Spontaneity of Redox Reaction
During operation of electrochemical cells, chemical energy is transformed into electrical energy and is expressed mathematically as the product of the cell's emf and the electric charge transferred through the external circuit.
- Electrical energy = EcellCtrans
where Ecell is the cell potential measured in volts (V) and Ctrans is the cell current integrated over time and measured in coulombs (C); Ctrans can also be determined by multiplying the total number of electrons transferred (measured in moles) times Faraday's constant (F).
The emf of the cell at zero current is the maximum possible emf. It is used to calculate the maximum possible electrical energy that could be obtained from a chemical reaction. This energy is referred to as electrical work and is expressed by the following equation:
- Wmax = Welectrical = –nF·Ecell,
where work is defined as positive into the system.
Since the free energy is the maximum amount of work that can be extracted from a system, one can write:
- ΔG = –nF·Ecell
A positive cell potential gives a negative change in Gibbs free energy. This is consistent with the cell production of an electric current from the cathode to the anode through the external circuit. If the current is driven in the opposite direction by imposing an external potential, then work is done on the cell to drive electrolysis.
A spontaneous electrochemical reaction (change in Gibbs free energy less than zero) can be used to generate an electric current in electrochemical cells. This is the basis of all batteries and fuel cells. For example, gaseous oxygen (O2) and hydrogen (H2) can be combined in a fuel cell to form water and energy, typically a combination of heat and electrical energy.
Conversely, non-spontaneous electrochemical reactions can be driven forward by the application of a current at sufficient voltage. The electrolysis of water into gaseous oxygen and hydrogen is a typical example.
The relation between the equilibrium constant, K, and the Gibbs free energy for an electrochemical cell is expressed as follows:
- ΔG° = –RT ln(K) = –nF·E°cell
Rearranging to express the relation between standard potential and equilibrium constant yields
- .
The previous equation can use Briggsian logarithm as shown below:
Read more about this topic: Electrochemistry
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