Redox titration curve

To evaluate a redox titration we must know the shape of its titration curve. In an acid-base titration or a complexation titration, a titration curve shows the change in concentration of H3O+ (as pH) or M + (as pM) as a function of the volume of titrant. For a redox titration, it is convenient to monitor electrochemical potential. 

You will recall from Chapter 6 that the Nernst equation relates the electrochemical potential to the concentrations of reactants and products participating in a redox reaction. Consider, for example, a titration in which the analyte in a reduced state, Ared) is titrated with a titrant in an oxidized state, Tox- The titration reaction is 

The electrochemical potential for the reaction is the difference between the reduction potentials for the reduction and oxidation half-reactions thus, 

After each addition of titrant, the reaction between the analyte and titrant reaches a state of equilibrium. The reaction s electrochemical potential, Frxm therefore, is zero, and 

Consequently, the potential for either half-reaction may be used to monitor the titration s progress. 

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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. 

How to sketch a redox titration curve see text for explanation. 

Experimental arrangement for recording a potentiometric redox titration curve. 

Further proof is given by the observation of two titrating groups of equal contributions in the heme redox titration curve. (From Mileni et ah,... 

Schwertmann, 1993). Such soils are characterized by a hydraulic conductivity somewhere in the profile which is too low to cope with the high rainfall, so that all pores will be filled with water for certain periods of time (see above). In this case, the oxygen supply is limited by the low level of O2 dissolved in the soil water (46 mg O2 at 25 °C) and reduction of Mn-oxides, nitrate and Fe oxides sets in. Soils containing Fe oxides are, therefore, redox-buffered (poised). The redox titration curve (Fig. 16.14) of a soil with 23 g kg Fe as Fe oxides shows buffering at two different pe -1- pH levels, one at ca. 11 and another at ca. 9, which indicate the presence of a more reducible (e. g. ferrihydrite) and a less reducible (e. g. goethite) Fe oxide, respectively, in accordance with their different solubilities (see Chap. 9). 

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. 

Shape of a Redox Titration Curve 16-1. Consider the titration in Figure 16-2. 

The Student Web Site, www.whfreeman.com/cica7e, has directions for experiments that may be reproduced for your use. At this Web site, you will also find lists of experiments from the Journal of Chemical Education, a few downloadable Excel spreadsheets, and a few Living Graph Java applets that allow students to manipulate graphs by altering data points and variables. Supplementary topics at the Web site include spreadsheets for precipitation titrations, microequilibrium constants, spreadsheets for redox titration curves, and analysis of variance. 

Alternately, it is possible to strip the metal off by applying a constant anodic current through the electrode. The potential of the electrode, when monitored as a function of time, gives an experimental curve, analogous to a normal redox titration curve (Fig. 24.4), which contains the quantitative and qualitative information. A sudden change in the potential occurs when all the metal deposited in the electrode has been depleted from the surface. The time required to... 

Figure 8.25. Redox titration curve of a model groundwater system (a) pe response and (b) pH response. Numbered segments correspond to sequential reduction of (1) 02(aq), (2) N03 (aq), (3) Mn02(s), (4) Fe(OH)3(s), and (5) S04"(aq). (From Scott and Morgan, 1990.)...

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. 

Redox titration curves are symmetric when the reactants combine in a 1 1 ratio. Otherwise, they are asymmetric. 

The data in the third column of Table 19-2 are plotted as curve B in Figure 19-3 to compare the two titrations. The two curves are identical for volumes greater than 25.10 mL because the concentrati ons of the two cerium species are identical in this region. It is also interesting that the curve for iron(Il) is symmetric around the equivalence point, but the curve for uranium(IV) is not. In general, redox titration curves are symmetric when the analyte and titrant react in a 1 1 molar ratio. 

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.. ...

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