Redox titration equivalence point

A selected list of redox indicators will be found in Table 8.26. A redox indicator should be selected so that its if" is approximately equal to the electrode potential at the equivalent point, or so that the color change will occur at an appropriate part of the titration curve. If n is the number of electrons involved in the transition from the reduced to the oxidized form of the indicator, the range in which the color change occurs is approximately given by if" 0.06/n volt (V) for a two-color indicator whose forms are equally intensely colored. Since hydrogen ions are involved in the redox equilibria of many indicators, it must be recognized that the color change interval of such an indicator will vary with pH. 

The equivalence point of a redox titration occurs when stoichiometrically equivalent amounts of analyte and titrant react. As with other titrations, any difference between the equivalence point and the end point is a determinate source of error. 

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. 

The scale of operations, accuracy, precision, sensitivity, time, and cost of methods involving redox titrations are similar to those described earlier in the chapter for acid-base and complexometric titrimetric methods. As with acid-base titrations, redox titrations can be extended to the analysis of mixtures if there is a significant difference in the ease with which the analytes can be oxidized or reduced. Figure 9.40 shows an example of the titration curve for a mixture of Fe + and Sn +, using Ce + as the titrant. The titration of a mixture of analytes whose standard-state potentials or formal potentials differ by at least 200 mV will result in a separate equivalence point for each analyte. 

Potcntiomctric Titrations In Chapter 9 we noted that one method for determining the equivalence point of an acid-base titration is to follow the change in pH with a pH electrode. The potentiometric determination of equivalence points is feasible for acid-base, complexation, redox, and precipitation titrations, as well as for titrations in aqueous and nonaqueous solvents. Acid-base, complexation, and precipitation potentiometric titrations are usually monitored with an ion-selective electrode that is selective for the analyte, although an electrode that is selective for the titrant or a reaction product also can be used. A redox electrode, such as a Pt wire, and a reference electrode are used for potentiometric redox titrations. More details about potentiometric titrations are found in Chapter 9. 

This expression enables us to calculate the exact concentration at the equivalence point in any redox reaction of the general type given above, and therefore the feasibility of a titration in quantitative analysis. 

It has been shown (Section 10.89) that the potential at the equivalence point is the mean of the two standard redox potentials. In Fig. 10.14, the curve shows the variation of the potential during the titration of 0.1 M iron(II) ion with... 

M cerium(IV) solution, and the equivalence point is at 1.10 volts. Ferroin changes from deep red to pale blue at a redox potential of 1.12 volts the indicator will therefore be present in the red form. After the addition of, say, a 0.1 per cent excess of cerium(IV) sulphate solution the potential rises to 1.27 volts, and the indicator is oxidised to the pale blue form. It is evident that the titration error is negligibly small. 

In principle, any type of titration can be carried out conductometrically provided that during the titration a substantial change in conductance takes place before and/or after the equivalence point. This condition can be easily fulfilled in acid-base, precipitation and complex-formation titrations and also the corresponding displacement titrations, e.g., a salt of a weak acid reacting with a strong acid or a metal in a fairly stable complex reacting with an anion to yield a very stable complex. However, for redox titrations such a condition is rarely met. 

In fact, any type of titration can be carried out potentiometrically provided that an indicator electrode is applied whose potential changes markedly at the equivalence point. As the potential is a selective property of both reactants (titrand and titrant), notwithstanding an appreciable influence by the titration medium [aqueous or non-aqueous, with or without an ISA (ionic strength adjuster) or pH buffer, etc.] on that property, potentiometric titration is far more important than conductometric titration. Moreover, the potentiometric method has greater applicability because it is used not only for acid-base, precipitation, complex-formation and displacement titrations, but also for redox titrations. 

The titration is represented in Fig. 2.22 by plotting the Pt electrode potential versus the titration parameter k. BB is the voltage curve for titration of Fe2+ with Ce4+ and B B that for titration of Ce4+ with Fe2+ they correspond exactly to the pH curves BB and B B in Fig. 2.18, with the exception that the initial point in Fig. 2.22 would theoretically have an infinitely negative and an infinitely positive potential, respectively. In practice this is impossible, because even in the absence of any other type of redox potential there will be always a trace of Fe3+ in addition to Fe2+ and of Ce3+ in addition to Ce4+ present. Further, half way through the oxidation or reduction the voltage corresponds to the standard reduction potentials of the respective redox couples it also follows that the equivalence point is represented by the mean value of both standard potentials ... 

