# Electrochemical Fit

by Nikolai Shokhirev

• Background
• Algorithm
• References

### Background

Given:

 Reaction constant Reduced complex [(TPP)FeII(DMF)] + L = [(TPP)FeII(L)] + DMF ß1II = K1II [(TPP)FeII(L)] + L =  [(TPP)FeII(L)2] K2II Oxidized complex [(TPP)FeIII(DMF)2]+ClO4 ¯ + L = [(TPP)FeIII(L)(DMF)]+ClO4 ¯ + DMF ß1III = K1III [(TPP)FeIII(L)(DMF)]+ClO4 ¯ + L = [(TPP)FeIII(L)2]+ClO4 ¯ + DMF K2III Net reactions (TPP)FeII(DMF)] + 2 L = [(TPP)FeII(L)2] + DMF ß2II = K1II K2II [(TPP)FeIII(DMF)2]+ClO4 ¯ + 2 L = [(TPP)FeIII(L)2]+ClO4 ¯ + 2 DMF ß2III = K1III K2III

The Nernst equation connects the reaction constants with electrochemical potential : (1)

The potential (E1/2)C  is the function of the ligand concentration [L] (an independent variable) and depends on the reaction constants (ß1II, ß2II, ß1III, ß2III) as parameters. The experimental potentials [(E1/2)C]kExp measured at concentrations [Lk] should match the values calculated from the Nernst equation [(E1/2)C]kTheor . It can happen only for the specific set of the reaction constants. In principle, it gives the way of determination of the reaction constants.

In the above equation added ligand concentrations x are assumed to be the same as the free ligand concentrations [L] in solution, since the amount of ligand removed from solution due to binding to the porphyrin is negligible.

In the case of very strong binding, one must use very low ligand concentrations in the titration to observe potential changes. In this situation the porphyrin concentrations are about the same as the added ligand concentrations, and so the equilibrium free ligand concentration is actually significantly less than the ligand concentration we have added (due to ligand binding to the porphyrin).  So a correction needs to be made to the ligand added concentrations to get the equilibrium free ligand concentrations. (2)

Here S is the effective total number of sites for the ligand to bind to, and S is less than two times the porphyrin concentration, and x is the ligand added concentrations. Ratio R is the ratio of these sites that have ligand bound. Ratio is estimated from: (3)

### Algorithm

The algorithm is based on the methods of lest squares: "A mathematical procedure for finding the best fitting curve to a given set of points by minimizing the sum of the squares of the offsets ("the residuals") of the points from the curve". The description of fitting algorithms are presented here .

Program ElectrochemicalFit .

### References

1. "Models of the Cytochromes. The Redox Properties and Thermodynamic Stabilities of Complexes of "Hindered" Iron(III) and Iron(II) Tetraphenylporphyrinates with Substituted Pyridines and Imidazoles", Nesset, M. J. M.; Shokhirev, N. V.; Enemark, P. D.; Jacobson, S. E.; Walker, F. A. Inorg. Chem. 1996, 35,5188-5200.
2. Least Squares Fitting. Wolfram Research. http://mathworld.wolfram.com/LeastSquaresFitting.html

###### ABC Tutorials | Data Processing | Indirect Measurements | NMR Tutorials ###### Home | Resumé |  Shokhirev.com |  Computing |  Links |  Publications Please e-mail me at nikolai@shokhirev.com

©Nikolai Shokhirev, Robert E. Berry 2002-2009

/html>