Comparative Balancing of Non-Redox and Redox Electrolytic Systems and Its Consequences

DOI: 10.4236/ajac.2013.410A1006   PDF   HTML     2,975 Downloads   4,893 Views   Citations

Abstract

In this paper, it is proved that linear combination 2·f(O) - f(H) of elemental balances: f(O) for O and f(H) for H is linearly independent on charge and elemental/core balances for all redox systems of any degree of complexity; it is the primary form of the Generalized Electron Balance (GEB), , considered as the Approach II to GEB. The Approach II is equivalent to the Approach I based on the principle of common pool of electrons. Both Approaches are illustrated on an example of titration of acidified (H2SO4) solution of H2C2O4 with KMnO4. It is also stated, on an example of titration of the same solution with NaOH, that 2·f(O) - f(H) is a linear combination of charge and elemental/core balances, i.e. it is not an independent balance when related to the non-redox system. These properties of 2·f(O) - f(H) can be extended on redox and non-redox systems, of any degree of complexity, i.e. the linear independency/dependency of 2·f(O) - f(H) on other balances related to a system in question is a criterion distinguishing redox and non-redox systems. The GEB completes the set of (charge and concentration) balances and a set of expressions for independent equilibrium constants needed for modeling the related redox system.

Share and Cite:

A. Michałowska-Kaczmarczyk and T. Michałowski, "Comparative Balancing of Non-Redox and Redox Electrolytic Systems and Its Consequences," American Journal of Analytical Chemistry, Vol. 4 No. 10A, 2013, pp. 46-53. doi: 10.4236/ajac.2013.410A1006.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] A. J. Bard and S. H. Simonsen, “The General Equation for the Equivalence Point Potential in Oxidation-Reduction Titrations,” Journal of Chemical Education, Vol. 37, No. 7, 1960, pp. 364-366.
http://dx.doi.org/10.1021/ed037p364
[2] E. Bishop, “Some Theoretical Considerations in Analytical Chemistry. Part VI. The Precise Calculation of Data for Redox Titration Curves,” Analytica Chimica Acta, Vol. 26, 1962, pp. 397-405.
http://dx.doi.org/10.1016/S0003-2670(00)88405-6
[3] J. A. Goldman, “The Equivalence Point Potential in Redox Titrations,” Analytica Chimica Acta, Vol. 33, 1965, pp. 217-218.
http://dx.doi.org/10.1016/S0003-2670(01)84877-7
[4] J. A. Goldman, “A General Equation for the Description of Redox Titration Curves,” Journal of Electroanalytical Chemistry, Vol. 11, No. 4, 1966, pp. 255-261.
http://dx.doi.org/10.1016/0022-0728(66)80090-6
[5] J. A. Goldman, “Further Considerations on Redox Titration Equations,” Journal of Electroanalytical Chemistry, Vol. 11, No. 6, 1966, pp. 416-424.
http://dx.doi.org/10.1016/0022-0728(66)80010-4
[6] J. A. Goldman, “The Locations of Inflection Points on Titration Curves for Symmetrical Redox Reactions,” Journal of Electroanalytical Chemistry, Vol. 14, No. 4, 1967, pp. 373-383.
http://dx.doi.org/10.1016/0022-0728(67)80018-4
[7] J. A. Goldman, “Redox Equilibria. V. The Locations of Inflection Points on Titration Curves for Homogeneous Reactions,” Journal of Electroanalytical Chemistry, Vol. 18, No. 1-2, 1968, pp. 41-45.
http://dx.doi.org/10.1016/S0022-0728(68)80158-5
