The titration curve for a precipitation titration follows the change in either the ana- lyte’s or titrant’s concentration as a function of the volume of titrant. For example, in an analysis for I– using Ag+ as a titrant
Ag+(aq)+ I–(aq) < = = = = > AgI(s)
the titration curve may be a plot of pAg or pI as a function of the titrant’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, let’s calculate the titration curve for the titration of 50.0 mL of 0.0500 M Cl– with 0.100 M Ag+. The reaction in this case is
Ag+(aq)+ Cl–(aq) < = = = = > AgCl(s)
The equilibrium constant for the reaction is
K = (Ksp)–1 = (1.8 x 10–10)–1 = 5.6 x 109
Since the equilibrium constant is large, we may assume that Ag+ and Cl– 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 Cl– is in excess. The concentration of unreacted Cl– after adding 10.0 mL of Ag+, for example, is
If the titration curve follows the change in concentration for Cl–, then we calculate pCl as
pCl = –log[Cl–] = –log(2.50 x 10–2) = 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 Ksp expression for AgCl
Ksp = [Ag+][Cl–] = 1.8 x 10–10
gives a pAg of 8.14.
At the equivalence point, we know that the concentrations of Ag+ and Cl– 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 acid–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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