Titration curves oxidation/reduction

In Sections 10.11-10.16 it is shown how the change in pH during acid-base titrations may be calculated, and how the titration curves thus obtained can be used (a) to ascertain the most suitable indicator to be used in a given titration, and (b) to determine the titration error. Similar procedures may be carried out for oxidation-reduction titrations. Consider first a simple case which involves only change in ionic charge, and is theoretically independent of the hydrogen-ion concentration. A suitable example, for purposes of illustration, is the titration of 100 mL of 0.1M iron(II) with 0.1M cerium(IV) in the presence of dilute sulphuric acid ... 

It is possible to titrate two substances by the same titrant provided that the standard potentials of the substances being titrated, and their oxidation or reduction products, differ by about 0.2 V. Stepwise titration curves are obtained in the titration of mixtures or of substances having several oxidation states. Thus the titration of a solution containing Cr(VI), Fe(III) and V(V) by an acid titanium(III) chloride solution is an example of such a mixture in the first step Cr(VI) is reduced to Cr(III) and V(V) to V(IV) in the second step Fe(III) is reduced to Fe(II) in the third step V(IV) is reduced to V(III) chromium is evaluated by difference of the volumes of titrant used in the first and third steps. Another example is the titration of a mixture of Fe(II) and V(IV) sulphates with Ce(IV) sulphate in dilute sulphuric acid in the first step Fe(II) is oxidised to Fe(III) and in the second jump V(IV) is oxidised to V(V) the latter change is accelerated by heating the solution after oxidation of the Fe(II) ion is complete. The titration of a substance having several oxidation states is exemplified by the stepwise reduction by acid chromium(II) chloride of Cu(II) ion to the Cu(I) state and then to the metal. 

Goldaman, J.A., Oxidation—Reduction Equilibria and Titration Curves , In Treatise on Analytical Chemistry, ed. by I.M. Kolthoff and PJ. Elving, 2nd ed., Vol. 3, New York, Interscience Publications, John Wiley Sons Inc., 1983. 

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). 

We now turn our attention to details of precipitation titrations as an illustration of principles that underlie all titrations. We first study how concentrations of analyte and titrant vary during a titration and then derive equations that can be used to predict titration curves. One reason to calculate titration curves is to understand the chemistry that occurs during titrations. A second reason is to learn how experimental control can be exerted to influence the quality of an analytical titration. For example, certain titrations conducted at the wrong pH could give no discernible end point. In precipitation titrations, the concentrations of analyte and titrant and the size of Ksp influence the sharpness of the end point. For acid-base titrations (Chapter 11) and oxidation-reduction titrations (Chapter 16). the theoretical titration curve enables us to choose an appropriate indicator. 

Fig. 9. A reductive titration of the crystalline bovine heart cytochrome c oxidase with dithionite. Absolute spectra for each oxidation state are shown for the Soret (A) and visible (B) regions. The difference spectra against the spectrum in the fully reduced state are given for the near-infrared region (C). The insets show titration curves against the electron equivalent per enzyme. The reaction mixture contained 7.5 jlM bovine heart cytochrome c oxidase in 0.1 M sodium phosphate buffer, pH 7.4. The enzyme preparation was stabilized with a synthetic non-ionic detergent, CH3(CH2)ii(0CH2CH2)80H. The light path was 1 cm.

The potential thus depends on the volume of the solution, and hence the position of the curve showing the variation of the oxidation-reduction potential during the course of the titration of H2Q by a strong oxidizing agent varies with the concentration of the solution. At constant volume equation (32) becomes... 

In Fe(II)-dichromate titrations, Winter and Moyer observed a time dependence of the potential after the end point. When potential readings were taken soon after each addition, an asymmetrical titration curve was observed, but when a time interval of 10 to 15 min was allowed after each addition, the curve approached the theoretical shape. We have noted that automatically recorded titration curves for the Fe(II)-dichromate titration show a considerably smaller potential jump than manually observed curves, the difference being due to lower potentials after the end point. But curves plotted with 15 s of waiting for each point differed only slightly from curves plotted with 150 s of waiting. Ross and Shain also studied the drift in potential of platinum electrodes with time and noted hysteresis effects in recorded potentiometric titration curves. These effects, due to oxidation and reduction of the platinum surface, are discussed below. 

Surface oxide formation undoubtedly is involved in the Fe(II)-dichromate titration curves, which Smith and Brandt found to be different when the direction of titration was reversed (Figure 15-2, right). Kolthoff and Tanaka found that the rate of oxidation with dichromate was slow, whereas the rate of reduction with Fe(II) was fast. Ross and Shain found the same sort of behavior and noted also that the rates of oxidation and reduction decreased in more dilute solutions. The oxidized surface in a dichromate solution may be largely covered with adsorbed dichromate, as chromium surfaces have been shown to be in some experiments with radio-chromium, so that it is relatively ineffective as an electron-transfer surface for the Fe(III)-Fe(II) system. 

In the foregoing discussion the indicator has tacitly been assumed to come rapidly to equilibrium at each point of the titration curve. That this is an over-simplihcation is evident from a number of experimental observations. Kolthoflf and Sarver found that the oxidation of diphenylamine with dichromate is induced by the Fe(II)-dichromate reaction. The direct oxidation is so slow that the indicator blank is best determined by comparison of the visual with the potentiometric end point. With ferroin. Smith and Brandt and Stockdale foimd that the reverse titration, dichromate with iron, gave satisfactory results at sufficiently high acidities, whereas the direct titration failed because the indicator could not be oxidized. Here the oxidation seems to be slow and the reduction rapid because of the irreversible nature of the oxidant and the reversible nature of the reductant. 

