The formalism realised according to the Generalised Approach to Electrolytic Systems (GATES) is presented and applied to typical redox systems known from the laboratory practice. In any redox system, the Generalized Electron Balance (GEB), perceived as the law of the matter conservation, is derivable from linear combination 2· f (O) – f (H) of elemental balances: f (O) for oxygen and f (H) for hydrogen. It is an equation linearly independent from other (charge and concentration) balances referred to an electrolytic redox system (aqueous media) of any degree of complexity, and named as the pr imary form of GEB and then denoted as pr -GEB. A compact equation for GEB is obtained from linear combination of 2· f (O) – f (H) with other (charge and concentration) balances. For a non-redox electrolytic system, of any degree of complexity, the balance 2· f (O) – f (H) is not an independent equation. In the derivation of GEB, all known components (species) of the system tested, taken in their real ( i . e ., hydrated) form, are involved in the balances, and none simplifying assumptions are needed. The redox systems are simulated with use of an iterative computer program.
KeywordsSolution ThermodynamicsGeneralized Approach To Electrolytic SystemsGeneralized Electron BalanceRedox Titration
Michalowski, T., Toporek, M., Michalowska-Kaczmarczyk, A.M. and Asuero, A.G. (2013) New Trends in Studies on Electrolytic Redox Systems. Electrochimica Acta, 109, 519-531. http://dx.doi.org/10.1016/j.electacta.2013.07.125
Michalowski, T., Michalowska-Kaczmarczyk, A.M. and Toporek, M. (2013) Formulation of General Criterion Distinguishing between Non-Redox and Redox Systems. Electrochimica Acta, 112, 199-211. http://dx.doi.org/10.1016/j.electacta.2013.08.153
Michalowska-Kaczmarczyk, A.M. and Michalowski, T. (2013) Comparative Balancing of Non-Redox and Redox Electrolytic Systems and Its Consequences. American Journal of Analytical Chemistry, 4, 46-53. http://dx.doi.org/10.4236/ajac.2013.410A1006
Michalowska-Kaczmarczyk, A.M. and Michalowski, T. (2014) Compact Formulation of Redox Systems According to GATES/GEB Principles, Journal of Analytical Sciences. Methods and Instrumentation, 4, 39-45.
Michalowski, T. (2010) The Generalized Approach to Electrolytic Systems: I. Physicochemical and Analytical Implications. Critical Reviews in Analytical Chemistry, 40, 2-16. http://dx.doi.org/10.1080/10408340903001292
Michalowski, T. (2011) Application of GATES and MATLAB for Resolution of Equilibrium, Metastable and Non-Equilibrium Electrolytic Systems. In: Michalowski, T., Ed., Applications of MATLAB in Science and Engineering, Chapter 1, InTech—Open Access Publisher in the Fields of Science, Technology and Medicine, Rijeka, Croatia. http://www.intechopen.com/books/show/title/applications-of-matlab-in-science-and-engineering .
Michalowski, T. (1994) Calculation of pH and Potential E for Bromine Aqueous Solutions. Journal of Chemical Education, 71, 560-562. http://dx.doi.org/10.1021/ed071p560
Michalowski, T. and Lesiak, A. (1994) Acid-Base Titration Curves in Disproportionating Redox Systems. Journal of Chemical Education, 71, 632-636. http://dx.doi.org/10.1021/ed071p632
Michalowski, T. and Lesiak, A. (1994) Formulation of Generalized Equations for Redox Titration Curves. Chemia Analityczna (Analytical Chemistry) (Warsaw), 39, 623-637.
Michalowski, T., Wajda, N. and Janecki, D. (1996) A Unified Quantitative Approach to Electrolytic Systems. Chemia Analityczna (Analytical Chemistry) (Warsaw), 41, 667-685.
Michalowski, T. (2001) Calculations in Analytical Chemistry with Elements of Computer Programming (in Polish). PK, Cracow.
