A variety of potentiometric titration data that give rise to sigmoid-shaped titration curves can be analyzed by procedures similar to those already discussed. For example, Ingman and coworkers [6] showed that mixtures of weak acids with values of pKa differing by only 0.12 units could be successfully determined with the aid of nonlinear regression analysis. Isbell and coworkers [7] applied the concept to precipitation titrations. Meites and Fanelli [8] showed that the reduced and oxidized forms of a redox couple could be determined from a single redox potentiometric titration. Meites [9] showed the possibility of detecting a 1% acidic impurity in solutions of an acid with a pKa differing from that of the analyte by only 0.57 units. Weighting of the error sum reflecting errors in both measured pH and volume of titrant have been recommended [3], Factors affecting the errors in such methods have been critically examined [10].

The stability constant is a fundamental characteristic of metal complexes. Titrations combined with nonlinear regression can be used to obtain stability constants of metal complexes. An excellent monograph on this subject is available [11],

Detection methods that directly measure the amount of a reactant, product, or titrant in a titration give data that can be described by the intersection of two straight lines. Methods falling into this category include spectropho-tometric, conductimetric, and amperometric titrations. In the example shown (Figure 5.4), the species detected is the titrant. Only a small signal is observed prior to the endpoint. Beyond the endpoint, the increasing concentration of the titrant in the solution causes a linear increase in signal with volume added. Other possible arrangements of intersecting straight line shapes for these so-called segmented titration curves can be obtained,

Figure 5.4 Simulated segmental titration curve characteristic of spectrophotometric, conductimetric, and amperometric titrations where the titrant is detected. The intersecting lines represent the model (Table 5.3) that can be used to fit such titration data and obtain the endpoint at their intersection, shown by the arrow.

volume of titrant

Figure 5.4 Simulated segmental titration curve characteristic of spectrophotometric, conductimetric, and amperometric titrations where the titrant is detected. The intersecting lines represent the model (Table 5.3) that can be used to fit such titration data and obtain the endpoint at their intersection, shown by the arrow.

Table 5.3 General Model for Linear Segmented Titration Curves

Assumptions: Titration data described by intersection of two straight lines; extreme outliers removed, such as near the endpoint, x0. Regression equations:

depending on the species detected [1J. In such cases, models employing two straight lines intersecting at the endpoint can be employed [12], Such a model is summarized in Table 5.3.

Thermometric titrations in thermostated vessels also give segmented titration curves when experimental conditions are controlled such that the temperature changes are kept small. Shukla and Meites [13] combined thermometric detection with acid-base titrations in micellar media and analyzed the data by using an intersecting straight line model. In the presence of certain types of micelles in solution, some weak acids and weak bases can be made stronger and are more easily titrated. By combining this concept with nonlinear regression analysis of thermometric titrations, the authors were able to determine simultaneously ortho- and parachlovo-phenol, which differ in pKa by only 0.08 units in water.

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