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

Area of Science:

• Thermodynamics
• Chemical Kinetics
• Biophysical Chemistry

Background:

• The van't Hoff equation is commonly used to determine enthalpy changes from equilibrium constant data.
• Heat capacity changes (ΔCp) can introduce subtle biases in van't Hoff enthalpy (ΔHvH) estimates, particularly with noisy experimental data.
• Distinguishing between statistical artifacts and physical phenomena in thermodynamic data analysis is crucial.

Purpose of the Study:

• To investigate the impact of small heat capacity changes on van't Hoff enthalpy estimates using Monte Carlo simulations.
• To assess the reliability of extracting heat capacity values from noisy van't Hoff plots.
• To provide a method for reconciling discrepancies between van't Hoff and calorimetric enthalpy measurements.

Main Methods:

• Monte Carlo simulations were employed to generate synthetic van't Hoff plots (ln K vs. 1/T).
• Simulated data incorporated varying small heat capacity changes within realistic noise levels.
• Nonlinear least squares analysis was performed to estimate thermodynamic parameters.

Main Results:

• Small heat capacity changes (-200 to +200 cal mol⁻¹ K⁻¹) systematically biased van't Hoff enthalpy estimates, even when curvature was not visually apparent.
• Extracting statistically reliable heat capacity values from noisy data proved challenging.
• Estimates of ΔCp and ΔHvH were highly correlated, indicating an ill-posed fitting problem.
• Nonlinear fits were often statistically indistinguishable from linear fits.

Conclusions:

• Apparent discrepancies between van't Hoff and calorimetric enthalpy estimates can serve as indicators of small, hidden heat capacity changes.
• Such discrepancies are frequently attributable to statistical artifacts rather than novel physical causes.
• Comparing van't Hoff and calorimetric enthalpy data provides a robust approach to interpret and reconcile thermodynamic measurements.