Use tabulated electrode potentials to calculate 𝛥𝐺rxn° for each reaction at 25 °C. c. O2( g) + 2 H2O(l) + 2 Cu(s)¡4 OH-(aq) + 2 Cu2+(aq)

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Identify the half-reactions involved in the given redox reaction. The reaction involves the reduction of O2 to OH- and the oxidation of Cu to Cu2+.

Write the half-reactions: \( \text{O}_2(g) + 4e^- + 2\text{H}_2\text{O}(l) \rightarrow 4\text{OH}^-(aq) \) and \( 2\text{Cu}(s) \rightarrow 2\text{Cu}^{2+}(aq) + 4e^- \).

Look up the standard electrode potentials (E°) for each half-reaction from a table of standard electrode potentials. For the reduction of O2, \( E^\circ = +0.40 \text{ V} \) and for the oxidation of Cu, \( E^\circ = -0.34 \text{ V} \).

Calculate the standard cell potential (E°cell) using the formula: \( E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}} \). Substitute the values from the previous step.

Use the relationship between the standard cell potential and the standard Gibbs free energy change: \( \Delta G^\circ_{\text{rxn}} = -nFE^\circ_{\text{cell}} \), where \( n \) is the number of moles of electrons transferred (4 in this case) and \( F \) is the Faraday constant (approximately 96485 C/mol). Substitute the values to find \( \Delta G^\circ_{\text{rxn}} \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Electrode Potentials

Electrode potentials, measured in volts, indicate the tendency of a chemical species to be reduced or oxidized. Standard electrode potentials (E°) are measured under standard conditions and are crucial for predicting the direction of redox reactions. The more positive the electrode potential, the greater the species' ability to gain electrons, thus driving the reaction forward.

Gibbs Free Energy (ΔG)

Gibbs Free Energy (ΔG) is a thermodynamic quantity that indicates the spontaneity of a reaction at constant temperature and pressure. A negative ΔG value signifies that a reaction is spontaneous, while a positive value indicates non-spontaneity. The relationship between ΔG and electrode potentials is given by the equation ΔG° = -nFE°, where n is the number of moles of electrons transferred, F is Faraday's constant, and E° is the standard cell potential.

Nernst Equation

The Nernst equation relates the cell potential of an electrochemical reaction to the concentrations of the reactants and products. It allows for the calculation of the cell potential under non-standard conditions, which can affect the Gibbs Free Energy. The equation is expressed as E = E° - (RT/nF)ln(Q), where Q is the reaction quotient, R is the gas constant, and T is the temperature in Kelvin.

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