Gibbs free energy

Exothermic reactions are not always spontaneous, and spontaneous reactions are not always exothermic. We can't say that a reaction will happen just because it releases energy.

But if we know the change of both enthalpy and entropy in a reaction, we can work out whether it would happen using the formula for Gibbs free energy:

G = H + TS

Where
G = Gibbs free energy
H = Enthalpy of formation of system
T = Temperature
S = Entropy of system

Reactions precede if the change in Gibbs free energy is negative, so in chemistry the following equation is more common:

ΔG = ΔH + TΔS

Where
ΔG = Change in Gibbs free energy
ΔH = Reaction enthalpy change
ΔS = Reaction entropy change

Gibbs free energy equation assumes a constant temperature and pressure, so we are assuming that any temperature change from the heat of ΔH is negligible.

We can try applying this equation to the evaporation of water, which has a positive enthalpy change (since bonds are being broken) and a negative entropy change (gaseous molecules can occupy more microstates).

To be spontaneous, ΔG has to be negative, which requires ΔH - TΔS to be below 0


Using data from wikipedia:

Heat of vaporisation of 1 mole of water = 40680 J / mol
Entropy of vaporisation of water = 108.9 J/(K mol)

So temperature has to be 373.56 Kelvin for ΔH = TΔS, and higher than this for the reaction to proceed, corresponding perfectly with the known boiling point of water.