Locating a Titration’s Equivalence Point

For most acid–base titrations the inflection point, the point on a titration curve having the greatest slope, very nearly coincides with the equivalence point. The red arrows in the following figure for example, indicate the equivalence points for the titrations of: (a) the 50.0 mL of 0.050 M H2A, a diprotic weak acid with a pKa1 of 3 and a pKa2 of 7; and (b) the a 50.0 mL mixture containing 0.075 M HA, a weak acid with a pKa of 3, and 0.025 M HB, a weak acid with a pKa of 7. For both titrations the titrant is 0.10 M NaOH.


The principal limitation to using an inflection point to locate the equivalence point is that an inflection point must be present. For some titrations the inflection point is missing or difficult to find. The figure below, for example, demonstrates the affect of a weak acid’s dissociation constant, Ka, on the shape of titration curve. The titration curves in this figure are for the titration of 50.0 mL of 0.100 M HA with 0.100 M NaOH. The pKa values for HA are (a) 1, (b) 3, (c) 5, (d) 7, (e) 9, and (f) 11. An inflection point is visible, even if barely so, for acid dissociation constants larger than 10–9, but is missing when Ka is 10–11.


An inflection point also may be missing or difficult to detect if the analyte is a multiprotic weak acid or weak base with successive dissociation constants that are similar in magnitude. The figure below shows titration curves for the diprotic weak acids maleic acid, malonic acid, and succinic acid. Each titration curve is for 50.0 mL of 0.0500 M weak acid using 0.100 M NaOH. Although each titration curve has equivalence points at 25.0 mL and 50.0 mL of NaOH, the titration curve for succinic acid shows only one inflection point.


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