Possible origin of differences between van't Hoff and calorimetric enthalpy estimates.

Monte Carlo simulations were used to reveal a subtle, hidden contribution to van't Hoff enthalpy estimates from small heat capacity changes. In simulated van't Hoff plots of ln K versus I/T, small heat capacity changes (-200 < or = delta Cp < or = +200 cal mol-1 K-1), for which curvature could not be discerned within the noise of the data, were found to systematically bias the slope, leading to apparently erroneous enthalpy estimates. Nonlinear least squares analysis of the simulated van't Hoff plots further revealed that it is difficult to extract statistically reliable delta Cp values from data with even modest noise levels. Estimates of delta Cp and delta HvH were found to be highly correlated, indicating an ill-posed nonlinear fitting problem. Nonlinear fits were found in many cases to be statistically no better than simpler linear fits. These simulations show, however, that if an independent calorimetric enthalpy estimate is available, apparent discrepancies between that value and estimates derived from van't Hoff plots may be used to infer the existence of a small heat capacity change and its sign. By this procedure, apparent differences between van't Hoff and calorimetric enthalpy estimates may be interpreted and reconciled. An important conclusion from these studies is that such differences most likely result for statistical reasons, rather than from underlying physical causes.