Calculate the standard cell potential and the standard free-energy change (in kilojoules) for the reaction below. (See Appendix D for standard reduction potentials.) <QUESTION REFERENCES APPENDIX D>

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Identify the half-reactions involved in the overall reaction and write their standard reduction potentials from Appendix D.

Determine which half-reaction will undergo oxidation and which will undergo reduction by comparing their standard reduction potentials.

Calculate the standard cell potential (E°_cell) using the formula: E°_cell = E°_cathode - E°_anode.

Use the Nernst equation to relate the standard cell potential to the standard free-energy change: ΔG° = -nFE°_cell, where n is the number of moles of electrons transferred and F is the Faraday constant (96,485 C/mol).

Convert the standard free-energy change from joules to kilojoules by dividing by 1,000.

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Key Concepts

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

Standard Cell Potential

The standard cell potential (E°) is the measure of the voltage produced by an electrochemical cell under standard conditions (1 M concentration, 1 atm pressure, and 25°C). It is calculated using the standard reduction potentials of the half-reactions involved in the cell. A positive E° indicates a spontaneous reaction, while a negative E° suggests non-spontaneity.

Standard Free Energy Change

The standard free energy change (ΔG°) quantifies the spontaneity of a reaction at standard conditions. It is related to the standard cell potential by the equation ΔG° = -nFE°, where n is the number of moles of electrons transferred and F is Faraday's constant (approximately 96485 C/mol). A negative ΔG° indicates that the reaction is spontaneous.

Half-Reactions and Reduction Potentials

Half-reactions represent the oxidation or reduction processes occurring in an electrochemical cell. Each half-reaction has an associated standard reduction potential, which indicates the tendency of a species to gain electrons. By combining the half-reactions and their potentials, one can determine the overall cell potential and the direction of electron flow in the cell.

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Standard Reduction Potentials

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Textbook Question

How are standard reduction potentials defined?

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Porous pellets of TiO₂ can be reduced to titanium metal at the cathode of an electrochemical cell containing molten CaCl₂ as the electrolyte. When the TiO₂ is reduced, the O^2-ions dis-solve in the CaCl₂ and are subsequently oxidized to O₂ gas at the anode. This approach may be the basis for a less expensive process than the one currently used for producing titanium.

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