Consider the following half-reactions and E° values: (c) Write the cell reaction for part (b), and calculate the values of E°, ∆G° (in kilojoules), and K for this reaction at 25 °C

Verified step by step guidance

1. Identify the two half-reactions involved in the electrochemical cell and their respective standard reduction potentials (E°).
2. Write the balanced overall cell reaction by combining the two half-reactions, ensuring that the number of electrons lost in the oxidation half-reaction equals the number of electrons gained in the reduction half-reaction.
3. Calculate the standard cell potential (E°_cell) by subtracting the standard reduction potential of the anode (oxidation) from the standard reduction potential of the cathode (reduction): E°_cell = E°_cathode - E°_anode.
4. Use the Nernst equation to calculate the standard Gibbs free energy change (∆G°) for the reaction: ∆G° = -nFE°_cell, where n is the number of moles of electrons transferred and F is the Faraday constant (approximately 96485 C/mol).
5. Calculate the equilibrium constant (K) for the reaction at 25 °C using the relationship between ∆G° and K: ∆G° = -RTlnK, where R is the universal gas constant (8.314 J/mol·K) and T is the temperature in Kelvin (298 K).

Key Concepts

Electrode Potential (E°)

Electrode potential, denoted as E°, is a measure of the tendency of a chemical species to be reduced, expressed in volts. It is determined under standard conditions (1 M concentration, 1 atm pressure, and 25 °C). The more positive the E° value, the greater the species' ability to gain electrons and undergo reduction, which is crucial for predicting the direction of electron flow in electrochemical cells.

Gibbs Free Energy (∆G°)

Gibbs free energy change (∆G°) is a thermodynamic quantity that indicates the spontaneity of a reaction at standard conditions. It is calculated using the equation ∆G° = -nFE°, where n is the number of moles of electrons transferred, F is Faraday's constant, and E° is the cell potential. A negative ∆G° indicates a spontaneous reaction, while a positive value suggests non-spontaneity.

Equilibrium Constant (K)

The equilibrium constant (K) quantifies the ratio of the concentrations of products to reactants at equilibrium for a given reaction. It is related to the Gibbs free energy change by the equation ∆G° = -RT ln(K), where R is the universal gas constant and T is the temperature in Kelvin. A larger K value indicates a reaction that favors product formation, while a smaller K suggests reactants are favored.