The Relationship Between emf and Free Energy

In Chapter 16, we showed the relationship between free energy and the spontaneity of a reaction. If you recall, a negative value for AG indicated a spontaneous reaction. In the last section, we saw that a positive cell voltage, or emf, indicates a spontaneous process. The free energy and emf can be related in equation 17.3, which states 

Because n and F are both positive, a positive cell emf (spontaneous reaction) will produce a negative AG (spontaneous reaction). On the AP exam, the symbol for Faraday s constant is written as 

Sample Calculate the standard free-energy change for the reaction shown below  

Answer To solve the problem we need to know the values for n and E. Let s begin by looking at E. Zinc is the anode in this reaction, and silver is the cathode. You can tell this in two ways the first is that the reduction potential for silver is more positive than zinc, and second because silveris being reduced in the reaction. Knowing this, we can use equation 19.2 to determine E. 

We already know that this will occur spontaneously because of the positive value for E. In the reaction, two electrons are transferred from Zn to 2Ag+, which is evident from the half reactions shown below  

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The dependence of emf on the activities or concentrations of the products and reactants of a cell reaction follows directly from a consideration of the relationship between emf and free energy change. For the cell reaction... 

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