# Gibbs free energy

Gibbs free energy ($\displaystyle G$) is energy that is available to do useful work. It can be thought of as a balance between enthalpy and entropy that accurately represents their roles in determining the spontaneity of a reaction. The change in free energy is defined by

$\displaystyle \Delta{} G = \Delta{} H - T \Delta{} S$.

The sign of $\displaystyle \Delta{} G$ tells us whether the reaction is spontaneous:

- $\displaystyle \Delta{} G < 0 \Rightarrow$ spontaneous
- $\displaystyle \Delta{} G > 0 \Rightarrow$ non-spontaneous

When $\displaystyle \Delta{} H$ and $\displaystyle \Delta{} S$ have different signs, we know the spontaneity right away. When they have the same signs, we have to use $\displaystyle \Delta{} G$ to determine which one overcomes the other.