# 9: Titrimetric Methods

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Titrimetry, in which volume serves as the analytical signal, first appears as an analytical method in the early eighteenth century. Titrimetric methods were not well received by the analytical chemists of that era because they could not duplicate the accuracy and precision of a gravimetric analysis. Not surprisingly, few standard texts from that era include titrimetric methods of analysis.

Precipitation gravimetry first developed as an analytical method without a general theory of precipitation. An empirical relationship between a precipitate’s mass and the mass of analyte in a sample—what analytical chemists call a gravimetric factor—was determined experimentally by taking a known mass of analyte through the procedure. Today, we recognize this as an early example of an external standardization. Gravimetric factors were not calculated using the stoichiometry of a precipitation reaction because chemical formulas and atomic weights were not yet available! Unlike gravimetry, the development and acceptance of titrimetry required a deeper understanding of stoichiometry, of thermodynamics, and of chemical equilibria. By the 1900s, the accuracy and precision of titrimetric methods were comparable to that of gravimetric methods, establishing titrimetry as an accepted analytical technique.

• 9.1: Overview of Titrimetry
In titrimetry we add a reagent, called the titrant, to a solution that contains another reagent, called the titrand, and allow them to react. Despite their difference in chemistry, all titrations share several common features. Before we consider individual titrimetric methods in greater detail, let’s take a moment to consider some of these similarities.
• 9.2: Acid–Base Titrations
In the overview to this chapter we noted that a titration’s end point should coincide with its equivalence point. To understand the relationship between an acid–base titration’s end point and its equivalence point we must know how the titrand’s pH changes during a titration.
• 9.3: Complexation Titrations
The earliest examples of metal–ligand complexation titrations are Liebig’s determinations, in the 1850s, of cyanide and chloride using, respectively, $$\text{Ag}^+$$ and $$\text{Hg}^{2+}$$ as the titrant. Practical applications were slow to develop because many metals and ligands form a series of metal–ligand complexes. In 1945, Schwarzenbach introduced EDTA as a titrant. The availability of a ligand that gives a single endpoint made complexation titrimetry a practical analytical method.
• 9.4: Redox Titrations
Analytical titrations using oxidation–reduction reactions were introduced shortly after the development of acid–base titrimetry. A titrant can serve as its own indicator if its oxidized and its reduced forms differ significantly in color, which initially limited redox titrations to a few titrants. Other titrants require a separate indicator. The first such indicator, diphenylamine, was introduced in the 1920s. Other redox indicators soon followed increasing the applicability of redox titrimetry.
• 9.5: Precipitation Titrations
Thus far in this chapter we have examined titrimetric methods based on acid–base, complexation, and oxidation–reduction reactions. A reaction in which the analyte and titrant form an insoluble precipitate also can serve as the basis for a titration. We call this type of titration a precipitation titration.
• 9.6: Problems
End-of-chapter problems to test your understanding of the topics in this chapter.