Category : Exam Preparation Tips
Van-t Hoff Differential Method
The van 't Hoff equation in chemical thermodynamics relates the change in the equilibrium constant, Keq, of a chemical equilibrium to the change in temperature, T, given the standard enthalpy change, ΔHo, for the process. It was proposed by Dutch chemist J.H. van't Hoff in 1884.
Under standard conditions
The van't Hoff equation is based on the assumption that the enthalpy and entropy are constant with temperature changes. In practice, the equation is experimentally approximate in that both enthalpy and entropy changes of a process (reaction) vary (each differently) with temperature. Its accuracy is determined in accounting for the curvature in the standard enthalpy changes over temperature. A major use of the equation is to estimate a new equilibrium constant at a new absolute temperature assuming a constant standard enthalpy change over the temperature range.
Under standard conditions, the van't Hoff equation is
where R is the gas constant. This can also be written as
Taking the definite integral of this differential equation between temperatures T1 and T2 gives
In this equation K1 is the equilibrium constant at absolute temperature T1, and K2 is the equilibrium constant at absolute temperature T2.
From the definition of Gibbs free energy
where S is the entropy of the system, and from the Gibbs free energy isotherm equation
The linear form of the van't Hoff equation can be obtained
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