∆G = ∆H – T∆S
where T is the absolute temperature.
Spontaneity of Reaction
In the equilibrium state, free energy is at a minimum. A process can occur spontaneously if the Gibbs
function decreases, i.e., ∆G < 0.
Because the temperature is always positive, i.e., in Kelvins, the effects of the signs of ΔH and ΔS and
the effect of temperature on spontaneity can be summarized as follows:
∆H ∆S Outcome
− + spontaneous at all temperatures
+ − nonspontaneous at all temperatures
+ + spontaneous only at high temperatures
− − spontaneous only at low temperaturesQualitatively, the equation ΔG = ΔH − TΔS, and more generally the whole notion of free energy, tell
us that there are two factors that favor a reaction: a decrease in energy in the form of enthalpy and
an increase in disorder. If these two factors are working against each other in a reaction, then
temperature will determine which is the more dominant factor—the higher the temperature, the
easier entropic considerations override enthalpic ones. Note also the implication that a reaction
that is favorable at one temperature may not be favorable at another. This, actually, should not be a
surprise; after all, for example, the melting of ice is expected to occur at 15 ºC, but not at −100 ºC
(assuming atmospheric pressure).
Standard Free Energy Change
1. If ΔG is negative, the reaction is spontaneous.
2. If ΔG is positive, the reaction is not spontaneous.
3. If ΔG is zero, the system is in a state of equilibrium; thus, ΔG = 0 and ΔH = TΔS at equilibrium.