REGRESSION ANALYSIS OF ISOBAR BOILING POINT OF WATER-ORGANIC BINARY MIXTURES
Abstract
We developed an algorithm for separating the non-stochastic contribution to the empirical dependence of the physicochemical properties of binary solutions on the concentrations of the components. The algorithm is based on the different behaviours of stochastic and deterministic coefficients of Fourier expansions. It was proved that the isolation of a non-additive part of the dependence allows a quantitative description of the contribution of the solvating effects on the system’s energy. In addition, this isolation is necessary for the analytical continuation of the studied function in the formalized area of negative values of concentrations. It was proved that the suggested development allows separating the stochastic part of the empirical data. We determined the qualitative criteria for the separation of deterministic and stochastic Fourier harmonics.
We suggested an efficient three-parameter basis for the regressive description of the isobar of the boiling points of binary solutions. It was proved that the first component of the basis already describes the greater part of non-stochastic empirical information. We formulated a two-stage algorithm for the regressive description of the isobar of the boiling point of aqueous-organic solutions. That algorithm can reduce the amount of necessary empirical information. We also calculated the regression model coefficients for a number of solutions with practical relevance. For most of the investigated solutions, one component of the three-parameter basis fully describes the empirical information. For less than 20% of the studied solutions, the regression basis needs to be supplemented with Fourier harmonics. The number of such harmonics does not exceed two. It was proved that the relative error of the proposed algorithm does not exceed 2% and can be explained by experimental errors.
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2. Preobrazhenskii M. А., Rudakov O. B. Russian Journal of Physical Chemistry A, 2015, vol. 89, no. 1, pp. 69-72. DOI: 10.7868/S0044453715010203
3. Chen A. J., Liu M., Zhen Y., et al. Journal of Solution Chemistry, 2013, vol. 42, no. 11, pp. 2213-2228. DOI:10.1007/s10953-013-0100-0
4. Nain A. K., Ansari S., Ali A. Journal of Solution Chemistry, 2014, vol. 43, no. 6, pp. 1032-1054. DOI 10.1007/s10953-014-0189-9
5. Wichterle A., Linek J., Wagner Z., Fontaine J.-C. Sosnkowska-Kehiaian K., Kehiaian H. V. Landolt-Börnstein Numerical Data and Functional Relationships in Science and Technology. New SeriesEdited by H.V. Kehiaian, Physical Chemistry vol. 13. Vapor-Liquid Equilibrium in Mixtures and Solutions Subvolume A1 Binary Liquid Systems of Nonelectrolytes. Part 1. Springer, Berlin, Heidelberg, New York, 2004, p. 377. Book DOI: 10.1007/978-3-540-49315-0
6. Croxton C. A. Liquid State Physics. A Statistical Mechanical Introduction. Cambridge University Press, Cambridge, UK, 1974, 421 p.
7. Lanczos C. Applied Analysis. Prentice Hall, Inc., New Jersey, USA, 1956, 221 p.
8. Rebertus D. W., Berne B. J., Chandler D. J. Journal of Chemical Physics, 1979, vol. 70, no. 7, pp. 3395-3400. DOI: http://dx.doi.org/10.1063/1.437871
9. Smolensky E. A., Maslov L. K., Shpilkin S. A., Zefirov N. S. Reports of the Academy of Sciences. Physical Chemistry, 1999, vol. 368, no. 2, рp. 219-222. (In Russian)
10. Wigner E. P. Simmetries and Reflections. Indiana University Press, Bloomington – London, UK, 1970, 318 p.
11. Krestov G. A. Thermodynamics of Ionic Processes in Solution. Leningrad, Chemistry Publ., 1984, 272 p. (In Russian)
12. Krestov G. A., Abrosimov V. K. Physical Chemistry of Solutions. Moscow, Nauka Publ., 1972, pp. 25-31. (In Russian)
13. Krestov G. A., Afanasyev V. N., Efremova L. S. Physico-Chemical Properties of Binary Solvent. Lenigrad, Chemistry Publ., 1988, 688 р. (In Russian)
14. Hargitai I., Hargitai M., Symmetry Through the Eyes of a Chemist. Plenum Press, New York & London, USA & UK, 1995, 496 p.
15. Schoenberg I. J. Bulletin of the American Mathematical Society, 1953, vol. 59, no. 3, pp. 199-230. DOI: https://doi.org/10.1090/S0002-9904-1953-09695-1
16. Max J. Methods and Techniques of Signal Processing of Physical Measurements. Moscow, Mir Publ., 1983,vol. 1, 312 p. (In Russian)
17. Boyd J. P. Chebyshev and Fourier Spectral Methods, University of Michigan, DOVER Publications Inc, Mineola, New York, USA, 2001, 668 p.
18. Grafakos L. Modern Fourier Analysis. Second Edition, Springer Science, Business Media, LLC, 2009, 521 p.
19. Preobrazhensky M. A., Rudakov O. B. Russian Chemical Bulletin. International Edition, 2014, vol. 63, no. 3, pp. 610-620. DOI: 10.1007/s11172-014-0482-1
20. Abramowitz M., Stegun I. A. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. U.S. Government Printing Office, New York, US, 1972, 1060 p.
21. Brémaud P. Fourier Analysis and Stochastic Processes. Springer Cham Heidelberg New York Dordrecht London, UK, 2014, 396 p.
22. Perry R. H., Green D. W. Perry's Chemical Engineers' Handbook. 8th Edition, McGraw-Hill, N.Y., USA, 2007, 2400 p.
23. Patil S. S., Mirgane S. R. International Journal of Chemical, Environmental and Pharmaceutical Research, 2011, vol. 2, no. 2-3, 72-82.
24. Durov V. A., Ageev E. P. The Thermodynamic Theory of Solutions. Moscow Librikom Publ., 2010, 248 p. (In Russian)
25. Anders V. Fourier Analysis and Its Applications. Series: Graduate Texts in Mathematics. 223, Springer-Verlag New York, Inc, New York Berlin Heidelberg. 2003, p. 73-103.
26. Tutubalin V. N. Probability Theory and Stochastic Processes. Fundamentals of Mathematical Apparatus and Applied Aspects. Moscow, MGU Publ., 1992, 400 p. (In Russian)
27. Schirmacher W. Theory of Liquids and Other Disordered Media. A Short Introduction. Springer International Publishing, Switzerland, 2015, 167 p.
28. Preobrazhenskii M. A., Rudakov O. B. Russian Journal of Physical Chemistry A, 2016, vol. 90, no. 1, pp. 109-112. DOI: 10.1134/S0036024416010234