With a low constant current -1 (see Fig. 3.71) one obtains the same type of curve but its position is slightly higher and the potential falls just beyond the equivalence point (see Fig. 3.72, anodic curve -1). In order to minimize the aforementioned deviations from the equivalence point, I should be taken as low as possible. Now, it will be clear that the zero current line (abscissa) in Fig. 3.71 yields the well known non-faradaic potentiometric titration curve (B B in Fig. 2.22) with the correct equivalence point at 1.107 V this means that, when two electroactive redox systems are involved, there is no real need for constant-current potentiometry, whereas this technique becomes of major advantage... 

Again for the titration of Ce(IV) with Fe(II) we shall now consider constant-potential amperometry at one Pt indicator electrode and do so on the basis of the voltammetric curves in Fig. 3.71. One can make a choice from three potentials eu e2 and e3, where the curves are virtually horizontal. Fig. 3.74 shows the current changes concerned during titration at e1 there is no deflection at all as it concerns Fe(III) and Fe(II) only at e2 and e3 there is a deflection at A = 1 but only to an extent determined by the ratio of the it values of the Ce and Fe redox couples. The establishment of the deflection point is easiest at e2 as it simply agrees with the intersection with the zero-current abscissa as being the equivalence point in fact, no deflection is needed in order to determine this intersection point, but if there is a deflection, the amperometric method is not useful compared with the non-faradaic potentiometric titration unless the concentration of analyte is too low. 

Titrations can often be conveniently followed potentiometrically and in many cases it is not the actual value of the electrode potential that is important but the pattern of changing potential as the composition of the solution varies - pH and redox measurements are particularly well suited to such methods. In many instances the equivalence point will be indicated by a significant change in potential (Figure 4.6) but sometimes the change at the equivalence point is difficult to... 

The two types of titration that you have encountered so far are acid-base and redox titrations. During a titration, the experimenter looks for a permanent colour change in the solution in the conical flask, usually due to the presence of an indicator. This is known as the end-point of the reaction. The equivalence point is the point at which the reaction is just complete. The ideal situation is when the equivalence point and the end-point are exactly the same. Choosing the correct indicator and carrying out titrations very carefully and accurately help to ensure that the equivalence point and the end-point are very close (see p. 37). 

In titrations involving 1 1 stoichiometry of reactants, the equivalence point is the steepest point of the titration curve. This is true of acid-base, complexometric, and redox titrations as well. For stoichiometries other than 1 1, such as 2Ag+ + CrO —> Ag2Cr04(s), the curve is not symmetric near the equivalence point. The equivalence point is not at the center of the steepest section of the curve, and it is not an inflection point. In practice, conditions are chosen such that titration curves are steep enough for the steepest point to be a good estimate of the equivalence point, regardless of the stoichiometry. 

The voltage change near the equivalence point increases as the difference between 6° of the two redox couples in the titration increases. The larger the difference in 6°, the greater the equilibrium constant for the titration reaction. For Figure 16-2, half-reactions 16-2 and 16-3 differ by 0.93 V, and there is a large break at the equivalence point in the titration curve. For Figure 16-3, the half-reactions differ by 0.47 V, so there is a smaller break at the equivalence point. 

The larger the difference in standard potential between titrant and analyte, the greater the break in the titration curve at the equivalence point. A redox titration is usually feasible if the difference between analyte and titrant is a 0.2 V. However, the end point of such a titration is not very sharp and is best detected potentiometrically. If the difference in formal potentials is a 0.4 V. then a redox indicator usually gives a satisfactory end point. 

B. Would indigo tetrasulfonate be a suitable redox indicator for the titration of Fe(CN)g with Tl3+ in 1 M HC1 Hint The potential at the equivalence point must be between the potentials for each redox couple.)... 

