A mercury battery uses the following electrode half-reactions: (b) Calculate ∆G° (in kilojoules) and K at 25 °C for the cell reaction.

Verified step by step guidance

1. Identify the half-reactions involved in the mercury battery. Typically, these might be the reduction of mercury(II) oxide and the oxidation of zinc.
2. Write the balanced overall cell reaction by combining the two half-reactions. Ensure 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 using the standard reduction potentials for each half-reaction: E°_cell = E°_cathode - E°_anode.
4. Use the Nernst equation to relate the standard cell potential to the standard Gibbs free energy change: ∆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, 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 for 25 °C).

Key Concepts

Gibbs Free Energy (∆G°)

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

Equilibrium Constant (K)

The equilibrium constant (K) quantifies 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 value indicates that products are favored, while a small K suggests reactants are favored. The relationship between K and Gibbs Free Energy allows for the calculation of K from ∆G° and vice versa, making it essential for analyzing electrochemical cells.

Electrode Half-Reactions

Electrode half-reactions represent the individual oxidation or reduction processes occurring at the electrodes of an electrochemical cell. Each half-reaction can be expressed in terms of the transfer of electrons, which is fundamental for calculating the overall cell reaction and its thermodynamic properties. Understanding these half-reactions is essential for determining the cell potential and subsequently calculating Gibbs Free Energy and the equilibrium constant for the entire cell reaction.