Calculate ΔG°rxn and E°cell for a redox reaction with n = 3 that has an equilibrium constant of K = 0.050 (at 25 °C).

Gibbs Free Energy (ΔG°rxn) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic process at constant temperature and pressure. It indicates the spontaneity of a reaction: a negative ΔG°rxn suggests that the reaction can occur spontaneously, while a positive value indicates non-spontaneity. The relationship between ΔG°rxn and the equilibrium constant (K) is given by the equation ΔG°rxn = -RT ln(K), where R is the universal gas constant and T is the temperature in Kelvin.

The Nernst Equation relates the cell potential (E°cell) of an electrochemical reaction to the concentrations of the reactants and products. It is expressed as E = E° - (RT/nF) ln(Q), where E° is the standard cell potential, n is the number of moles of electrons transferred, F is Faraday's constant, and Q is the reaction quotient. This equation allows for the calculation of E°cell from the equilibrium constant (K) using the relationship E°cell = (RT/nF) ln(K), which connects thermodynamics and electrochemistry.

The equilibrium constant (K) is a dimensionless number that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. It provides insight into the extent of a reaction: a large K indicates that products are favored, while a small K suggests that reactants are favored. The value of K is directly related to the standard Gibbs free energy change (ΔG°rxn) and can be used to determine the spontaneity and direction of a reaction.