The Karl Fischer titration of water uses a buret to deliver reagent or coulometry to generate reagent. In bipotentiometric endpoint detection, the voltage needed to maintain a constant current between two Pt electrodes is measured. The voltage changes abruptly at the equivalence point, when one member of a redox couple is either created or destroyed. 

Equations 16-9 and 16-10 are analogous to the Henderson-Hasselbalch equation of acid-base buffers. Prior to the equivalence point, the redox titration is buffered to a potential near E+ = formal potential for Fc 1 Fe2+ by the presence of Fe 1 and Fe2+. After the equivalence point, the reaction is buffered to a potential near E+ = formal potential for Ce4+ Ce3+. [R. de Levie Redox Buffer Strength, J. Chem. Ed. 1999, 76, 574.]... 

Another specialized form of potentiometric endpoint detection is the use of dual-polarized electrodes, which consists of two metal pieces of electrode material, usually platinum, through which is imposed a small constant current, usually 2-10 /xA. The scheme of the electric circuit for this kind of titration is presented in Figure 4.1b. The differential potential created by the imposition of the ament is a function of the redox couples present in the titration solution. Examples of the resultant titration curve for three different systems are illustrated in Figure 4.3. In the case of two reversible couples, such as the titration of iron(II) with cerium(IV), curve a results in which there is little potential difference after initiation of the titration up to the equivalence point. Hie titration of arsenic(III) with iodine is representative of an irreversible couple that is titrated with a reversible system. Hence, prior to the equivalence point a large potential difference exists because the passage of current requires decomposition of the solvent for the cathode reaction (Figure 4.3b). Past the equivalence point the potential difference drops to zero because of the presence of both iodine and iodide ion. In contrast, when a reversible couple is titrated with an irreversible couple, the initial potential difference is equal to zero and the large potential difference appears after the equivalence point is reached. 

When the equivalence point is reached, the Fe2+ will have been totally consumed (the large equilibrium constant ensures that this will be so), and the potential will then be controlled by the concentration ratio of Ce3+/Ce4+. The idea is that both species of a redox couple must be present in reasonable concentrations for a concentration to control the potential of an electrode of this kind. If one works out the actual cell potentials for various concentrations of all these species, the resulting titration curve looks much like the familiar acid-base titration curve. The end point is found not by measuring a particular cell voltage, but by finding what volume of titrant gives the steepest part of the curve. 

Any titration involves the progressive change of the activities (or concentrations) of the titrated and titrating species and, in principle, can be done potentiometrically. However, for an accurate determination it is necessary that there is a fairly rapid variation in equilibrium potential in the region of the equivalence point. Useful applications are redox, complexation, precipitation, acid-base titrations, etc. From the titration curve it is possible to calculate values of the formal potentials of the titrated and titrating species, as explained below. 

Bipotentiometric titrations, that is potentiometric titrations with a constant imposed passage of current of the order of 5-10 /iA, usually between two platinum electrodes, should also be mentioned here. These are not strictly speaking potentiometric titrations, since /= 0, but they involve a reading of potential. The current flow provokes the occurrence of a half-reaction. Where there is a dominant redox couple before and after the endpoint, the potential difference registered is more or less constant, but in the zone of the equivalence point there is generally a... 

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. 

The electrical circuit consists of two electrodes a redox indicator electrode and a reference electrode that also passes current. A fixed potential difference is applied and the equivalence point is calculated from the intersection of the two straight lines that show the variation of current before and after the endpoint in a plot of current as a function of added titrant volume. The plots can have various forms, depending on whether the titrated species or titrant are or are not electroactive. Figure 14.1 shows the four possible cases. Sometimes the potential difference applied is less than that necessary to reach the mass-transport-limited current, but sufficient to give good results. 

Biamperometric titrations involve the use of two redox electrodes in solution, and are applicable only to titrations where there is a reversible system before or after the endpoint there is no reference electrode. The application of a potential difference causes one electrode to be anode and the other cathode. A current passes due to oxidation or reduction, respectively, of a species present in solution, decreasing to / = 0 at the equivalence point alternatively it may be that 7 = 0 until the equivalence... 

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