Free Energy

The free energy of a system, represented by the letter "G", is defined as the energy of a system that is free to do work at constant temperature and pressure. Mathematically,  the change in free energy  is defined as:

where G is the free energy (sometimes called the Gibbs free energy, named after its discoverer), DH is the change in enthalphy, T is the temperature, and DS is the entropy change all of the system. At a constant temperature and pressure, the direction of any spontaneous change is toward a lower free energy. During a reaction, the amount of free energy decreases until the reaction reaches equilibrium.  If the reaction goes to completion, the free energy minimum occurs very close to the point in the reaction only pure products are present.  When DG is a negative number the reaction will occur spontaneously.  A positive DG means that this reaction will need and energy input to occur.  It is not spontaneous if DG is positive.

A table relating all of the state properties summarized above -- enthalphy change, entropy change, and change in free energy -- is shown below. These are the conditions that favor a spontaneous reaction occuring:
 
 
 

Enthalphy Change Entropy Change Spontaneous Reaction?  Exothermic  (DH < 0) Increase  (DS > 0) Yes, DG < 0  Exothermic  (DH < 0) Decrease (DS < 0) If  |T DS| < |DH|  Endothermic (DH > 0) Increase  (DS > 0) If  T DS > DH  Endothermic (DH > 0) Decrease (DS < 0) No,  DG > 0

The relationship between free energy, enthalpy, temperature and spontaneity is clear when considering the changes in state of water.  Solid water, or ice, is a very ordered, crystalline material.  Given the 2nd Law of Thermodynamics, you might conclude that ice will spontaneously change state to water since the entropy of liquid water is much lower than ice.  In fact this only occurs when the temperature is greater than 0^oC.  At lower temperatures the TDS term is smaller than  DH which means DG is positive.  A positive DG means the reaction is not spontaneous.

An Enthalpy and Gibbs Free Energy Calculator is provided to give you an opportunity to experiment with these relationships.