# The Free Energy-Emf Relation

The change in free energy (Î”G) is the maximum amount of energy that is available to do useful work. In an electrochemical cell, this free energy is equal to electrical work which is equal to the product of the number electrons, the Faraday constant, and the electrochemical cell's emf.

In this equation, n is the number of equivalents of electrons transferred in the reaction, F is the Faraday constant (96,500 Coulombs), and E0cell (cell's emf). From this equation, we can deduce that if the emf is positive, the corresponding change in free energy (Î”G) will be negative. In other words, if the emf is positive the reaction is most likely to be spontaneous. On the other had, if the emf of a cell is negative, the Î”G will be positive indicating a nonspontaneous reaction.

Example

Calculate the standard free energy change at 25Â°C for the redox reaction in Example 12-1. (Faraday constant = 96,500 coulombs)

Solution

From the previous example, we know that the emf of this reaction is 1.10 V. The formula for Î”G in terms of the potential difference is:

Here, the number of electrons transferred is 2. This number is obtained by examining the balanced equation and evaluating the change in oxidation numbers. For example, copper ions with +2 oxidation state changed to copper (solid) with an oxidation state of 0. In other words, each half-reaction involves two electrons

Notice that the change in free energy is negative and this indicates that the reaction is likely to be spontaneous.