Combining the well-known formula for the Gibbs free energy of reaction
where  is the entropy of the system, with the Gibbs free energy isotherm equation:
we obtain
Differentiation of this expression with respect to the variable  while assuming that both and  are independent of  yields the Van 't Hoff equation. These assumptions are expected to break down somewhat for large temperature variations.
Provided that  and  are constant, the preceding equation gives  as a linear function of  and hence is known as the linear form of the Van 't Hoff equation. Therefore, when the range in temperature is small enough that the standard reaction enthalpy and reaction entropy are essentially constant, a plot of the natural logarithm of the equilibrium constant versus the reciprocal temperature gives a straight line. The slope of the line may be multiplied by the gas constant  to obtain the standard enthalpy change of the reaction, and the intercept may be multiplied by  to obtain the standard entropy change.