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Potentiometric titration is a fairly standard undergraduate chemistry experiment. A typical application of the potentiometric titration is to determine the solubility product of a sparingly soluble salt, such as silver chloride (1), from the titration endpoint. The endpoint can be determined by inspection of the titration curve (Fig. 1a), or more precisely, from the maximum of the first derivative or the x-intercept of the second derivative of potential with respect to titrant volume (Fig. 1b). Although most students have no problem with the theory, the analysis of the experimental data is tedious. Spreadsheet techniques have been introduced to facilitate the collection and analysis of data (2, 3). However, owing to the presence of experimental error, even when the moving-average method is applied to smooth the data, the result may not be satisfactory (Fig. 1b). Moreover, a slightly different endpoint may be obtained from the graphs because numerical differentiation is employed. Here, an alternative approach, using a curve-fitting technique, is introduced. While most students are familiar with fitting experimental data to a straight line, few realize that the same principle can be applied to other mathematical functions.
A typical titration curve is shown in Figure la. Recognizing the similarity in the...