Michalowski, T. (2007) Complementarity of Physical and Chemical Laws in the Context of Electrolytic Systems. In: Maciejowska, I., Ruszak, M. and Witkowski, S., Eds, Use of Information Technology in Academic Teaching of Chemistry, Jagiellonian University, Cracow, 155-161. http://www.chemia.uj.edu.pl/~ictchem/book.html
Michalowski, T., Baterowicz, A., Madej, A. and Kochana, J. (2001) Extended Gran Method and Its Applicability for Simultaneous Determination of Fe(II) and Fe(III). Analytica Chimica Acta, 442, 287-293. http://dx.doi.org/10.1016/S0003-2670(01)01172-2
Michalowski, T., Toporek, M. and Rymanowski, M. (2005) Overview on the Gran and Other Linearization Methods Applied in Titrimetric Analyses. Talanta, 65, 1241-1253. http://dx.doi.org/10.1016/j.talanta.2004.08.053
Michalowski, T., Kupiec, K. and Rymanowski, M. (2008) Numerical Analysis of the Gran Methods A Comparative Study. Analytica Chimica Acta, 606, 172-183. http://dx.doi.org/10.1016/j.aca.2007.11.020
Ponikvar, M., Michalowski, T., Kupiec, K., Wybraniec, S. and Rymanowski, M. (2008) Experimental Verification of the Modified Gran Methods Applicable to Redox Systems. Analytica Chimica Acta, 628, 181-189. http://dx.doi.org/10.1016/j.aca.2008.09.012
Inczedy, J. (1976) Analytical Applications of Complex Equilibia. E. Horwood, Chichester.
Lurie, Yu. (1971) Handbook of Analytical Chemistry (in Russian). Izd. Khimia, Moscow.
Trasatti, S. (1986) The Absolute Electrode Potential: An Explanatory Note (Recommendations 1986). International Union of Pure and Applied Chemistry, Pure and Applied Chemistry, 58, 955-966. http://dx.doi.org/10.1351/pac198658070955
Tsiplakides, D. and Vayenas, C.G. (2002) The Absolute Potential Scale in Solid State Electrochemistry. Solid State Ionics, 152-153, 625-639. http://dx.doi.org/10.1016/S0167-2738(02)00396-X
Tsiplakides, D. and Vayenas, C.G. (2011) Electrode Work Function and Absolute Potential Scale in Solid State Electrochemistry. In: Comninellis, C., Doyle, M. and Winnick, J., Eds., Energy and Electrochemical Processes for a Cleaner Environment, Electrochemical Society Proceedings, Inc., 206. http://www.iupac.org/publications/pac/1986/pdf/5807x0955.pdf
Asuero, A.G. and Michalowski, T. (2011) Comprehensive Formulation of Titration Curves for Complex Acid-Base Systems and Its Analytical Implications. Critical Reviews in Analytical Chemistry, 41, 151-187. http://dx.doi.org/10.1080/10408347.2011.559440
Michalowski, T., Ponikvar-Svet, M., Asuero, A.G. and Kupiec, K. (2012) Thermodynamic and Kinetic Effects Involved with pH Titration of As(III) with Iodine in a Buffered Malonate System. Journal of Solution Chemistry, 41, 436-446. http://dx.doi.org/10.1007/s10953-012-9815-6
Michalowski, T., Pietrzyk, A., Ponikvar-Svet, M. and Rymanowski, M. (2010) The Generalized Approach to Electrolytic Systems: II. The Generalized Equivalent Mass (GEM) Concept. Critical Reviews in Analytical Chemistry, 40, 17-29. http://dx.doi.org/10.1080/10408340903001342
Michalowski, T., Asuero, A.G., Ponikvar-Svet, M., Toporek, M., Pietrzyk, A. and Rymanowski, M. (2012) Liebig-Deniges Method of Cyanide Determination: A Comparative Study of Two Approaches. Journal of Solution Chemistry, 41, 1224-1239. http://dx.doi.org/10.1007/s10953-012-9864-x
Michalowski, T., Rymanowski, M. and Pietrzyk, A. (2005) Nontypical Bronsted Acids and Bases. Journal of Chemical Education, 82, 470-472. http://dx.doi.org/10.1021/ed082p470
Pourbaix, M. (1963) Atlas of Electrochemical Equilibria. Gauthier-Villars, Paris.
