Analytical Chem istry - DePauw University

434 Analytical Chemistry 2.0Excess Titrant BranchTemperatureTitration BranchFigure 9.15 Typical thermometric titration curve. The endpoint,shown by the red arrow, is found by extrapolating the titrationbranch and the excess titration branch.tion branch. The temperature continues to rise with each addition of titrantuntil we reach the equivalence point. After the equivalence point, anychange in temperature is due to the titrant’s enthalpy of dilution, and thedifference between the temperatures of the titrant and titrand. Ideally, theequivalence point is a distinct intersection of the titration branch and theexcess titrant branch. As shown in Figure 9.15, however, a thermometrictitration curve usually shows curvature near the equivalence point due toan incomplete neutralization reaction, or to the excessive dilution of thetitrand and the titrant during the titration. The latter problem is minimizedby using a titrant that is 10–100 times more concentrated than the analyte,although this results in a very small end point volume and a larger relativeerror. If necessary, the end point is found by extrapolation.Although not a particularly common method for monitoring acid–basetitrations, a thermometric titration has one distinct advantage over thedirect or indirect monitoring of pH. As discussed earlier, the use of anindicator or the monitoring of pH is limited by the magnitude of the relevantequilibrium constants. For example, titrating boric acid, H 3 BO 3 , withNaOH does not provide a sharp end point when monitoring pH because,boric acid’s K a of 5.8 10 –10 is too small (Figure 9.16a). Because boricacid’s enthalpy of neutralization is fairly large, –42.7 kJ/mole, however, itsthermometric titration curve provides a useful endpoint (Figure 9.16b).9B.3 Titrations in Nonaqueous SolventsVolume of TitrantThus far we have assumed that the titrant and the titrand are aqueous solutions.Although water is the most common solvent in acid–base titrimetry,switching to a nonaqueous solvent can improve a titration’s feasibility.For an amphoteric solvent, SH, the autoprotolysis constant, K s , relatesthe concentration of its protonated form, SH 2 + , to that of its deprotonatedform, S –0