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274 Modern Analytical Chemistry

9 A Overview of Titrimetry

Titrimetric methods are classified into four groups based on the type of reaction in-
titrimetry
Any method in which volume is the volved. These groups are acid–base titrations, in which an acidic or basic titrant re-
signal. acts with an analyte that is a base or an acid; complexometric titrations involving a
metal–ligand complexation reaction; redox titrations, where the titrant is an oxidiz-
titrant ing or reducing agent; and precipitation titrations, in which the analyte and titrant
The reagent added to a solution react to form a precipitate. Despite the difference in chemistry, all titrations share
containing the analyte and whose several common features, providing the focus for this section.
volume is the signal.

9A.1 Equivalence Points and End Points
For a titration to be accurate we must add a stoichiometrically equivalent amount
of titrant to a solution containing the analyte. We call this stoichiometric mixture
equivalence point the equivalence point. Unlike precipitation gravimetry, where the precipitant is
The point in a titration where added in excess, determining the exact volume of titrant needed to reach the equiv-
stoichiometrically equivalent amounts of alence point is essential. The product of the equivalence point volume, V eq , and the
analyte and titrant react.
titrant’s concentration, C T , gives the moles of titrant reacting with the analyte.
Moles titrant = V eq ´C T
Knowing the stoichiometry of the titration reaction(s), we can calculate the moles
of analyte.
Unfortunately, in most titrations we usually have no obvious indication that
the equivalence point has been reached. Instead, we stop adding titrant when we
end point reach an end point of our choosing. Often this end point is indicated by a change in
The point in a titration where we stop the color of a substance added to the solution containing the analyte. Such sub-
adding titrant. stances are known as indicators. The difference between the end point volume and
the equivalence point volume is a determinate method error, often called the titra-
indicator tion error. If the end point and equivalence point volumes coincide closely, then
A colored compound whose change in
color signals the end point of a titration. the titration error is insignificant and can be safely ignored. Clearly, selecting an ap-
propriate end point is critical if a titrimetric method is to give accurate results.
titration error
The determinate error in a titration due 9 A.2 Volume as a Signal*
to the difference between the end point
and the equivalence point. Almost any chemical reaction can serve as a titrimetric method provided that
three conditions are met. The first condition is that all reactions involving the
titrant and analyte must be of known stoichiometry. If this is not the case, then
the moles of titrant used in reaching the end point cannot tell us how much ana-
lyte is in our sample. Second, the titration reaction must occur rapidly. If we add
titrant at a rate that is faster than the reaction’s rate, then the end point will ex-
ceed the equivalence point by a significant amount. Finally, a suitable method
must be available for determining the end point with an acceptable level of accu-
racy. These are significant limitations and, for this reason, several titration strate-
gies are commonly used.
+
–
A simple example of a titration is an analysis for Ag using thiocyanate, SCN ,
as a titrant.
–
+
Ag (aq) + SCN (aq) t AgSCN(s)
*Instead of measuring the titrant’s volume we also can measure its mass. Since the titrant’s density is a measure of its
mass per unit volume, the mass of titrant and volume of titrant are proportional.