Walling, C. (1975) Fenton’s Reagent Revisited. Accounts of Chemical Research, 8, 125-131. http://dx.doi.org/10.1021/ar50088a003
Luehrs, D.C. and Roher, A.E. (2007) Demonstration of the Fenton Reaction. Journal of Chemical Education, 84, 1290. http://dx.doi.org/10.1021/ed084p1290
Wink, D.A., Wink, C.B., Nims, R.W. and Ford, P.C. (1994) Oxidizing Intermediates Generated in the Fenton Reagent: Kinetic Arguments against the Intermediacy of the Hydroxyl Radical. Environmental Health Perspectives, 102, 11-15. http://dx.doi.org/10.1289/ehp.94102s311
De Heredia, J.B., Torregrosa, J., Dominguez, J.R. and Perez, J.A. (2001) Kinetic Model for Phenolic Compound Oxidation by Fenton’s Reagent. Chemosphere, 45, 85-90. http://dx.doi.org/10.1016/S0045-6535(01)00056-X
Panzella, L., Manini, P., Napolitano, A. and d’Ischia, M. (2004) Free Radical Oxidation of (E)-Retinoic Acid by the Fenton Reagent: Competing Epoxidation and Oxidative Breakdown Pathways and Novel Products of 5,6-Epoxyretinoic Acid Transformation. Chemical Research in Toxicology, 17, 1716-1724. http://dx.doi.org/10.1021/tx049794b
Lin, Y.H. and Wang, T.H. (2001) Weibull Modeling of the Fenton’s Oxidation Process. Journal of Environmental Science and Health. Part A, Toxic/Hazardous Substances & Environmental Engineering, 36, 17-23. http://dx.doi.org/10.1081/ESE-100000468
Goldstein, S., Meyerstein, D. and Czapski, G. (1993) The Fenton Reagents. Free Radical Biology and Medicine, 15, 435-445. http://dx.doi.org/10.1016/0891-5849(93)90043-T
Pietrzkowski, Z., Nemzer, B., Spórna, A., Stalica, P., Treser, W., Keller, R., Jimenez, R., Michalowski, T. and Wybraniec, S. (2010) Influence of Betalain-Rich Extract on Reduction of Discomfort Associated with Osteoarthritis. New Medicine, 1, 12-17.
Nemzer, B., Pietrzkowski, Z., Spórna, A., Stalica, P., Thresher, W., Michalowski, T. and Wybraniec, S. (2011) Betalainic and Nutritional Profiles of Pigment-Enriched Red Beet Root (Beta vulgaris L.) Dried Extracts. Food Chemistry, 127, 42-53. http://dx.doi.org/10.1016/j.foodchem.2010.12.081
Wybraniec, S. and Michalowski, T. (2011) New Pathways of Betanidin and Betanin Enzymatic Oxidation. Journal of Agricultural and Food Chemistry, 59, 9612-9622. http://dx.doi.org/10.1021/jf2020107
Wybraniec, S., Stalica, P., Spórna, A., Nemzer, B., Pietrzkowski, Z. and Michalowski, T. (2011) Antioxidant Activity of Betanidin: Electrochemical Study in Aqueous Media. Journal of Agricultural and Food Chemistry, 59, 12163-12170. http://dx.doi.org/10.1021/jf2024769
Wybraniec, S., Starzak, K., Skopińska, A., Szaleniec, M., Slupski, J., Mitka, K., Kowalski, P. and Michalowski, T. (2013) Effects of Metal Cations on Betanin Stability in Aqueous-Organic Solutions. Food Science and Biotechnology, 22, 353-363. http://dx.doi.org/10.1007/s10068-013-0088-7
Wybraniec, S., Starzak, K., Skopińska, A., Nemzer, B., Pietrzkowski, Z. and Michalowski, T. (2013) Studies on Non-Enzymatic Oxidation Mechanism in Neobetanin, Betanin and Decarboxylated Betanins. Journal of Agricultural and Food Chemistry, 61, 6465-6476. http://dx.doi.org/10.1021/jf400818s
Bard, A.J. and Simonsen, S.H. (1960) The General Equation for the Equivalence Point Potential in Oxidation-Reduction Titrations. Journal of Chemical Education, 37, 364-366. http://dx.doi.org/10.1021/ed037p364
Bishop, E. (1962) Some Theoretical Considerations in Analytical Chemistry: Part VI. The Precise Calculation of Data for Redox Titration Curves. Analytica Chimica Acta, 26, 397-405. http://dx.doi.org/10.1016/S0003-2670(00)88405-6
