Asymmetric titration curve

When the titration curve is symmetrical about the equivalence point the end point, defined by the maximum value of AE/AV, is identical with the true stoichiometrical equivalence point. A symmetrical titration curve is obtained when the indicator electrode is reversible and when in the titration reaction one mole or ion of the titrant reagent reacts with one mole or ion of the substance titrated. Asymmetrical titration curves result when the number of molecules or ions of the reagent and the substance titrated are unequal in the titration reaction, e.g. in the reaction... 

The curve is not symmetric about the equivalence point, because the stoichiometry of reactants is 2 1, not 1 1. Still, the curve is so steep near the equivalence point that negligible error is introduced if the center of the steep part is taken as the end point. Demonstration 16-1 provides an example of an asymmetric titration curve whose shape also depends on the pH of the reaction medium. 

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. 

The titration of Fe(ll) with permanganate yields a particularly asymmetrical titration curve because of the different number of electrons involved in the two half-reactions. Consider the titration of 25.00 mL of 0.1 M Fe(II) with 0.1 M MnOj. The R-" concentration is maintained at 1.0 M throughout the titration. Use a spreadsheet to generate a theoretical titration curve and a first- and second-derivative plot. Do the inflection points obtained from the maximum of the first-derivative plot or the zero crossing of the second-derivative plot correspond to the equivalence point Explain why or why not. 

Rgure 1 (A) Symmetric titration curve compleximetric titration of copper ion, using a copper-selective electrode. (B) Asymmetric titration curve compleximetric titration of nickel using a copper-selective electrode. 

An asymmetric titration curve will be encountered whenever the titrant and the analyte react in a ratio that is not 1 1. 

It can be shown mathematically that considerable error results in asymmetric titration curves with poorly defined jumps if the inflection point (= maximum in the first derivative) is assumed to be the equivalence point [218]. Unfortunately, this is not taken into account often enough. The fact that many analysts have few problems with asymmetric titration curves plotted in this way, even though they have falsely indicated the end point, comes about because precisely the same mistake is made in determining the titer of the titrating solutions. The errors, in effect, cancel one another to a large extent. Also, with large, sharp jumps this error is normally negligibly small. 

These errors arising from asymmetric titration curves, as well as from interfering ion indications were reckoned with by Carr [219,220]. He started with the empirical form of the Nemst equation ... 

The magnitude of the end point jump depends on the equilibrium constant of the corresponding titration reaction, as well as on the concentration of the starting solution. Since the error in determining the end point of asymmetric titration curves becomes increasingly smaller with sharper end point jumps, both of these factors (starting solution concentration and equilibrium constant) will be considered as a function of various parameters. In a precipitation titration 3 is defined as ... 

In the original work, the influence of both of these normalized parameters and b on analysis accuracy was investigated with the help of a computer, assuming that, as is usually the case, the inflection point in the titration curve plot is taken to be the end point of the chemical reaction. Syimnetric precipitation titrations come out the best, showing no systematic errors even with relatively large jSp values of 0.1 to 0.01 and b = 0. For asymmetric titration curves, with u = for example, an error of 55.3% results with ]8p = 0.1 and ft = 0. 

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. 

By differentiating the titration curve twice and then equating the second derivative to zero, it can be shown that for a symmetrical titration curve ( i = the point of maximum slope theoretically coincides with the equivalence point. This conclusion is the basis for potentiometric end-point detection methods. On the other hand, if 2> the titration curve is asymmetrical in the vicinity of the equivalence point, and there is a small titration error if the end point is taken as the inflection point In practice the error from this source is usually insignificant compared with such errors as inexact stoichiometry, slowness of titration reaction, and slowness of attainment of electrode equilibria. 

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. 

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

Study of the Titration Curve of Stannic Ions by Chromous Ions—Generalization to All Asymmetrical Titrations... 

The investigated titration may be studied like other asymmetrical titrations after the standard (or formal) potentials are replaced with the apparent one at the working pH, provided the latter is a constant. The general equation of the titration curve is... 

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

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