[8] J. A. Goldman, “Redox Equilibria. Part VI. General Titration Curve Equation for Homogeneous and Symmetrical Redox Reactions,” Journal of Electroanalytical Chemistry, Vol. 19, No. 3, 1968, pp. 205-214.
http://dx.doi.org/10.1016/S0022-0728(68)80119-6
[9] A. Meretoja, O. Lukkari and E. Hakoila, “Redox Titrations—II. Location of Inflection Points on Titration Curves for Homogeneous Redox Reactions,” Talanta, Vol. 25, No. 10, 1978, pp. 557-562.
http://dx.doi.org/10.1016/0039-9140(78)80146-5
[10] J. Stur, M. Bos and W. E. van der Linden, “A Generalized Approach for the Calculation and Automation of Potentiometric Titrations Part 2. Redox Titrations,” Analytica Chimica Acta, Vol. 158, 1984, pp. 125-129.
http://dx.doi.org/10.1016/S0003-2670(00)84819-9
[11] R. de Levie, “A Simple Expression for the Redox Titration Curve,” Journal of Electroanalytical Chemistry, Vol. 323, No. 1-2, 1992, pp. 347-355.
http://dx.doi.org/10.1016/0022-0728(92)80022-V
[12] R. de Levie, “Advanced Excel for Scientific Data Analysis,” 2nd Edition, Oxford University Press, New York, 2008.
[13] G. Raj, “Advanced Physical Chemistry,” 35th Edition, GOEL Publ. House, 2009.
[14] T. Michalowski, “Calculation of pH and Potential E for Bromine Aqueous Solutions,” Journal of Chemical Education, Vol. 71, No. 7, 1994, pp. 560-562.
http://dx.doi.org/10.1021/ed071p560
[15] T. Michalowski and A. Lesiak, “Acid-Base Titration Curves in Disproportionating Redox Systems,” Journal of Chemical Education, Vol. 71, No. 8, 1994, pp. 632-636.
http://dx.doi.org/10.1021/ed071p632
[16] T. Michalowski and A. Lesiak, “Formulation of Generalized Equations for Redox Titration Curves,” Chemia Analityczna, Vol. 39, No. 4, 1994, pp. 623-637.
[17] T. Michalowski, N. Wajda and D. Janecki, “A Unified Quantitative Approach to Electrolytic Systems,” Chemia Analityczna, Vol. 41, No. 4, 1996, pp. 667-685.
[18] T. Michalowski, “Calculations in Analytical Chemistry with Elements of Computer Programming,” 2001.
http://suw.biblos.pk.edu.pl/resourceDetails&rId=3974.
[19] T. Michalowski, A. Baterowicz, A. Madej and J. Kochana, “An Extended Gran Method and Its Applicability for Simultaneous Determination of Fe(II) and Fe(III),” Analytica Chimica Acta, Vol. 442, No. 2, 2001, pp. 287-293.
http://dx.doi.org/10.1016/S0003-2670(01)01172-2
[20] T. Michalowski, M. Toporek and M. Rymanowski, “Overview on the Gran and Other Linearization Methods Applied in Titrimetric Analyses,” Talanta, Vol. 65, No. 5, 2005, pp. 1241-1253.
http://dx.doi.org/10.1016/j.talanta.2004.08.053
[21] T. Michalowski, M. Rymanowski and A. Pietrzyk, “Nontypical Bronsted Acids and Bases,” Journal of Chemical Education, Vol. 82, No. 3, 2005, pp. 470-472.
http://dx.doi.org/10.1021/ed082p470
[22] T. Michalowski, K. Kupiec and M. Rymanowski, “Numerical Analysis of the Gran Methods: A Comparative Study,” Analytica Chimica Acta, Vol. 606, No. 2, 2008, pp. 172-183. http://dx.doi.org/10.1016/j.aca.2007.11.020
[23] M. Ponikvar, T. Michalowski, K. Kupiec, S. Wybraniec and M. Rymanowski, “Experimental Verification of the Modified Gran Methods Applicable to Redox Systems,” Analytica Chimica Acta, Vol. 628, No. 2, 2008, pp. 181-189. http://dx.doi.org/10.1016/j.aca.2008.09.012
[24] T. Michalowski and A. Pietrzyk, “Complementarity of Physical and Chemical Laws of Conservation in Aspect of Electrolytic Systems (in Polish),” Wiadomosci Chemiczne, Vol. 61, No. 7-8, 2007, pp. 625-640.