Goldman, J.A. (1965) The Equivalence Point Potential in Redox Titrations. Analytica Chimica Acta, 33, 217-218. http://dx.doi.org/10.1016/S0003-2670(01)84877-7
Goldman, J.A. (1966) Further Considerations on Redox Titration Equations. Journal of Electroanalytical Chemistry, 11, 416-424. http://dx.doi.org/10.1016/0022-0728(66)80010-4
Goldman, J.A. (1966) A General Equation for the Description of Redox Titration Curves. Journal of Electroanalytical Chemistry, 11, 255-261. http://dx.doi.org/10.1016/0022-0728(66)80090-6
Goldman, J.A. (1967) The Locations of Inflection Points on Titration Curves for Symmetrical Redox Reactions. Journal of Electroanalytical Chemistry and Interfacial Electrochemistry, 14, 373-383. http://dx.doi.org/10.1016/0022-0728(67)80018-4
Goldman, J.A. (1968) Redox Equilibria, Part IV. Titration Curve Equations for Homogeneous and Symmetrical Redox Reactions. Journal of Electroanalytical Chemistry and Interfacial Electrochemistry, 16, 47-59. http://dx.doi.org/10.1016/S0022-0728(68)80276-1
Goldman, J.A. (1968) Redox Equilibria: V. The Locations of Inflection Points on Titration Curves for Homogeneous Reactions. Journal of Electroanalytical Chemistry and Interfacial Electrochemistry, 18, 41-45. http://dx.doi.org/10.1016/S0022-0728(68)80158-5
Goldman, J.A. (1968) Redox Equilibria: Part VI. A Completely General Titration Curve Equation for Homogeneous and Symmetrical Redox Reactions. Journal of Electroanalytical Chemistry and Interfacial Electrochemistry, 19, 205-214. http://dx.doi.org/10.1016/S0022-0728(68)80119-6
Sriramam, K. (1976) A Study on the Theory of Action of Reversible Redox Indicators. Talanta, 23, 864-866. http://dx.doi.org/10.1016/0039-9140(76)80107-5
Meretoja, A., Lukkari, O. and Hakoila, E. (1978) Redox Titrations-II. Location of Inflection Points on Titration Curves for Homogeneous Redox Reactions. Talanta, 25, 557-562. http://dx.doi.org/10.1016/0039-9140(78)80146-5
Stur, J., Bos, M. and van der Linden, W.E. (1984) A Generalized Approach for the Calculation and Automation of Potentiometric Titrations Part 2. Redox Titrations. Analytica Chimica Acta, 158, 125-129. http://dx.doi.org/10.1016/S0003-2670(00)84819-9
de Levie, R. (1992) A Simple Expression for the Redox Titration Curve. Journal of Electroanalytical Chemistry, 323, 347-355. http://dx.doi.org/10.1016/0022-0728(92)80022-V
da Conceicao Silva Barreto, M., de Lucena Medeiros, L. and César de Holanda Furtado, P. (2001) Indirect Potentiometric Titration of Fe(III) with Ce(IV) by Gran’s Method. Journal of Chemical Education, 78, 91. http://dx.doi.org/10.1021/ed078p91
Michalowski, T., Toporek, M. and Rymanowski, M. (2007) pH-Static Titration: A Quasistatic Approach. Journal of Chemical Education, 84, 142-150. http://dx.doi.org/10.1021/ed084p142
Nóbrega, J.A. and Rocha, F.R.P. (1997) Ionic Strength Effect on the Rate of Reduction of Hexacyanoferrate(III) by Ascorbic Acid: A Flow Injection Kinetic Experiment. Journal of Chemical Education, 74, 560-562. http://dx.doi.org/10.1021/ed074p560
Huang, T.H., Salter, G., Kahn, S.L. and Gindt, Y.M. (2007) Redox Titration of Ferricyanide to Ferrocyanide with Ascorbic Acid: Illustrating the Nernst Equation and Beer-Lambert Law. Journal of Chemical Education, 84, 1461-1463. http://dx.doi.org/10.1021/ed084p1461
Labarca, M. and Lombardi, O. (2008) The End of the Dream of Unity. Current Science, 94, 438-439.