Calorimetric vs. van't Hoff binding enthalpies from isothermal titration calorimetry: Ba2+-crown ether complexation

The 1:1 complexation reaction between Ba(2+) and 18-crown-6 ether is re-examined using isothermal titration calorimetry (ITC), with the goal of clarifying previously reported discrepancies between reaction enthalpies estimated directly (calorimetric) and indirectly, from the temperature dependence of the reaction equilibrium constant K (van't Hoff). The ITC thermograms are analyzed using three different non-linear fit models based on different assumptions about the data error: constant, proportional to the heat and proportional but correlated. The statistics of the fitting indicate a preference for the proportional error model, in agreement with expectations for the conditions of the experiment, where uncertainties in the delivered titrant volume should dominate. With attention to proper procedures for propagating statistical error in the van't Hoff analysis, the differences between Delta H(cal) and Delta H(vH) are deemed statistically significant. In addition, statistically significant differences are observed for the Delta H(cal) estimates obtained for two different sources of Ba(2+), BaCl(2) and Ba(NO(3))(2). The effects are tentatively attributed to deficiencies in the standard procedure in ITC of subtracting a blank obtained for pure titrant from the thermogram obtained for the sample.