Gibbs–Helmholtz equation

The Gibbs–Helmholtz equation is a thermodynamic equation used for calculating changes in the Gibbs energy of a system as a function of temperature. It is named after Josiah Willard Gibbs and Hermann von Helmholtz. ( ∂ ( G T ) ∂ T ) p = − H T 2 , {displaystyle left({frac {partial ({frac {G}{T}})}{partial T}} ight)_{p}=-{frac {H}{T^{2}}},} for the differential of G, and remembering The Gibbs–Helmholtz equation is a thermodynamic equation used for calculating changes in the Gibbs energy of a system as a function of temperature. It is named after Josiah Willard Gibbs and Hermann von Helmholtz. Equation The equation is: where H is the enthalpy, T the absolute temperature and G the Gibbs free energy of the system, all at constant pressure p. The equation states that the change in the G/T ratio at constant pressure as a result of an infinitesimally small change in temperature is a factor H/T2. The typical applications are to chemical reactions. The equation reads: with ΔG as the change in Gibbs energy and ΔH as the enthalpy change (considered independent of temperature). The o denotes standard pressure (1 bar). Integrating with respect to T (again p is constant) it becomes: This equation quickly enables the calculation of the Gibbs free energy change for a chemical reaction at any temperature T2 with knowledge of just the Standard Gibbs free energy change of formation and the Standard enthalpy change of formation for the individual components. Also, using the reaction isotherm equation, that is