# Why is Gibbs free energy useful?

Dec 30, 2017

Why....?

#### Explanation:

Well, to quote a text-book, the $\text{Gibbs free energy}$ is the single, unequivocal criterion as to the spontaneity of chemical change...

And it is normally introduced by quoting an enthalpy term, and an entropy term...i.e...

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

...and this function can be further related to the thermodynamic equilibrium constant for a given reaction....by the relation....

$\ln {K}_{\text{eq}} = \frac{- \Delta {G}^{\circ}}{R T}$

And quite clearly, ONLY negative $\Delta {G}^{\circ}$ values will give rise to a positive ${K}_{\text{eq}}$ value, and thus only reactions with negative $\Delta {G}^{\circ}$ values are spontaneous.