Sycamore High School AP Chemistry

Welcome to this tutorial on Gibbs free energy

The Gibbs free energy, originally called available energy, was developed in the 1870s by the American mathematician Josiah Willard Gibbs.

"Available energy" is the greatest amount of mechanical work which can be obtained from a given quantity of a certain substance in a given initial state, without increasing its total volume or allowing heat to pass to or from external bodies, except such as at the close of the processes are left in their initial condition.

J.W. Gibbs, “A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces,“ Transactions of the Connecticut Academy of Arts and Sciences 2, Dec. 1873, pp. 382-404 (quotation on p. 400).

The formula for calculating Gibbs free energy is:

dG=dH-TdS

For a reaction to be spontaneous, dG MUST be negative!

There are four possible scenarios one can encounter.

If enthalpy (dH) is negative (the reaction is exothermic) and entropy (dS) is positive, then:

1

dG = dH - TdS

dG becomes negative in ALL occasions and the reaction is ALWAYS spontaneous.

If enthalpy (dH) is positive (the reaction is endothermic) and entropy (dS) is negative, then:

2

dG = dH - TdS

dG becomes positive in ALL occasions and the reaction is NEVER spontaneous.

These two scenarios are rather easy, almost trivial. It is the next two that require some thought.

What if the signs on enthalpy and entropy are in opposition to each other (both positive or both negative)?

If enthalpy (dH) is negative (the reaction is exothermic) and yet entropy (dS) is also negative, then:

3

dG = dH - TdS

dG can be either positive or negative, it now becomes dependent upon the variable T.

If the temperature is low, then the enthalpy portion dictates the sign of dG:

3

dG = dH -

TdS

- -

With a low enough temperature, dG will be negative and the reaction will be spontaneous.

So, in general, if a reaction has negative values for both dH and dS, then it will be spontaneous at lower temperatures.

If enthalpy (dH) is positive (the reaction is endothermic) and yet entropy (dS) is also positive, then:

4

dG = dH - TdS

dG can be either positive or negative, it now becomes dependent upon the variable T.

If the temperature is high, then the entropy portion dictates the sign of dG:

4

dG = dH

- TdS

+ +

With a high enough temperature, dG will be negative and the reaction will be spontaneous.

And, in general, if a reaction has positive values for both dH and dS, then it will be spontaneous at higher temperatures.

Ack! What if dG is equal to zero?!

That's a great question.

Maybe this picture will help answer your question, AND show how dG must be negative for a reaction to proceed.