Relations Between E, AG, and

As pointed out previously, the value of the standard cell voltage, E°, is a measure of the spontaneity of a cell reaction. In Chapter 17, we showed that the standard free energy change, AG°, is a general criterion for reaction spontaneity. As you might suppose, these two quantities have a simple relation to one another and to the equilibrium constant, K, for the cell reaction. 

It can be shown by a thermodynamic argument that we will not go through here that these two quantities are related by the equation 

Notice from this equation that AG° and E° have opposite signs. This is reasonable a spontaneous reaction is one for which AG° is negative but E° is positive. 

Redox reactions, like all reactions, eventually reach a state of equilibrium. It is possible to calculate the equilibrium constant for a redox reaction from the standard voltage. To do that, we start with the relation obtained in Chapter 17  

We have just seen that AG° = — nFE°. It follows that 

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