A voltaic cell is based on Ag+ (aq) > Ag (s) and Fe3+ (aq) > Fe2+ (aq) half-cells. Use S° values in Appendix C and the relationship between cell potential and free-energy change to predict whether the standard cell potential increases or decreases when the temperature is raised above 25 °C.

Verified step by step guidance

Step 1: Identify the half-reactions involved in the voltaic cell. The given half-reactions are Ag^+ (aq) + e^- -> Ag (s) and Fe^3+ (aq) + e^- -> Fe^2+ (aq).

Step 2: Determine the standard cell potential (E°) for the cell by using the standard reduction potentials from a reference table. Calculate E° = E°(cathode) - E°(anode).

Step 3: Use the Nernst equation to understand how cell potential (E) changes with temperature. The Nernst equation is E = E° - (RT/nF) * ln(Q), where R is the gas constant, T is the temperature in Kelvin, n is the number of moles of electrons transferred, F is Faraday's constant, and Q is the reaction quotient.

Step 4: Consider the entropy change (ΔS°) for the cell reaction. Use the relationship ΔG° = ΔH° - TΔS° and ΔG° = -nFE° to relate entropy change to cell potential.

Step 5: Analyze how an increase in temperature affects the cell potential. If ΔS° is positive, increasing temperature will increase the cell potential, and if ΔS° is negative, increasing temperature will decrease the cell potential.

Key Concepts

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

Standard Cell Potential (E°)

The standard cell potential (E°) is the measure of the voltage produced by a voltaic cell under standard conditions (1 M concentration, 1 atm pressure, and 25 °C). It is determined by the difference in reduction potentials of the half-reactions involved. A positive E° indicates a spontaneous reaction, while a negative E° suggests non-spontaneity.

Gibbs Free Energy (ΔG)

Gibbs free energy (ΔG) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. The relationship between cell potential and free energy is given by the equation ΔG = -nFE°, where n is the number of moles of electrons transferred and F is Faraday's constant. A negative ΔG indicates a spontaneous process.

Temperature Dependence of Cell Potential

The standard cell potential can be affected by temperature changes, as described by the Nernst equation. Generally, an increase in temperature can affect the equilibrium position of the half-reactions, potentially altering the E° value. For exothermic reactions, increasing temperature typically decreases E°, while for endothermic reactions, it may increase E°.

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