The titration curve for a precipitation titration follows the change in either the ana- lyteâ€™s or titrantâ€™s concentration as a function of the volume of titrant.

**Titration Curves**

The titration curve
for a precipitation titration follows
the change in either the ana-
lyteâ€™s or titrantâ€™s concentration as a function
of the volume of titrant.
For example, in an analysis for
Iâ€“ using Ag+ as a titrant

Ag+(*aq*)+ Iâ€“(*aq*)
< = = = = > AgI(*s*)

the
titration curve may be a plot of pAg or pI as a function
of the titrantâ€™s volume. As we have done
with previous titrations, we first show
how to calculate the titra- tion curve
and then demonstrate how to quickly
sketch the titration curve.

As an example, letâ€™s calculate the
titration curve for the titration of 50.0 mL of 0.0500
M Clâ€“
with 0.100 M Ag+. The reaction in this
case is

Ag+(*aq*)+ Clâ€“(*aq*) < = = = = > AgCl(*s*)

The equilibrium constant for the reaction is

*K *= (*K*_{sp})â€“1 = (1.8 x 10â€“10)â€“1 = 5.6 x 109

Since the equilibrium constant is large,
we may assume that Ag+ and
Clâ€“ react completely.

By
now you are familiar with our approach
to calculating titration curves. The first task is to calculate the volume of Ag+ needed to reach the equivalence point. The stoichiometry of the reaction requires
that

shows that we need 25.0 mL of Ag+ to reach the equivalence point.

Before the equivalence point
Clâ€“ is in excess. The concentration of unreacted
Clâ€“ after adding 10.0 mL of Ag+,
for example, is

If the titration curve follows the change in concentration for Clâ€“, then we calculate pCl as

pCl = â€“log[Clâ€“] = â€“log(2.50 x 10â€“2) = 1.60

However, if we wish to follow the change in concentration for Ag+ then we must first calculate its concentration. To do so we use the *K*_{sp} expression for AgCl

*K*_{sp} = [Ag+][Clâ€“] = 1.8 x 10â€“10

gives a pAg of 8.14.

At
the equivalence point,
we know that
the concentrations of Ag+ and Clâ€“ are equal. Using
the solubility product
expression

At the equivalence point, therefore, pAg and pCl are both 4.89.

After the equivalence point,
the titration mixture
contains excess Ag+. The con- centration of Ag+ after adding 35.0 mL of titrant
is

or a pCl of 7.82.
Additional results for the titration curve are shown
in Table 9.21 and Figure 9.41.

As we have done for acidâ€“base, complexometric titrations, and redox titrations, we now show how to quickly sketch a precipitation titration curve
using a minimum
number of calculations

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Modern Analytical Chemistry: Titrimetric Methods of Analysis : Precipitation Titration Curves |

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