negative gibbs free energy = rxn happens

Predicting Spontaneity: How Its Done

Predicting the Spontaneity of a Reaction can be a tricky business. On the surface you would think that the Change in Enthalpy (Delta H rx ) would predict whether a reaction is spontaneous or not simply by applying the First Law of Thermodynamics. If Delta H were negative that would mean that the chemical system would lose energy to the surroundings and that should make the products more stable. According to the First Law all systems tend toward lower (more stable) energy state. However the first law considers the total energy of the system. It doesn't take into account that maybe some of this energy change would involve an entropy increase big enough to make a reaction that might be predicted to be non-spontaneous to actually be spontaneous. Indeed there are some reactions that are spontaneous at low temperatures whereas others are spontaneous at only high temperatures. Therefore Delta H is not a fool proof way of predicting spontaneity.

Others might consider using the Change in Entropy of a reaction system to be a good indicator or predictor of spontaneity. According to the Second Law systems tend toward higher entropy so it might be concluded that if the change in Entropy is positive this would indicate spontaneity. The problem with that is that the second law is referring to "isolated" systems that have no input from the outside environment. If that happens and it is more than likely it will, then Delta S would not always predict spontaneity. There are systems that have a negative Delta S such as The precipitation of a slightly soluble salt from a chemical reaction which occurs spontaneously. What happens when you pour a solution of NaCl together with a solution of Silver Nitrate?

So what will be a good predictor? A good predictor of spontaneity would be one that considers the Delta H, the Delta S, and the temperature since there are some reactions as noted above that seem to respond to changes of temperature even though we find the Delta H and Delta S would be approximately the same at any temperature.

Gibbs-Helmholtz Equation



Professor Gibbs and Helmholtz came up with a relationship that took all three of these factors into consideration. This is known as the Gibbs Helmholtz Equation:

Delta G rx = Delta H rx - T(Delta S rx )

Let's identify each term in this very important equation.


The Delta H rx represents the total energy exchange that takes place between the system and its environment.
The T(Delta S rx ) term represents the energy eused to take care of the intermolecular activity. This is wasted energy and has to be subtracted from the total energy. An analogy can be drawn here between a mechanical engine and a chemical reaction (engine). When a mechanical engine performs useful work not all of the energy output of the engine goes toward that end. Some of the energy output is wasted due to friction of moving parts. That is why we never have a perpetual motion engine. The friction of the moving parts will be wasted energy and must be subtracted from the total energy output to get the net useful energy capable of performing a task or work.
Delta G represents that net useful energy of a chemical system (engine). Due to the fact that molecules in motion will rub up against each other more or less depending on how independent they are of one another (the higher the entropy the more independent they are). This molecular friction (T Delta S) will siphon off from the total energy (Delta H) to result in net energy capable of performing a task (Delta G).

If Delta G is negative then the net useful energy will be released to perform work. This will occur spontaneously. On the other hand if Delta G is positive then the net energy will have to be absorbed from the environment and therefore the reaction cannot occur unless something is done on the outside.
A third possibility is if Delta G was equal to zero. At that value the system is in a state of equilibrium. If one knows the Delta H and Delta S then one can determine the equilibrium temperature for the system by setting Delta G equal to 0 and solving for T. This equilibrium temperature would be the break even point for systems that might be positive or negative depending upon the temperature.