If the equilibrium constant for a one-electron redox reaction at 298 K is 8.7 * 10^4, calculate the corresponding ∆G° and E°.

Name: Chemistry: The Central Science
Author: Brown
ISBN: 9780134414232

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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 = 8.7 * 10^4. Calculate the natural logarithm of K, ln(8.7 * 10^4).

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 = 1 for a one-electron 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 constants n and F to find E°.

주요 개념

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Equilibrium Constant (K)

The equilibrium constant (K) quantifies the ratio of the concentrations of products to reactants at equilibrium for a reversible reaction. In redox reactions, a higher K value indicates a greater tendency for the reaction to proceed in the forward direction, favoring product formation. This constant is crucial for calculating thermodynamic properties like Gibbs free energy and cell potential.

Gibbs Free Energy (∆G°)

Gibbs free energy (∆G°) is a thermodynamic potential that indicates the spontaneity of a reaction 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. A negative ∆G° suggests that the reaction is spontaneous under standard conditions.

Electrode Potential (E°)

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 favorable reaction, while a negative E° suggests non-spontaneity.