Van't Hoff equation

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The Van't Hoff equation in chemical thermodynamics relates the change in temperature to the change in the equilibrium constant given the enthalpy change. It assumes enthalpy change is constant over the temperature range. The equation was first derived by Jacobus Henricus van 't Hoff.

\ln \left( {\frac{{K_2 }}{{K_1 }}} \right) = - \frac{{\Delta H^\circ }}{R}\left[ {\frac{1}{{T_2 }} - \frac{1}{{T_1 }}} \right]

In this equation \ K_1 is the equilibrium constant at absolute temperature \ T_1 and \ K_2 is the equilibrium constant at absolute temperature \ T_2. \ \Delta H^\circ is the enthalpy change and \ R is the gas constant.

In another notation:

\ln \left( K \right) = - \frac{{\Delta H^\circ }}{R}\left[ {\frac{1}{{T }}}\right] + \frac{{\Delta S^\circ }}{R}

a plot of the natural logarithm of the equilibrium constant measured for a certain equilibrium versus the reciprocal temperature gives a straight line, the slope of which is the negative of the enthalpy change divided by the gas constant and the intercept of which is equal to the entropy change \ \Delta S^\circ divided by the gas constant.

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