Given the following reduction half-reactions:
Fe³⁺(aq) + e^- → Fe²⁺(aq) E°_red = +0.77 V
S₂O₆^2-(aq) + 4 H⁺(aq) + 2 e^- → 2 H₂SO₃(aq) E°_red = +0.60 V
N₂O(g) + 2 H⁺(aq) + 2 e^- → N₂(g) + H₂O(l) E°_red = -1.77 V
VO²⁺(aq) + 2 H⁺(aq) + e^- → VO²⁺ + H₂O(l) E°_red = +1.00 V
(b) Calculate ∆G° for each reaction at 298 K.

검증된 단계별 안내

Identify the formula to calculate the standard Gibbs free energy change (\( \Delta G^\circ \)) for a redox reaction: \( \Delta G^\circ = -nFE^\circ_{cell} \), where \( n \) is the number of moles of electrons transferred, \( F \) is the Faraday constant (approximately 96485 C/mol), and \( E^\circ_{cell} \) is the standard cell potential.

For each half-reaction, determine the number of electrons transferred (\( n \)) from the balanced equation.

Calculate the standard cell potential (\( E^\circ_{cell} \)) for each reaction. Since these are reduction half-reactions, \( E^\circ_{cell} \) is simply the given \( E^\circ_{red} \) value for each reaction.

Substitute the values of \( n \), \( F \), and \( E^\circ_{cell} \) into the \( \Delta G^\circ \) formula for each reaction to find the standard Gibbs free energy change.

Ensure the units are consistent, typically converting \( \Delta G^\circ \) to kJ/mol by dividing the result by 1000, as \( F \) is in C/mol and \( E^\circ_{cell} \) is in V (J/C).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Standard Reduction Potential (E°red)

Standard reduction potential (E°red) is a measure of the tendency of a chemical species to gain electrons and be reduced. It is measured in volts and is determined under standard conditions (1 M concentration, 1 atm pressure, and 25°C). A higher E°red value indicates a greater likelihood of reduction occurring, which is crucial for predicting the direction of redox reactions.

Gibbs Free Energy (∆G°)

Gibbs free energy (∆G°) is a thermodynamic quantity that indicates the spontaneity of a reaction at constant temperature and pressure. It is calculated using the equation ∆G° = -nFE°cell, where n is the number of moles of electrons transferred, F is Faraday's constant, and E°cell is the cell potential. A negative ∆G° value signifies that the reaction is spontaneous under standard conditions.

Half-Reaction Method

The half-reaction method involves breaking down redox reactions into their oxidation and reduction components. Each half-reaction can be analyzed separately to determine the E°red values and the overall cell potential. This method is essential for calculating the Gibbs free energy change for the entire reaction, as it allows for the identification of the number of electrons transferred and the respective potentials involved.