Redox Titration Curve Equations

at any stage during the titration the reduced form of the titrant and the oxidized form of the system being titrated are equivalent. 

Utilizing the treatment developed in Chapter 7 to describe concentrations in terms of f fractions, we have 

Selected points along the titration curve are calculated in a manner that closely resembles those we used in the last two chapters. With oxidation-reduction titrations, the method is even simpler when we recognize that on either side of the equivalence point there is an excess of one of the two redox couples, allowing us to calculate the concentration ratio of oxidized to reduced forms of the substance being titrated or of the titrant. Knowing 

What are the pE values of a 50 mL portion of a solution of 0.005 M SnCl2 when (a) 5 mL (b) 60 mL of a 0.01 M FeClj titrant have been added The two points have been selected so that they typify calculations on each side of the equivalence point. 

Note that in the logarithm, the amoimt in mmoles rather than the concentrations were used. The solution volumes cancel out in a ratio. Hence, except for very dilute solutions and, of course, activity coefficient changes, pE will be independent of total concentrations. 

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Anyone with a serious need to calculate redox titration curves should use a spreadsheet with a more general set of equations than we use in this section.5 The supplement at www.freeman.com/qca explains how to use spreadsheets to compute redox titration curves. 

We will use standard electrode potentials throughout the rest of this text to calculate cell potentials and equilibrium constants for redox reactions as well as to calculate data for redox titration curves. You should be aware that such calculations sometimes lead to results that are significantly different from those you would obtain in the laboratory. There are two main sources of these differences (1) the necessity of using concentrations in place of activities in the Nernst equation and (2) failure to take into account other equilibria such as dissociation, association, complex formation, and solvolysis. Measurement of electrode potentials can allow us to investigate these equilibria and determine their equilibrium constants, however. 

The Inverse Master Equation Approach for Redox Titration Curves... 

Spreadsheet Summary in Chapter 10 of Applications of Microsoft Excel in Analytical Chemistry, Excel is used to obtain a values for redox species. These show how the species concentrations change throughout a redox titration. Redox titration curves are developed by both a stoichiometric and a master equation approach. The stoichiometric approach is also used for a system that is pH dependent. 

Fig. 6 (C) shows the redox titration curve consisting of data points from triplet signals produced in samples poised at various potentials at pH 11. Again, the solid curve is a fit for the Nernst equation based on a one-electron change. The empty-circled data points are taken from the reductive titrations, and several data points (solid-dots) are shown for the reverse oxidative titration. All points coincide reasonably well with the theoretical curve, confirming that the redox reaction is reversible.The redox potential of estimated from the titration curve is -604 mV, very close to the value derived from the attenuated absorbance-change measurements by Klimov etal.. ...

Before we discuss redox titration curves based on reduction-oxidation potentials, we need to learn how to calculate equilibrium constants for redox reactions from the half-reaction potentials. The reaction equilibrium constant is used in calculating equilibrium concentrations at the equivalence point, in order to calculate the equivalence point potential. Recall from Chapter 12 that since a cell voltage is zero at reaction equilibrium, the difference between the two half-reaction potentials is zero (or the two potentials are equal), and the Nemst equations for the halfreactions can be equated. When the equations are combined, the log term is that of the equilibrium constant expression for the reaction (see Equation 12.20), and a numerical value can be calculated for the equilibrium constant. This is a consequence of the relationship between the free energy and the equilibrium constant of a reaction. Recall from Equation 6.10 that AG° = —RT In K. Since AG° = —nFE° for the reaction, then... 

The study given here is uncommon since it is systematically based on the general equations governing the redox titration curves and, more precisely, by starting with them. This is not the case in the literature, in which the general equations are rarely mentioned. 

In the practice of potentiometric titration there are two aspects to be dealt with first the shape of the titration curve, i.e., its qualitative aspect, and second the titration end-point, i.e., its quantitative aspect. In relation to these aspects, an answer should also be given to the questions of analogy and/or mutual differences between the potentiometric curves of the acid-base, precipitation, complex-formation and redox reactions during titration. Excellent guidance is given by the Nernst equation, while the acid-base titration may serve as a basic model. Further, for convenience we start from the following fairly approximate assumptions (1) as titrations usually take place in dilute (0.1 M) solutions we use ion concentrations in the Nernst equation, etc., instead of ion activities and (2) during titration the volume of the reaction solution is considered to remain constant. 

Construct a coulometric titration curve of 100.0 mL of a 1 M H2SO4 solution containing Fe(ll) titrated with Ce(lV) generated from 0.075 M Ce(lll). The titration is monitored by potentiometry. The initial amount of Fe(II) present is 0.05182 mmol. A constant current of 20.0 mA is used. Find the time corresponding to the equivalence point. Then, for about 10 values of time before the equivalence point, use the stoichiometry of the reaction to calculate the amount of Fe produced and the amount of Fe + remaining. Use the Nemst equation to find the system potential. Find the equivalence point potential in the usual manner for a redox titration. For about 10 times after the equivalence point, calculate the amount of Ce " produced from the electrolysis and the amount of Ce + remaining. Plot the curve of system potential versus electrolysis time. 

T raditionally, titration curve calculations are described in terms of equations that are valid only for parts of the titration. Equations will be developed here that reliably describe the entire curve. This will be done first for acid-base titration curves. In following chapters, titration curves for other reaction systems (metal complexation, redox, precipitation) will be developed and characterized in a similar fashion. For all, graphical and algebraic means of locating the endpoints will be described, colorimetric indicators and how they function will be explained, and the application of these considerations to (1) calculation of titration errors, (2) buffo design and evaluation, (3) sharpness of titrations, and finally, (4) in Chapter 18, the use of titration curve data to the determination of equilibrium constants will be presented. 

This approach is effective not only for calculations involving individual solutions. The PBE and other balance equations apply to titration curve calculations as well. A single, easily derived, equation suffices to describe all points on a titration curve, be it for acid-base, complexometric, redox, or precipitation titrations. 

The concept of formal potentials has been developed for the mathematical treatment of redox titrations, because it was quickly realized that the standard potentials cannot be used to explain potentiometric titration curves. Generally, formal potentials are experimentally determined using equations similar to Eq. (1.2.24) because it is easy to control the overall concentrations of species in the two redox states. For calculating formal potentials it would be necessary to know the standard potential, all equilibrium constants of side reactions , and the concentrations of all solution constituents. In many cases this is still impossible as many equilibrium constants and the underlying chemical equilibria are still unknown. It is the great advantage of the concept of formal potentials to enable a quantitative description of the redox... 

Fig. 6. (A) Plot of amplitude of light-induced pheophytin-reduction signal vs. ambient potential of the medium. (B) Effed of ambient redox potential on the extent of light-induced PS-II reaction-center triplet signal in pea chloroplast particles. (C) Plot of the extent of the light-induced triplet EPR signal in (B) vs. redox potential. Open and closed circles are for reductive and oxidative titrations, respedively. The solid curve is a computer fit of the Nernst equation with n=1 and E , was estimated to be -604 mV. Figure source (A) Klimov. Allakhverdiev. Demeter and Krasnovsky (1979) Photoreduction ofpheophytin in photosystem 2 ofchloroplasts with respect to the redox potential of the medium. DokI Akad NaukSSSR 249 229 (B and C) Rutherford, Mullet and Crofts (1981) Measurement of the midpoint potential of the pheophytin acceptor of photosystem II. FEBS Lett 123 236,237...

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