Gibbs energy and spontaneity

Gibbs energy is defined as G = H − TS; at constant temperature ΔG = ΔH − TΔS.

At constant temperature and pressure, ΔG < 0 means spontaneous, ΔG > 0 means non-spontaneous (the reverse is spontaneous), and ΔG = 0 means equilibrium.

ΔH < 0 and ΔS > 0: ΔG is negative at all temperatures, always spontaneous.

ΔH > 0 and ΔS < 0: ΔG is positive at all temperatures, never spontaneous.

ΔH < 0 and ΔS < 0: spontaneous only at low temperature, when |ΔH| > |TΔS|.

ΔH > 0 and ΔS > 0: spontaneous only at high temperature, when TΔS > ΔH.

The temperature at which ΔG changes sign is T = ΔH/ΔS, assuming both stay roughly constant; convert ΔS to kJ K⁻¹ mol⁻¹ before dividing into ΔH in kJ mol⁻¹.