Final answer:
To calculate the free energy change for the reaction, we first determine the electrochemical cell potential and then use it in the Gibbs free energy equation to find the standard free energy change. The correct answer is -89 kJ, corresponding to answer choice (d).
Step-by-step explanation:
The student is asking for the calculation of the free energy change per mole of Cu2+ formed in a redox reaction involving copper and silver ions. At 25 °C, using the given standard reduction potentials for the half-reactions of copper and silver, we can determine the standard electrochemical cell potential (E° cell) for the overall reaction. The standard free energy change (ΔG°) can then be calculated using the formula ΔG° = -nFE° cell, where 'n' is the number of moles of electrons exchanged in the reaction and 'F' is the Faraday constant (96,485 C/mol).
For the given reaction, the standard reduction potentials are: Cu2+ + 2e- → Cu (E° = 0.34 V) and Ag+ + e- → Ag (E° = 0.80 V). Since silver is being reduced and copper is being oxidized, the overall cell potential (E° cell) can be calculated by subtracting the standard reduction potential of copper from that of silver (0.80 - 0.34 = 0.46 V). As two moles of electrons are exchanged per mole of Cu2+ formed, we can insert this value into the standard free energy change equation to get ΔG°. The calculation becomes ΔG° = -2 mol × 96,485 C/mol × 0.46 V. Converting joules to kilojoules, the final answer demonstrates that the free energy change per mole of Cu2+ formed is -89 kJ. Therefore, the correct answer is (d) -89 kJ.