If the equilibrium constant for a two-electron redox reaction at 298 K is 1.5 * 10⁻⁴, calculate the corresponding ∆G° and E°.

Verified step by step guidance

Step 1: Recall the relationship between the equilibrium constant (K) and the standard Gibbs free energy change (∆G°) using the equation: ∆G° = -RT ln(K), where R is the universal gas constant (8.314 J/mol·K) and T is the temperature in Kelvin.

Step 2: Substitute the given values into the equation: R = 8.314 J/mol·K, T = 298 K, and K = 1.5 * 10⁻⁴. Calculate the natural logarithm of the equilibrium constant, ln(K).

Step 3: Calculate ∆G° by substituting the values of R, T, and ln(K) into the equation ∆G° = -RT ln(K).

Step 4: Use the relationship between ∆G° and the standard cell potential (E°) for a redox reaction: ∆G° = -nFE°, where n is the number of moles of electrons transferred (n = 2 for this reaction) and F is the Faraday constant (96485 C/mol).

Step 5: Rearrange the equation to solve for E°: E° = -∆G°/(nF). Substitute the calculated value of ∆G° and the known values of n and F to find E°.

Key Concepts

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

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. For redox reactions, K can indicate the extent to which reactants are converted to products, with larger values suggesting a greater tendency for the reaction to proceed forward.

Gibbs Free Energy (∆G°)

Gibbs free energy (∆G°) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic process at constant temperature and pressure. It is related to the equilibrium constant by the equation ∆G° = -RT ln(K), where R is the universal gas constant and T is the temperature in Kelvin.

Standard Electrode Potential (E°)

The standard electrode potential (E°) is a measure of the tendency of a chemical species to be reduced, expressed in volts. It is related to the Gibbs free energy change by the equation ∆G° = -nFE°, where n is the number of moles of electrons transferred and F is Faraday's constant. A positive E° indicates a spontaneous reaction under standard conditions.

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Standard Cell Potential

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