# 9: Helmholtz and Gibbs Energies

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• 9.1: Helmholtz Energy
Above we have answered the question: what is entropy really, but we still do not have a general criterion for spontaneity, just one that works in an isolated system. Let's fix that now. It leads to two new state functions that prove to be most useful ones of thermodynamics.
• 9.2: Gibbs Energy
• 9.3: The Maxwell Relations
To fully exploit the power of the state functions we need to develop some mathematical machinery by considering a number of partial derivatives.
• 9.4: The Enthalpy of an Ideal Gas
The enthalpy of an ideal Gas Is independent of pressure.
• 9.5: Gibbs-Helmholtz Relation (Gibbs Energy-Chang)
Gibbs energy is the energy of a chemical reaction that can be used to do non-mechanical work.
• 9.6: The Gibbs-Helmholtz Equation
The first order partial on G versus P is the volume V; this allows us to find the dependence of G on P by simply integrating over the volume V from one pressure to the other.

9: Helmholtz and Gibbs Energies is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.