Relation de van 't Hoff

The Van 't Hoff equation relates the change in the equilibrium constant, Keq, of a chemical reaction to the change in temperature, T, given the standard enthalpy change, ΔrH⊖, for the process. The subscript means "reaction" and the superscript means "standard". It was proposed by Dutch chemist Jacobus Henricus van 't Hoff in 1884 in his book Études de Dynamique chimique (Studies in Dynamic Chemistry). The Van 't Hoff equation has been widely utilized to explore the changes in state functions in a thermodynamic system. The Van 't Hoff plot, which is derived from this equation, is especially effective in estimating the change in enthalpy and entropy of a chemical reaction. The standard pressure, , is used to define the reference state for the Van 't Hoff equation, which is where ln denotes the natural logarithm, is the thermodynamic equilibrium constant, and R is the ideal gas constant. This equation is exact at any one temperature and all pressures, derived from the requirement that the Gibbs free energy of reaction be stationary in a state of chemical equilibrium. In practice, the equation is often integrated between two temperatures under the assumption that the standard reaction enthalpy is constant (and furthermore, this is also often assumed to be equal to its value at standard temperature). Since in reality and the standard reaction entropy do vary with temperature for most processes, the integrated equation is only approximate. Approximations are also made in practice to the activity coefficients within the equilibrium constant. A major use of the integrated equation is to estimate a new equilibrium constant at a new absolute temperature assuming a constant standard enthalpy change over the temperature range. To obtain the integrated equation, it is convenient to first rewrite the Van 't Hoff equation as The definite integral between temperatures T1 and T2 is then In this equation K1 is the equilibrium constant at absolute temperature T1, and K2 is the equilibrium constant at absolute temperature T2.