Equivalence point potential

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. 

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. 

When the potential of the indicator electrode at the equivalence point is known, either from a previous experiment or from calculations, the end point can be determined simply by adding the titrant solution until this equivalence-point potential is reached. This technique is analogous to ordinary titrations with indicators and is very convenient and rapid this procedure can be very readily followed when an auto-titrator is employed. 

Another method uses a preset equivalence point potential applied across the electrodes by means of a calibrated potentiometer. A difference between this potential and that of the electrodes causes an error signal, which is amplified. This causes the electronic switch to close, permitting a flow of electricity through the solenoid-operated valve of the burette. As the signal approaches zero, the flow of titrant ceases as the current to the solenoid is switched off. 

Second-derivative titrators have the advantage that no preknowledge of the equivalence point potential is required. The signal processor calculates the second derivative of the electrode potential of the indicator electrode. Change in the sign of the second derivative causes a switching device to turn off the flow of the titrant. 

At the equivalence point, the concentrations of cerium(IV) and iron(II) are minute and cannot be obtained from the stoichiometry of the reaction. Fortunately, equivalence-point potentials are easily obtained by taking advantage of the fact that the two reactant species and the two product species have known concentration ratios at chemical equivalence. 

Obtain an expression for the equivalence-point potential in the titration of 0.0500 M U with 0.1000 M Ce ". Assume both solutions are 1.0 M in H2SO4. 

We see that in this titration, the equivalence-point potential u... 

Figure 1 9-4 Spreadsheet and plot for titration of 50.00 mL of 0.0500 M Fe " with 0.1000 M Ce. Prior to the equivalence point, the system potential is calculated from the and Fe + concentrations. After the equivalence point, the Ce and Ce + concentrations are used in the Nernst equation. The Fe concentration in cell B7 is calculated from the number of millimoles of Ce added, divided by the total volume of solution. The formula used for the first volume is shown in documentation cell A21. In cell Cl, [Fe- ] is calculated as the initial number of millimoles of Fe present, minus the number of millimoles of Fe formed, divided by the total solution volume. Documentation cell A22 gives the formula for the 5.00-mL volume. The system potential prior to the equivalence point is calculated in cells F7 F12 by using the Nernst equation, expressed for the first volume by the formula shown in documentation cell A23. In cell F13, the equivalence-point potential is found from the average of the two formal potentials, as shown in documentation cell A24. After the equivalence point, the Ce(lll) concentration (cell D14) is found from the number of millimoles of Fe- initially present divided by the total solution volume, as shown for the 25.10-mL volume by the formula in documentation cell D21. The Ce(IV) concentration (El 4) is found from the total number of millimoles of Ce(lV) added, minus the number of millimoles of Fe + initially present, divided by the total solution volume, as shown in documentation cell D22. The system potential in cell FI4 is found from the Nernst equation as shown in documentation cell D23. The chart is then the resulting titration curve.

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. 

Equivalence-point potential The electrode potential of the system in an oxidation/reduction titration when the amount of titrant that has been added is chemically equivalent to the amount of analyte in the sample. 

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... 

E% must be near the equivalence point potential. A potential change of 120 raV is needed for a color change for n = 1 (of the indicator half-reaction) and 60 mV for n = 2. 

E% is near the equivalence point potential of the titration, where there is a rapid change in potential in excess of 0.12 V, then the color change occurs at the equivalence point. Again, this is analogous to the requirement that the pKa value of an acid-base indicator be near the pH of the equivalence point. 

Oxidation of chloride ion is not a problem with dichromate. However, the formal potential of the Cr207 /Cr + couple is reduced from 1.33 to 1.00 V in 1 M hydrochloric acid, and phosphoric acid must be added to reduce the potential of the Fe /Fe-" couple. Such addition is also necessary because it decreases the equivalence point potential to near the standard potential for the diphenylamine sulfonate indicator (0.84 V). Otherwise, the end point would occur too soon. 

A. J. Bard and S. H. Simpsonsen, The General Equation for the Equivalence Point Potential in Oxidation-Reduction Titrations, J. Chem. Educ., 37 (1960) 364. 

It is possible to calculate the equivalence point potential by noting that we cannot ignore the small concentrations of Sn " " and Ce remaining, even though the overall reaction may be close to completion. The stoichiometry at the equivalence point demands that... 

Develop the curve for the titration of 10 mL of 0.10 M FeS04 in a 1.0 M H2SO4 medium with 0.05 M Ce(S04)2- Obtain the difference curve. Compare the equivalence point potential obtained from the curve to that calculated from Equation 10-3. 

Such plottings were systematically carried out on a few materials 94,118, Measurements were also performed over ranges wider than those delineated by the basic requirement of a predominant ionic conductivity. The equivalent-point-potentials measured under these conditions were certainly erroneous but they appeared not to depend upon the measuring conditions and to be characteristic of the material. They allowed us to determine the redox stability intervals over an extended range where the potential scale is unknown but fixed. The additional data are very useful in practice to predict the risks of errors in the measurements with solid state electrochemical cells. ... 

For points before the equivalence point, potential data are computed from the analyte standard potential and the analytical concentrations of the analyte and its reaction product. Post-equivalence point data are based upon the standard potential for the titrant and its analytical concentrations. The equivalence point potential is computed from the two standard potentials and the stoichiometric relation between the analyte and titrant. 

The equivalence point potential is the average of the formal potentials of both couples. The fact that the equivalence point potential is equal to their half-sum is due to the equality ni = ri2. This result cannot be generalized to asymmetrical titrations. Notice also for this example that the equivalence point potential is independent of the titrand concentration (see later). 

Calculating the derivative d(S ldE from the general equation shows that it never vanishes. As a result and according to the mentioned assumption, the first equivalence point potential is such that... 

As the different standard potentials are markedly different, we can assume that the first equivalence point potential is well below E°u and, thus, that the exponential ei3 is quasi-null ... 

The second equivalence point potential is given by the relation... 

When phosphoric acid, which complexes ferric iron, is added, there is a decrease in the equivalence point potential value and the color change of the sulfonated diphenylamine at the equivalence point becomes very sharp ... 

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