The free energy change for a reaction, \(\Delta G,\) is an extensive property. What is an extensive property? Surprisingly, one can calculate \(\Delta G\) from the cell potential, \(\mathscr{E}\), for the reaction. This is surprising because \(\mathscr{E}\) is an intensive property. How can the extensive property \(\Delta G\) be calculated from the intensive property \(\mathscr{E}\) ?

An extensive property is a property that depends on the amount of material or substance present. It scales with the size or quantity of the system. Examples of extensive properties include mass, volume, and energy. On the other hand, an intensive property is a property that does not depend on the amount of material or substance. It is independent of the size or quantity of the system. Examples of intensive properties include temperature, pressure, and density.

The free energy change (ΔG) for a reaction is the change in the Gibbs free energy, which is a thermodynamic potential that measures the maximum reversible work that may be performed by a system at constant temperature and pressure. In essence, ΔG can be understood as the capacity of a system to perform useful work or to drive chemical reactions. Since ΔG depends on the energy content of the reactants and products in a reaction, it is an extensive property.

Cell potential (ℰ) is the measure of the potential difference between the two electrodes in an electrochemical cell when no current flows through the cell. It is related to the driving force of the chemical reaction and can be thought of as the "push" that drives electrons from the anode to the cathode in a redox reaction. Cell potential is determined by the composition of materials in the cell and the temperature at which the cell is operating. As it is independent of the amount of material, ℰ is an intensive property.

It may seem counterintuitive that an extensive property like ΔG can be calculated from an intensive property like ℰ. However, this is possible due to the relationship between the two properties in electrochemical reactions. The relationship between ΔG and ℰ is given by the equation: ΔG = -nFℰ In this equation, n is the number of moles of electrons involved in the redox reaction, and F is the Faraday constant (approximately 96485 C/mol), which represents the electric charge per mole of electrons. Since n is an extensive property (related to the amount of material), the product of n, F, and ℰ gives us an extensive property - the free energy change, ΔG. This relationship enables us to calculate the extensive property ΔG by using the intensive property ℰ, considering the number of moles of electrons involved in the reaction and the Faraday constant.