Editing Gibbs–Helmholtz equation (section)

==Chemical reactions and work==

{{Main|Thermochemistry}}

The typical applications of this equation are to [[chemical reaction]]s. The equation reads:<ref>Chemical Thermodynamics, D.J.G. Ives, University Chemistry, Macdonald Technical and Scientific, 1971, {{ISBN|0-356-03736-3}}</ref>

:<math>\left( \frac{\partial ( \Delta G^\ominus/T ) } {\partial T} \right)_p = - \frac {\Delta H^\ominus} {T^2}</math>

with Δ''G'' as the change in Gibbs energy due to reaction, and Δ''H'' as the [[enthalpy of reaction]] (often, but not necessarily, assumed to be independent of temperature). The <s>o</s> denotes the use of [[Standard state|standard states]], and particularly the choice of a particular standard pressure (1 bar), to calculate Δ''G'' and Δ''H''.

Integrating with respect to ''T'' (again ''p'' is constant) yields:

:<math> \frac{\Delta G^\ominus(T_2)}{T_2} - \frac{\Delta G^\ominus(T_1)}{T_1} = \Delta H^\ominus \left(\frac{1}{T_2} - \frac{1}{T_1}\right) </math>

This equation quickly enables the calculation of the Gibbs free energy change for a chemical reaction at any temperature ''T''<sub>2</sub> 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,<ref>Chemistry, Matter, and the Universe, R.E. Dickerson, I. Geis, W.A. Benjamin Inc. (USA), 1976, {{ISBN|0-19-855148-7}}</ref> that is

:<math>\frac{\Delta G^\ominus}{T} = -R \ln K </math>

which relates the Gibbs energy to a chemical [[equilibrium constant]], the [[van 't Hoff equation]] can be derived.<ref>Chemical Thermodynamics, D.J.G. Ives, University Chemistry, Macdonald Technical and Scientific, 1971, {{ISBN|0-356-03736-3}}</ref>

Since the change in a system's Gibbs energy is equal to the maximum amount of non-expansion work that the system can do in a process, the Gibbs–Helmholtz equation may be used to estimate how much non-expansion work can be done by a chemical process as a function of temperature.<ref name="P Chem 1">{{cite book |last1=Gerasimov |first1=Ya |title=Physical Chemistry Volume 1 |date=1978 |publisher=MIR Publishers |location=Moscow  |page=118 |edition=1st}}</ref> For example, the capacity of rechargeable electric batteries can be estimated as a function of temperature using the Gibbs–Helmholtz equation.<ref name="P Chem 2">{{cite book |last1=Gerasimov |first1=Ya |title=Physical Chemistry Volume 2 |date=1978 |publisher=MIR Publishers |location=Moscow  |page=497 |edition=1st}}</ref>