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Ch.20 - Electrochemistry
Brown - Chemistry: The Central Science 14th Edition
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBrown 14th EditionCh.20 - ElectrochemistryProblema 54
Capitolo 20, Problema 54

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

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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°.

Concetti chiave

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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.
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Equilibrium Constant K

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.
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Gibbs Free Energy of Reactions

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.
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Relationship between ∆E°, ∆G°, and K
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