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Ch.19 - Electrochemistry
All textbooksTro 4th EditionCh.19 - ElectrochemistryProblem 65b,c
Chapter 19, Problem 65b,c

Use tabulated electrode potentials to calculate ∆G°rxn for each reaction at 25 °C. b. Br2(l) + 2 Cl–(aq) → 2 Br–(aq) + Cl2(g) c. MnO2(s) + 4 H+(aq) + Cu(s) → Mn2+(aq) + 2 H2O(l) + Cu2+(aq)

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Identify the half-reactions involved in the overall reaction. For the reduction half-reaction: MnO2(s) + 4 H+(aq) + 2 e- → Mn2+(aq) + 2 H2O(l). For the oxidation half-reaction: Cu(s) → Cu2+(aq) + 2 e-.
Look up the standard electrode potentials (E°) for each half-reaction from the standard electrode potential table. You will find E° for MnO2/Mn2+ and Cu/Cu2+.
Calculate the standard cell potential (E°cell) for the overall reaction using the formula: E°cell = E°cathode - E°anode, where MnO2/Mn2+ is the cathode (reduction) and Cu/Cu2+ is the anode (oxidation).
Use the relationship between the Gibbs free energy change (∆Gr°) and the cell potential to calculate ∆Gr°xn. The formula to use is: ∆Gr° = -nFE°cell, where n is the number of moles of electrons transferred in the balanced equation (which is 2 in this case), and F is the Faraday constant (approximately 96485 C/mol).
Ensure all units are consistent, particularly that temperature is in Kelvin if needed, and calculate ∆Gr°xn for the reaction at 25 °C (298 K).

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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. Standard electrode potentials (E°) are measured under standard conditions (1 M concentration, 1 atm pressure, and 25 °C). These values are crucial for predicting the direction of redox reactions and calculating the Gibbs free energy change (∆Gr°) for reactions.
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Standard Cell Potential

Gibbs Free Energy (∆Gr°)

Gibbs free energy change (∆Gr°) is a thermodynamic quantity that indicates the spontaneity of a reaction at standard conditions. It can be calculated using the equation ∆Gr° = -nFE°, where n is the number of moles of electrons transferred, F is Faraday's constant, and E° is the cell potential. A negative ∆Gr° indicates a spontaneous reaction.
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Gibbs Free Energy of Reactions

Redox Reactions

Redox reactions involve the transfer of electrons between species, where one species is oxidized (loses electrons) and another is reduced (gains electrons). In the given reaction, manganese dioxide (MnO2) is reduced to manganese ions (Mn2+), while copper (Cu) is oxidized to copper ions (Cu2+). Understanding the oxidation states and half-reactions is essential for calculating overall cell potentials.
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Related Practice
Textbook Question

Calculate E°cell for each balanced redox reaction and determine if the reaction is spontaneous as written. c. PbO2(s) + 4 H+(aq) + Sn(s) → Pb2+(aq) + 2 H2O(l) + Sn2+(aq)

Textbook Question

Which metal cation is the best oxidizing agent? a. Pb2+ b. Cr3+ c. Fe2+ d. Sn2+

Textbook Question

Use tabulated electrode potentials to calculate ∆G°rxn for each reaction at 25 °C. a. 2 Fe3+(aq) + 3 Sn(s) → 2 Fe(s) + 3 Sn2+(aq) b. O2(g) + 2 H2O(l) + 2 Cu(s) → 4 OH–(aq) + 2 Cu2+(aq) c. Br2(l) + 2 I–(aq) → 2 Br–(aq) + I2(s)

Textbook Question

Calculate the equilibrium constant for each of the reactions in Problem 65.