What are the values of x and y for the following reaction if E° = 0.91 V and ∆G° = -527 kJ?

검증된 단계별 안내

Identify the relationship between Gibbs free energy change (\( \Delta G^\circ \)) and the standard cell potential (\( E^\circ \)) using the equation: \( \Delta G^\circ = -nFE^\circ \), where \( n \) is the number of moles of electrons transferred and \( F \) is the Faraday constant (approximately 96485 C/mol).

Rearrange the equation to solve for \( n \): \( n = \frac{-\Delta G^\circ}{FE^\circ} \).

Substitute the given values into the equation: \( \Delta G^\circ = -527 \text{ kJ} = -527000 \text{ J} \) and \( E^\circ = 0.91 \text{ V} \).

Calculate \( n \) using the rearranged equation: \( n = \frac{-(-527000 \text{ J})}{96485 \text{ C/mol} \times 0.91 \text{ V}} \).

Interpret the value of \( n \) to determine the stoichiometric coefficients \( x \) and \( y \) in the balanced redox reaction, ensuring that the number of electrons transferred corresponds to the calculated \( n \).

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주요 개념

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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 determined under standard conditions (1 M concentration, 1 atm pressure, and 25°C). A positive E° indicates a greater likelihood of reduction, while a negative E° suggests a tendency to oxidize. In this question, E° = 0.91 V indicates a favorable reaction direction.

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. A negative ∆G° value, such as -527 kJ, indicates that the reaction is spontaneous under standard conditions. The relationship between ∆G° and E° is given by the equation ∆G° = -nFE°, where n is the number of moles of electrons transferred and F is Faraday's constant.

Stoichiometry of Redox Reactions

Stoichiometry in redox reactions involves balancing the number of electrons transferred between oxidizing and reducing agents. The values of x and y in the reaction typically represent the coefficients of the reactants and products in the balanced equation. Understanding the stoichiometry is essential for determining how many moles of each species are involved, which directly relates to the values of n in the Gibbs free energy equation and the overall reaction balance.