Analytical Chem istry - DePauw University

Chapter 9 Titrimetric Methods4311211pH109phenolphthalein’spH range87623 24 25 26 27Volume of NaOH (mL)Fi n d i n g t h e En d p o i n t b y Mo n i t o r i n g pHbromothymol blue’spH rangeFigure 9.13 Portion of the titration curve for50.0 mL of 0.050 M CH 3 COOH with 0.10 MNaOH, highlighting the region containing theequivalence point. The end point transitions forthe indicators phenolphthalein and bromothymolblue are superimposed on the titration curve.An alternative approach for locating a titration’s end point is to continuouslymonitor the titration’s progress using a sensor whose signal is a functionof the analyte’s concentration. The result is a plot of the entire titrationcurve, which we can use to locate the end point with a minimal error.The obvious sensor for monitoring an acid–base titration is a pH electrodeand the result is a potentiometric titration curve. For example,Figure 9.14a shows a small portion of the potentiometric titration curve forthe titration of 50.0 mL of 0.050 M CH 3 COOH with 0.10 M NaOH, focusingon the region containing the equivalence point. The simplest methodfor finding the end point is to locate the titration curve’s inflection point,as shown by the arrow. This is also the least accurate method, particularly ifthe titration curve has a shallow slope at the equivalence point.Another method for locating the end point is to plot the titration curve’sfirst derivative, which gives the titration curve’s slope at each point alongthe x-axis. Examine Figure 9.14a and consider how the titration curve’sslope changes as we approach, reach, and pass the equivalence point. Becausethe slope reaches its maximum value at the inflection point, the firstderivative shows a spike at the equivalence point (Figure 9.14b).The second derivative of a titration curve may be more useful than thefirst derivative because the equivalence point intersects the volume axis.Figure 9.14c shows the resulting titration curve.Derivative methods are particularly useful when titrating a sample thatcontains more than one analyte. If we rely on indicators to locate the endpoints, then we usually must complete separate titrations for each analyte.If we record the titration curve, however, then a single titration is sufficient.See Chapter 11 for more details about pHelectrodes.