Concentrations and Dissociation Constants of Weak Acids
The method can be used to estimate the dissociation constants of weak acids, as well as their concentrations (Gran, 1952). With an acid represented by HA, where
- ,
we have at any i'th point in the titration of a volume of acid at a concentration by base of concentration . In the linear regions away from equivalence,
- and
are valid approximations, whence
- , or
- or, because ,
- .
A plot of versus will have a slope over the linear acidic region and an extrapolated x-intercept, from which either or can be computed. The alkaline region is treated in the same manner as for a titration of strong acid. Figure 2 gives an example; in this example, the two x-intercepts differ by about 0.2 mL but this is a small discrepancy, given the large equivalence volume (0.5% error).
Similar equations can be written for the titration of a weak base by strong acid (Gran, 1952; Harris, 1998).
Read more about this topic: Gran Plot
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