The shape of the curve for an oxidation-reduction titration depends on the nature of the system under consideration. The titration curve in Fig. 7 is symmetric about the equivalence point because the molar ratio of oxidant to reductant is equal to unity. An asymmetrical curve results if the ratio differs from this value. Solutions containing two oxidizing or reducing agents yield titration curves containing two inflection points if the standard potentials for the two species are different by more than approximately 0.2 V. Fig. 8 shows the titration curve for a mixture of iron(II) and titanium(III) with cerium(rV). The first additions of cerium are used by more readily oxidized titanium(III) ion, thus, the first step in the titration curve corresponds to titanium and the second to iron. 

Twin polarized platinum microelectrodes are conveniently used for endpoint detection for oxidation-reduction titrations. Consider a titration curve for oxidation-reduction titration where both reactants behave reversibly at the electrodes. An example of this kind of titration is titration of iron(II) with cerium(IV) (Fig. 14A). At the starting point of the titration, no current is observed because no suitable cathode reactant is available. With addition of cerium(IV), a mixture of iron(II) and iron(III) is produced, which permits the passage of current. Beyond the midpoint in the titration, iron(III) becomes in excess, and the current is then regulated by decreasing iron(II) concentration. At the equivalence point, the current approaches zero because iron(III) are present, and the applied potential is not great enough to cause these to react at the electrode. Beyond the equivalence point, the current rises again because both cerium(III) and cerium(IV) are present to react at the electrodes. 

Because most redox indicators respond to changes in electrode potential, the vertical axis in oxidation/reduction titration curves is generally an electrode potential instead of the logarithmic p-functions that were used for complex formation and... 

In earlier chapters, we considered the effects of reactant concentrations and completeness of the reaction on titration curves. Here, we describe the effects of these variables on oxidation/reduction titration curves. 

As we have just seen, system for oxidation/reduction titration is usually independent of dilution. Consequently, titration curves for oxidation/reduction reactions are usually independent of analyte and reagent concentrations. This characteristic is in distinct contrast to that observed in the other types of titration curves we have encountered. 

How is an oxidation/reduction titration curve generated through the use of standard electrode potentials for the analyte species and the volumetric titrant ... 

Under what circumstance is the curve for an oxidation/reduction titration asymmetric about the equivalence point ... 

All the methods of end point detection discussed in the previous paragraphs are based on the assumption that the titration curve is symmetrical about the equivalence point and that the inflection in the curve coiresponds to this point. This assumption is valid if the titrant and analyte react in a 1 1 ratio and if the electrode reaction is reversible. Many oxidation/reduction reactions, such as the reaction of iron(II) with permanganate, do not occur in equimolar fashion. Even so, such titration curves are often so steep at the end point that vei little error is introduced by assuming that the curves are symmetrical. 

An inert indicator electrode constructed of platinum is ordinarily used to detect end points in oxidation/reduction titrations. Occasionally, other inert metals such as silver, palladium, gold, and mercury are used instead. Titration curves similar to those constructed in Section 19D are usually obtained, although they may be displaced along the potential (vertical) axis as a consequence of the high ionic strengths. End points are determined by the methods described earlier in this chapter. 

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.. ...

Fig. 9 shows the titration results for the following samples chloroplast lamellae and TSF-1 particles, both measured at 820 nm, and the CPI complex measured at 820 as well as 703 nm. Each sample was titrated oxidatively (starting with 100 pM ferrocyanide and adding ferricyanide to a maximum concentra tion of 10 mM) and reductively (starting with 1-5 mM ferricyanide and adding ferrocyanide to a maximum concentration of 10 mM). The titration is a plot of the light-induced AA V5. the actual redox-potential of the medium or the ferri-/ferrocyanide ratio as shown in Fig. 9. The plot of the data points clearly show that the titration was completely reversible and that P700 was in redox equilibrium with the ferri-/ferro-cya-nide couple. The solid line is the theoretical Nernst curve for a one-electron transition and the data points agree well with the theoretical course. The titration curve for both the chloroplast lamellae and the TSF-1, as well as D144 (data not shown here), yielded an value of+492 mV.

In contrast, when the CPI complex was titrated both oxidatively and reductively and monitored at both 820 and 703 nm, the data points also fell on a theoretical Nemst curve for a one-electron transition, but the results yielded a lower value of-i-427 mV, 65 mV less positive than that ofthe chloroplast lamellae or TSF-I particles. These results indicate that chloroplast particles obtained by harsher detergent treatment or samples that have been altered through aging, for example, would result in a lower redox potential. This finding probably can explain many (although perhaps not all) ofthe discrepancies in the redox-potential values reported by various groups over a period of forty years. 

Where potentiometric titrations, other than those involving pH measurement are concerned, such as precipitation, complexation, oxidation-reduction, nonaqueous media, etc., the data obtained will be in the form of E versus V. All of the titration theory, and that of titration curves, will apply to such titrations, as will the general methods of endpoint location. 

Therefore, the values of pEMe0 determined by averaging the titration data from the initial section of the titration curve (characterized by a sharp e.m.f. reduction at small titrant additions) are just the dissociation constant of the studied oxide, to an accuracy determined by the natural spread of the experimental data. It should be emphasized, however, that the values of the pEMeQ concentration constant calculated in such a way, contain an appreciable error, caused by the fact that the initial concentration of the titrant in the halide melt is comparable in magnitude with that of oxygen-containing admixtures in the pure melt. 

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... 

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