Calculate ΔG°_rxn and E°_cell for a redox reaction with n = 2 that has an equilibrium constant of K = 25 (at 25 °C).

Verified step by step guidance

Identify the relationship between the equilibrium constant (K) and the standard Gibbs free energy change (ΔG°_rxn) using the equation: ΔG°_rxn = -RT ln(K), where R is the universal gas constant (8.314 J/mol·K) and T is the temperature in Kelvin (298 K for 25 °C).

Substitute the given values into the equation: ΔG°_rxn = -(8.314 J/mol·K)(298 K) ln(25).

Calculate the natural logarithm of the equilibrium constant, ln(25).

Use the calculated value of ln(25) to find ΔG°_rxn by completing the multiplication and division in the equation.

Relate ΔG°_rxn to the standard cell potential (E°_cell) using the equation: ΔG°_rxn = -nFE°_cell, where n is the number of moles of electrons transferred (n = 2) and F is Faraday's constant (96485 C/mol). Solve for E°_cell by rearranging the equation: E°_cell = -ΔG°_rxn / (nF).

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Gibbs Free Energy (ΔG°)

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

Nernst Equation

The Nernst Equation relates the cell potential (E) 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 is essential for calculating the cell potential under non-standard conditions and understanding how concentration affects the electrochemical reaction.

Equilibrium Constant (K)

The equilibrium constant (K) is a dimensionless value 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 reactants are favored. The relationship between K and standard cell potential (E°) is given by the equation E° = (RT/nF) ln(K), linking thermodynamics and electrochemistry.