# van 't Hoff equation

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, ΔH, for the process. It was proposed by Dutch chemist Jacobus Henricus van 't Hoff in 1884 in his book Études de dynamique chimique (Studies in Dynamic Chemistry). This equation is sometimes also referred to as the Vukančić–Vuković equation.

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, or total energy, and entropy, or amount of disorder, of a chemical reaction

Under standard conditions, the van 't Hoff equation is

${\displaystyle {\frac {d}{dT}}\ln K_{\mathrm {eq} }={\frac {\Delta H^{\ominus }}{RT^{2}}}}$

where R is the ideal gas constant. This equation is exact at any one temperature. In practice, the equation is often integrated between two temperatures under the assumption that the reaction enthalpy ΔH is constant. Since in reality ΔH and ΔS do vary with temperature for most processes, the integrated equation is only approximate.

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.

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