Redox titration calculation

Sketching a Redox Titration Curve As we have done for acid-base and complexo-metric titrations, we now show how to quickly sketch a redox titration curve using a minimum number of calculations. 

Where Is the Equivalence Point In discussing acid-base titrations and com-plexometric titrations, we noted that the equivalence point is almost identical with the inflection point located in the sharply rising part of the titration curve. If you look back at Figures 9.8 and 9.28, you will see that for acid-base and com-plexometric titrations the inflection point is also in the middle of the titration curve s sharp rise (we call this a symmetrical equivalence point). This makes it relatively easy to find the equivalence point when you sketch these titration curves. When the stoichiometry of a redox titration is symmetrical (one mole analyte per mole of titrant), then the equivalence point also is symmetrical. If the stoichiometry is not symmetrical, then the equivalence point will lie closer to the top or bottom of the titration curve s sharp rise. In this case the equivalence point is said to be asymmetrical. Example 9.12 shows how to calculate the equivalence point potential in this situation. 

Calculate or sketch (or both) titration curves for the following (unbalanced) redox titration reactions at 25 °C. Assume that the analyte is initially present at a concentration of 0.0100 M and that a 25.0-mL sample is taken for analysis. The titrant, which is the underlined species in each reaction, is 0.0100 M. 

Fig. 7. A comparison of the FTIR and EPR redox titrations of the D. gigas hydro-genase. Top panel FTIR titration based on the height of the low-frequency band. For experimental conditions, see (65). Bottom panel Calculated potentials obtained from EPR-monitor titration and the TED model (80). The vertical axis represents the proportion of a redox species.

Following are some examples of analytical calculations involving redox titrations. 

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. 

D. W. King, A General Approach for Calculating Spedation and Poising Capacity of Redox Systems with Multiple Oxidation States Application to Redox Titrations and the Generation of pe-pH Diagrams, J. Chem. Ed. 2002, 79, 1135. 

FIGURE 4.5 A flow diagram for a redox titration, summarizing the calculations needed to determine the concentration of a KMn04 solution by titration of a known mass of H2C204. 

Not all redox titrations have a well-defined equivalence point, and amperometric titrations1, in which a potential corresponding normally to that necessary to attain the mass-transport-limited current is applied to the working (indicator) electrode, permit the calculation of the titration endpoint through measurements done far from the equivalence point. Titrations can be done in flow systems, and in this sense it is possible to alter the quantity of added titrant so as to obtain greater accuracy in the determination of the equivalence point2. 

While the redox titration method is potentiometric, the spectroelectrochemistry method is potentiostatic [99]. In this method, the protein solution is introduced into an optically transparent thin layer electrochemical cell. The potential of the transparent electrode is held constant until the ratio of the oxidized to reduced forms of the protein attains equilibrium, according to the Nemst equation. The oxidation-reduction state of the protein is determined by directly measuring the spectra through the tranparent electrode. In this method, as in the redox titration method, the spectral characterization of redox species is required. A series of potentials are sequentially potentiostated so that different oxidized/reduced ratios are obtained. The data is then adjusted to the Nemst equation in order to calculate the standard redox potential of the proteic species. Errors in redox potentials estimated with this method may be in the order of 3 mV. 

If both the half-reactions involved in a redox titration can be made to behave reversibly at a suitable electrode, the shapes of the titration curves should conform closely to the calculated values, though as pointed out above, the electrode potential reaches its equilibrium value more and more slowly with increasing dilution. 

Balance equations for redox reactions in aqueous solution, using the halfreaction method, and calculate the concentrations of substances during redox titrations (Section 11.4, Problems 27-40). 

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. 

At this point, we should mention that some redox titration expressions are more complex than those presented here for a basic 1 1 situation. If you are interested in exploring the master equation approach for pH-dependent redox titrations or other situations, consult the paper by de Levie. You can find the details of the calculations for the two plots in this feature in Chapter 10 of Applications of Microsoft Excel in Analytical Chemistry. 

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. 

Fig. 6. Direct redox titration of FeS-X by monitoring the amplitude of light-induced EPR signal at 9 K as a function of redox potential. (A) EPR spectra of PS-1 particles titrated to -680 and -749 mV recorded in the dark (solid lines) and under illumination (dashed lines). (B) Plot of EPR signal at g=1.76 vs. potential. The solid-line plot was calculated from the Nernst equation for n=1 and E = -705 mV. Figure source Chamorovsky and Cammack (1982) Direct determination of the midpoint potential of the acceptor X in chloroplast photosystem I by electrochemical reduction and ESR spectroscopy. Photobiochem Photobiophys 4 198, 199,...

Redox titrations require the same type of calculations (based on the mole method) as acid-base neutralizations. The difference is that the equations and the stoichiometry tend to be more complex for redox reactions. The following is an example of a redox titration. 

Calculations of this type are used for the redox titrations described in Chapter 14. 

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... 

Because there is generally no difficulty in finding a.suitable indicator electrode, redox titrations are widely used an inert metal such as platinum is usually satisfactory for the electrode. Both the oxidized and reduced forms are usually soluble and their ratio varies throughout the titration. The potential of the indicating electrode will vary in direct proportion to log as in the calculated potential for the... 

Pterin-Molybdenum Redox Chemistry. The early studies focused on Mo(vi) and tetrahydropterin reagents to closely mimic the Mo and pterin portions of Moco. These studies showed that a variety of dioxo-Mo(vi) complexes reacted with tetrahydropterins to produce intensely colored mono-0x0 Mo complexes, but the reports offered different interpretations of what reaction had occurred and what resulting oxidation states of molybdenum and pterin had been produced, even when X-ray structures of the product Mo-pterin complexes were available. A clear picture of the electronic structure was eventually developed from redox titrations, reactivity studies, theoretical calculations and X-ray photoelectron spectroscopy (XPS) studies. 

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... 

By chemical redox titration, the concentration of active P700 determined. The ratio of Chl/P QQ was calculated using an extinction coefficient of 64 000 at 700 nm. 

Based on this model, and by using the values of the different quantities determined experimentally (the protonation constants of the oxidized and reduced forms determined by titration, volume changes during the redox transformation, the number of redox centers calculated from the charge consumed), the calculations led to reasonable results which are in accordance with earlier findings. Figures 5.4 and 5.5 show the results of the calculation for the solvent and ion populations. 

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