pitzer coefficients in the low-concentration range, when used in their model, predict more accurate σ values of aqueous MnCl2 in the specified range. The values of the Pitzer coefficients depend on the concentration range of the experimental data used in the least-squares fitting program. It is, thus, a selection of the solvent activity model that plays a dominant role in the calculation of surface tension of the electrolyte solutions by the model of Li et al.1 In other words, if a more accurate thermodynamic model is used for the input of the osmotic coefficients, the resultant predictions of the surface tension are expected to be more accurate. Second, the authors have extended their procedure to the calculation of the surface tension of the mixed electrolyte solutions. Though their extension is simple, it is not logical in view of the importance of the mixing terms in the Pitzer equations. The mixing (binary) terms in the Pitzer equations are the result of the interactions between the ions with like charges, indicated by θ. In some cases, the higher order (ψ) terms are also used. The use of the Pitzer equations without a due consideration of the mixing terms would amount to the large errors in the predictions of osmotic coefficients and thereby of surface tensions. This is evident from the analysis of Figures 6-9 of their paper. As a matter of fact, the experimental surface tension data listed in their Table 3 extend to high ionic concentrations and involve a variety of ions. The symmetries (symmetric or asymmetric mixing) of ions of the mixtures and their charges can be examined in light of the Friedman theory.5 The obviation of these mixing terms in the systems listed in their Table 3 has a serious impact on the prediction of the surface tensions of the electrolyte solutions. In summary, it is important to point out that it is safer to use the model of Li et al.1 for the prediction of the surface tensions of electrolyte solutions, if one can be certain of the effectiveness of the thermodynamic model in correlating the osmotic coefficients of these solutions. The concentration range, in which a given thermodynamic model is applicable with excellent accuracy, should be borne in mind while using the equation of Li et al.1 Acknowledgment Our work on the solutions is supported by a grantin-aid by the Department of Science and Technology, New Delhi, under Project No. SP/S1/H-29/94.
10.1021/ie991073y CCC: $18.00 © 1999 American Chemical Society Published on Web 09/10/1999
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Ind. Eng. Chem. Res., Vol. 38, No. 10, 1999
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) Butler, J. A. V. Thermodynamics of Surfaces of Solutions. Proc. R. Soc., London 1932, 135A, 348. (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) Robinson, R. A.; Stokes, R. H. Electrolyte Solutions, 2nd ed.; Butterworth’s Publications: London, 1959. (5) Friedman, H. L. Ionic Solution Theory; Wiley-Interscience: New York, 1962.
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