Symmetrical titrations

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... 

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. 

E° for the Mn- /Mn04 couple is 1.51 V. Note that the potential, halfway between the two E° potentials is 1.14 V. The equivalence point (inflection point) for this un-symmetrical titration reaction is therefore closer to the titrant couple and the titration curve is unsymmetrical. 

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. 

The titrations for which 2 = i are sometimes called symmetrical titrations. Moreover, in the above example, 2 = i = 1 ... 

Further Considerations Concerning Symmetrical Titrations Titration Error... 

The preceding results are valid for all symmetric titrations ( i = 2. with, in particular, i = ti2 > 1). The general (and rigorous) equation of the curve describing the titration corresponding to reaction (17.2) is... 

Case of a Symmetric Titration Titration of A Halide by Silver Ions and Inversely... 

We call symmetric titrations those putting ions that bring the same (but opposite) electrical charge face to face, such as Ag+ and Cl ions, for example. We also want to make clear that in this chapter, fluoride ions are excluded when we speak of halides. 

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. 

For a completely symmetrical curve, the end-point can be easily established as the inflection point through which a tangent can be drawn here for convenience the "rings method (Fig. 2.23) can be used, where the inflection point is obtained by intersection of the titration curve with the line joining centres of fitting circles (marked on a thin sheet of transparant plastic see ref. 61). 

A l,3,5-tris(hydroxyalkylphenyl)benzene unit has been used as a template for the development of various symmetrical hosts. Their possibilities to form stable hydrogen bonds and therefore, their abilities to recognize glycosides have been studied by titration NMR with different octyl glycosides. In most of the cases, the existence of association processes was evidenced.119,120... 

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. 

For Reaction 16-1, the titration curve in Figure 16-2 is symmetric near the equivalence point because the reaction stoichiometry is 1 1. Figure 16-3 shows the curve calculated for the titration of Tl+ by IO3 in 1.00 M HC1. 

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. 

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