[25] http://www.chemia.uj.edu.pl/~ictchem/book.html
[26] T. Michalowski, “The Generalized Approach to Electrolytic Systems: I. Physicochemical and Analytical Implications,” Critical Reviews in Analytical Chemistry, Vol. 40, No. 1, 2010, pp. 2-16.
http://dx.doi.org/10.1080/10408340903001292
[27] T. Michalowski, A. Pietrzyk, M. Ponikvar-Svet and M. Rymanowski, “Critical Reviews in Analytical Chemistry,” Vol. 40, No. 1, 2010, pp. 17-29.
http://dx.doi.org/10.1080/10408340903001292
[28] T. Michalowski, “Application of GATES and MATLAB for Resolution of Equilibrium, Metastable and Non-Equilibrium Electrolytic Systems,” Chapter 1, In: T. Michalowski, Ed., Applications of MATLAB in Science and Engineering, InTech, 2011, pp. 1-35.
http://www.intechopen.com/books/show/title/applications-of-matlab-in-science-and-engineering
[29] T. Michalowski, M. Ponikvar-Svet, A. G. Asuero and K. Kupiec, “Thermodynamic and Kinetic Effects Involved in the pH Titration of As(III) with Iodine in a Buffered Malonate System,” Journal of Solution Chemistry, Vol. 41, No. 3, 2012, pp. 436-446.
http://dx.doi.org/10.1007/s10953-012-9815-6
[30] T. Michalowski, M. Toporek, A. M. Michalowska-Kaczmarczyk and A. G. Asuero, “New Trends in Studies on Electrolytic Redox Systems,” Electrochimica Acta, Vol. 109, 2013, pp. 519-531.
[31] B. Nemzer, Z. Pietrzkowski, A. Spórna, P. Stalica, W. Thresher, T. Michalowski and S. Wybraniec, “Betalainic and Nutritional Profiles of Pigment-Enriched Red Beet Root (Beta vulgaris L.) Dried Extracts,” Food Chemistry, Vol. 127, No. 1, 2011, pp. 42-53.
http://dx.doi.org/10.1016/j.foodchem.2010.12.081
[32] S. Wybraniec and T. Michalowski, “New Pathways of Betanidin and Betanin Enzymatic Oxidation,” Journal of Agricultural and Food Chemistry, Vol. 59, No. 17, 2011, pp. 9612-9622. http://dx.doi.org/10.1021/jf2020107
[33] S. Wybraniec, P. Stalica, A. Spórna, B. Nemzer, Z. Pietrzkowski and T. Michalowski, “Antioxidant Activity of Betanidin: Electrochemical Study in Aqueous Media,” Journal of Agricultural and Food Chemistry, Vol. 59, No. 22, 2011, pp. 12163-12170.
http://dx.doi.org/10.1021/jf2024769
[34] S. Wybraniec, K. Starzak, A. Skopińska, M. Szaleniec, J. Slupski, K. Mitka, P. Kowalski and T. Michalowski, “Effects of Metal Cations on Betanin Stability in Aqueous-Organic Solutions,” Food Science and Biotechnology, Vol. 22, No. 2, 2013, pp. 353-363.
http://dx.doi.org/10.1007/s10068-013-0088-7
[35] S. Wybraniec, K. Starzak, A. Skopińska, B. Nemzer, Z. Pietrzkowski and T. Michalowski, “Studies on Non-Enzymatic Oxidation Mechanism in Neobetanin, Betanin and Decarboxylated Betanins, Journal of Agricultural and Food Chemistry, Vol. 61, No. 26, 2013, pp. 6465–6476.
[36] http://en.wikipedia.org/wiki/System_of_linear_equations
[37] J. Inczedy, “Analytical Applications of Complex Equilibria,” Horwood, Chichester, 1976.
[38] Yu. Lurie, “Handbook of Analytical Chemistry,” Mir Publishers, Moscow, 1975.
[39] B. P. Nikolsky, “Guide-Book for Chemist (in Russian),” Vol. 3, Khimia, Moscow, 1964.
[40] T. Michalowski, A. M. Michalowska-Kaczmarczyk and M. Toporek, “Formulation of General Criterion Distinguishing between Non-Redox and Redox Systems,” Electrochimica Acta.

  
comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.