Analytical Chem istry - DePauw University

Chapter 9 Titrimetric Methods427difference between an equivalence point and its corresponding end point isa source of determinate error. It is even possible that an equivalence pointdoes not have a useful end point.Wh e r e is Th e Eq u i v a l e n c e Po i nt ?Earlier we learned how to calculate the pH at the equivalence point for thetitration of a strong acid with a strong base, and for the titration of a weakacid with a strong base. We also learned to quickly sketch a titration curvewith only a minimum of calculations. Can we also locate the equivalencepoint without performing any calculations. The answer, as you might guess,is often yes!For most acid–base titrations the inflection point, the point on a titrationcurve having the greatest slope, very nearly coincides with the equivalencepoint. 3 The red arrows in Figure 9.9, for example, indicate the equivalencepoints for the titration curves from Example 9.1. An inflection pointactually precedes its corresponding equivalence point by a small amount,with the error approaching 0.1% for weak acids or weak bases with dissociationconstants smaller than 10 –9 , or for very dilute solutions.The principal limitation to using an inflection point to locate the equivalencepoint is that the inflection point must be present. For some titrationsthe inflection point may be missing or difficult to find. Figure 9.10, forexample, demonstrates the affect of a weak acid’s dissociation constant, K a ,on the shape of titration curve. An inflection point is visible, even if barelyso, for acid dissociation constants larger than 10 –9 , but is missing when K ais 10 –11 .An inflection point also may be missing or difficult to detect if theanalyte is a multiprotic weak acid or weak base with successive dissociationconstants that are similar in magnitude. To appreciate why this is true let’sconsider the titration of a diprotic weak acid, H 2 A, with NaOH. Duringthe titration the following two reactions occur.3 Meites, L.; Goldman, J. A. Anal. Chim. Acta 1963, 29, 472–479.1412pH1086(f)(e)(d)420(c)(b)(a)0 10 20 30 40 50 60 70Volume of NaOH (mL)Figure 9.10 Weak acid–strong base titration curves for the titrationof 50.0 mL of 0.100 M HA with 0.100 M NaOH. The pK avalues for HA are (a) 1, (b) 3, (c) 5, (d) 7, (e) 9, and (f) 11.