Gibbs–Helmholtz equation
/ GIB-z HELM-holts /
The Gibbs–Helmholtz equation is a shortcut that lets you predict how a reaction's free energy will shift with temperature without re-measuring it at every degree. Think of it as a recipe: feed it the heat a reaction gives off (its enthalpy) at one temperature, and it tells you how the free energy — and so the equilibrium — will slide as you warm or cool the system.
Its content is that the way Gibbs free energy changes with temperature is governed by enthalpy. In a tidy form it says that d(ΔG°/T)/dT = −ΔH°/T², which simply means: knowing the enthalpy of a reaction is enough to track how its standard free energy responds to a change in temperature. The companion van 't Hoff equation does the same job for the equilibrium constant.
Why it matters: it underlies the everyday rule that heating shifts equilibria — pushing endothermic reactions forward and pulling exothermic ones back — and it powers the practical trick of finding a reaction's enthalpy from how its equilibrium constant varies with temperature. The honest caveat: the simple version treats ΔH° as roughly constant over the temperature range, which holds for modest spans but frays over very wide ones.
Measure a reaction's equilibrium constant at several temperatures, plot ln K against 1/T, and the slope hands you ΔH° straight off — the Gibbs–Helmholtz idea turned into a working laboratory recipe.
Temperature dependence of equilibrium reveals the reaction's enthalpy.
Don't confuse this with the Gibbs–Helmholtz relation's close relative, the van 't Hoff equation: they carry the same physics but one is written for ΔG° and the other for ln K. Both rest on the same approximation that enthalpy varies little over the range studied.