Calculate ∆G°_rxn and K for each reaction. b. The reaction of Cr³⁺(aq) and Cr(s) to form Cr²⁺(aq). [The electrode potential of Cr²⁺(aq) to Cr(s) is -0.91 V.]

검증된 단계별 안내

Identify the half-reactions involved in the given reaction. The reaction involves Cr3+(aq) being reduced to Cr2+(aq) and Cr(s) being oxidized to Cr2+(aq).

Write the standard reduction potentials for each half-reaction. You are given that the electrode potential for Cr2+(aq) to Cr(s) is -0.91 V. You will need to find or be given the standard reduction potential for Cr3+(aq) to Cr2+(aq).

Calculate the standard cell potential (E°cell) for the overall reaction using the formula: E°cell = E°cathode - E°anode. Here, the cathode is the reduction of Cr3+ to Cr2+, and the anode is the oxidation of Cr(s) to Cr2+.

Use the Nernst equation to relate the standard cell potential to the standard Gibbs free energy change (∆G°rxn) using the formula: ∆G°rxn = -nFE°cell, where n is the number of moles of electrons transferred in the balanced equation, and F is the Faraday constant (approximately 96485 C/mol).

Calculate the equilibrium constant (K) for the reaction using the relationship between ∆G°rxn and K: ∆G°rxn = -RTlnK, where R is the universal gas constant (8.314 J/mol·K) and T is the temperature in Kelvin. Rearrange to solve for K.

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주요 개념

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

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. The change in Gibbs Free Energy (∆Gr°xn) for a reaction indicates whether the reaction is spontaneous (negative ∆G) or non-spontaneous (positive ∆G). It is calculated using the equation ∆G = ∆H - T∆S, where ∆H is the change in enthalpy, T is the temperature in Kelvin, and ∆S is the change in entropy.

Electrode Potential

Electrode potential is the measure of the tendency of a chemical species to be reduced, expressed in volts. In electrochemistry, the standard electrode potential (E°) is used to predict the direction of electron flow in a redox reaction. A more positive E° indicates a greater likelihood of reduction, while a more negative E° suggests a greater likelihood of oxidation. The electrode potential is crucial for calculating Gibbs Free Energy changes in electrochemical reactions.

Equilibrium Constant (K)

The equilibrium constant (K) is a dimensionless value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. It is related to the Gibbs Free Energy change by the equation ∆G° = -RT ln(K), where R is the universal gas constant and T is the temperature in Kelvin. A larger K value indicates a reaction that favors product formation, while a smaller K value suggests a reaction that favors reactants.

Calculate ∆G°rxn and K for each reaction. b. The reaction of Cr3+(aq) and Cr(s) to form Cr2+(aq). [The electrode potential of Cr2+(aq) to Cr(s) is -0.91 V.]