Temperature and Free Energy

Temperature and Free Energy

The values of ΔG^o are tabulated at 25^oC, but we are often interested in examining reactions at other temperatures. How is the free-energy change affected by temperature. The answer is given by the Gibbs-Helmholtz equation.

ΔG = ΔH - TΔS

We can summarize the effect of temperature on free-energy as follows:

ΔH^o ΔS^o ΔG^o Description

- + - Spontaneous at all T

+ - + Nonspontaneous at all T

- - + or - Spontaneous at low T;
Nonspontaneous at high T

+ + + or - Spontaneous at low T;
Nonspontaneous at high T

We can also use the Gibbs-Helmholtz equation to find the temperature (if there is one) at which a reaction changes from being spontaneous to nonspontaneous or vice versa. At this point of change the system will be at equilibrium, and we recall that at equilibrium ΔG = 0. Substituting this into the Gibbs-Helmholtz equation and solving for T we get:

ΔG = 0 = ΔH^o - TΔS^o

T = ΔH^o / ΔS^o

Back to Thermodynamics Index Page

ΔH^o	ΔS^o	ΔG^o	Description
-	+	-	Spontaneous at all T
+	-	+	Nonspontaneous at all T
-	-	+ or -	Spontaneous at low T; Nonspontaneous at high T
+	+	+ or -	Spontaneous at low T; Nonspontaneous at high T