Introduction

The Van't Hoff equation describes how the equilibrium constant (K_eq) of a reaction varies with temperature (T). It is derived from the definition of the Gibbs free energy as well as the Gibbs free energy isotherm equation.

Standard* Gibbs free energy (ΔG^ϴ) where:

• R is the universal gas constant (8.314 J/mol/K)
• T is the absolute temperature (in Kelvin),
• K_eq is the equilibrium constant.

 Standard Gibbs free energy (ΔG^ϴ) isotherm where:

• ΔH^ϴ is the standard enthalpy change.
• ΔS^ϴ is the standard entropy change.
  
  

Substituting the expression for ΔG^ϴand rearrangement gives the logarithmic form of the Van’t Hoff equation:

A Van't Hoff plot allows the estimation of the enthalpy (H) and entropy (S) of a reaction. To obtain such a plot, the equilibrium constant must be measured at different reaction temperatures. The natural logarithm of the equilibrium constant (ln K_eq) is then plotted against the reciprocal temperature (1/T), where ΔH is the slope and ΔS the y-intercept of the plot.

A guide on experimental setup and Software handling can be found in Thermodynamics Measurements.

Data Interpretation:

Enthalpy (ΔH) describes the overall heat exchanged during binding, indicating whether the process is endothermic or exothermic. A negative ΔH value suggests an exothermic interaction (heat is released), often driven by favorable specific interactions such as hydrogen bonds, van der Waals forces, or hydrophobic effects, which reduce the system's free energy. Entropy (ΔS) represents the degree of disorder or freedom within the system. A positive ΔS value indicates increased disorder, commonly resulting from the release of structured water molecules upon binding, a phenomenon known as desolvation. Together, ΔH and ΔS, determine whether binding is enthalpically or entropically favored. Enthalpic binders are characterized by strong, specific interactions that release heat, while entropic binders benefit from an increase in system disorder, often due to the displacement of ordered solvent molecules.

Use Cases and Limitations

The Van't Hoff plot is most effective over a small temperature range, typically between 15°C and 40°C, where enthalpy and entropy are roughly constant. Significant non-linear behavior suggests the need to consider temperature-dependent effects or potential changes in the molecular state, such as protein unfolding or oligomerization.

* Note: The superscript '' denotes "standard".