Gibbs free energy

Gibbs free energy ($G$) 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

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

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

• $\mathrm{\Delta }G<0⟹$ spontaneous
• $\mathrm{\Delta }G>0⟹$ non-spontaneous

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