Potential formal

Formal potentials vary appreciably with the nature and concentration of the present acid. Thus for Fe We + system, the standard oxidation potential is - 0.77 volt where as formal potential E ° = - 0.73 volts in IfMlHClO, - 0.68 volt in IfMfHgSO and - 0.61 volt in [O.bfMfHgPO + IfMlHgSO ]. Evidently complexation is least in perchloric acid and greatest in phosphoric acid. 

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Transition point is at higher potential than the tabulated formal potential because the molar absorptivity of the reduced form is very much greater than that of the oxidized form. 

Standard potentials are tabulated except when a solution composition is stated the latter are formal potentials and the concentrations are in mol/liter. 

Half-reaction Standard or formal potential Solution composition... 

Although EXo /ATcd is standard-state potential for the analyte s half-reaction, a matrix-dependent formal potential is used in its place. After the equivalence point, the potential is easiest to calculate using the Nernst equation for the titrant s half-reaction, since significant quantities of its oxidized and reduced forms are present. 

Substituting these concentrations into equation 9.17 along with the formal potential for the Fe 3-/pg2+ half-reaction from Appendix 3D, we find that the potential is... 

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. 

Another problem is that the Nernst equation is a function of activities, not concentrations. As a result, cell potentials may show significant matrix effects. This problem is compounded when the analyte participates in additional equilibria. For example, the standard-state potential for the Fe "/Fe " redox couple is +0.767 V in 1 M 1TC104, H-0.70 V in 1 M ITCl, and -H0.53 in 10 M ITCl. The shift toward more negative potentials with an increasing concentration of ITCl is due to chloride s ability to form stronger complexes with Fe " than with Fe ". This problem can be minimized by replacing the standard-state potential with a matrix-dependent formal potential. Most tables of standard-state potentials also include a list of selected formal potentials (see Appendix 3D). 

Determining the Standard-State Potential To extract the standard-state potential, or formal potential, for reaction 11.34 from a voltammogram, it is necessary to rewrite the Nernst equation... 

H3ASO4 + 2H3O++ 2e- HASO2 + 4H2O Conditions for formal potentials E° ) are listed next to the potential. 

The reduction potentials for the actinide elements ate shown in Figure 5 (12—14,17,20). These ate formal potentials, defined as the measured potentials corrected to unit concentration of the substances entering into the reactions they ate based on the hydrogen-ion-hydrogen couple taken as zero volts no corrections ate made for activity coefficients. The measured potentials were estabhshed by cell, equihbrium, and heat of reaction determinations. The potentials for acid solution were generally measured in 1 Af perchloric acid and for alkaline solution in 1 Af sodium hydroxide. Estimated values ate given in parentheses. 

Standard potentials are determined with full consideration of activity effects, and are really limiting values. They are rarely, if ever, observed directly in a potentiometric measurement. In practice, measured potentials determined under defined concentration conditions (formal potentials) are very useful for predicting the possibilities of redox processes. Further details are given in Section 10.90. 

Standard potentials Ee are evaluated with full regard to activity effects and with all ions present in simple form they are really limiting or ideal values and are rarely observed in a potentiometric measurement. In practice, the solutions may be quite concentrated and frequently contain other electrolytes under these conditions the activities of the pertinent species are much smaller than the concentrations, and consequently the use of the latter may lead to unreliable conclusions. Also, the actual active species present (see example below) may differ from those to which the ideal standard potentials apply. For these reasons formal potentials have been proposed to supplement standard potentials. The formal potential is the potential observed experimentally in a solution containing one mole each of the oxidised and reduced substances together with other specified substances at specified concentrations. It is found that formal potentials vary appreciably, for example, with the nature and concentration of the acid that is present. The formal potential incorporates in one value the effects resulting from variation of activity coefficients with ionic strength, acid-base dissociation, complexation, liquid-junction potentials, etc., and thus has a real practical value. Formal potentials do not have the theoretical significance of standard potentials, but they are observed values in actual potentiometric measurements. In dilute solutions they usually obey the Nernst equation fairly closely in the form ... 

If the colour intensities of the two forms differ considerably the intermediate colour is attained at potential somewhat removed from Efn, but the error is unlikely to exceed 0.06 volt. For a sharp colour change at the end point, Efn should differ by about at least 0.15 volt from the standard (formal) potentials of the other systems involved in the reaction. 

The standard redox potential is 1.14 volts the formal potential is 1.06 volts in 1M hydrochloric acid solution. The colour change, however, occurs at about 1.12 volts, because the colour of the reduced form (deep red) is so much more intense than that of the oxidised form (pale blue). The indicator is of great value in the titration of iron(II) salts and other substances with cerium(IV) sulphate solutions. It is prepared by dissolving 1,10-phenanthroline hydrate (relative molecular mass= 198.1) in the calculated quantity of 0.02M acid-free iron(II) sulphate, and is therefore l,10-phenanthroline-iron(II) complex sulphate (known as ferroin). One drop is usually sufficient in a titration this is equivalent to less than 0.01 mL of 0.05 M oxidising agent, and hence the indicator blank is negligible at this or higher concentrations. 

The standard or formal potential of ferroin can be modified considerably by the introduction of various substituents in the 1,10-phenanthroline nucleus. The most important substituted ferroin is 5-nitro-l,10-phenanthroline iron(II) sulphate (nitroferroin) and 4,7-dimethyl-1,10-phenanthroline iron(II) sulphate (dimethylferroin). The former (E° = 1.25 volts) is especially suitable for titrations using Ce(IV) in nitric or perchloric acid solution where the formal potential of the oxidant is high. The 4,7-dimethylferroin has a sufficiently low formal potential ( e = 0.88 volt) to render it useful for the titration of Fe(II) with dichromate in 0.5 JVf sulphuric acid. 

Mention should be made of one of the earliest internal indicators. This is a 1 per cent solution of diphenylamine in concentrated sulphuric acid, and was introduced for the titration of iron(II) with potassium dichromate solution. An intense blue-violet coloration is produced at the end point. The addition of phosphoric(V) acid is desirable, for it lowers the formal potential of the Fe(III)-Fe(II) system so that the equivalence point potential coincides more nearly with that of the indicator. The action of diphenylamine (I) as an indicator depends upon its oxidation first into colourless diphenylbenzidine (II), which is the real indicator and is reversibly further oxidised to diphenylbenzidine violet (III). Diphenylbenzidine violet undergoes further oxidation if it is allowed to stand with excess of dichromate solution this further oxidation is irreversible, and red or yellow products of unknown composition are produced. 

Formal potential measurements show that the redox potential of the Ce(IV)-Ce(III) system is greatly dependent upon the nature and the concentration of the add present thus the following values are recorded for the adds named in molar solution H2S04 1.44V, HN03 1.61V, HC104 1.70V, and in 8M perchloric add solution the value is 1.87 V. 

The equilibrium potential for a given reaction is related to the formal potential ... 

FIGURE 2-3 Concentration distribution of the oxidized and reduced forms of the redox couple at different times during a cyclic voltammetric experiment corresponding to the initial potential (a), to the formal potential of the couple during the forward and reversed scans (b, d), and to the achievement of a zero reactant surface concentration (c). 

The position of the peaks on the potential axis (Ep) is related to the formal potential of the redox process. The formal potential for a reversible couple is centered between E and E ... 

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