Refer to the tabulated values of ∆G°_f in Appendix IIB to calculate E°_cell for the fuel-cell breathalyzer, which employs the following reaction. ((∆G° for HC₂H₃O₂(g) = -374.2 kJ/mol.)
CH₃CH₂OH(g) + O₂(g) → HC₂H₃O₂(g) + H₂O(g)

Verified step by step guidance

1. Identify the given reaction: \( \text{CH}_3\text{CH}_2\text{OH(g)} + \text{O}_2\text{(g)} \rightarrow \text{HC}_2\text{H}_3\text{O}_2\text{(g)} + \text{H}_2\text{O(g)} \).
2. Use the formula \( \Delta G^\circ = -nFE^\circ_{\text{cell}} \) to relate \( \Delta G^\circ \) and \( E^\circ_{\text{cell}} \), where \( n \) is the number of moles of electrons transferred and \( F \) is the Faraday constant (96485 C/mol).
3. Calculate \( \Delta G^\circ \) for the reaction using \( \Delta G^\circ = \sum \Delta G^\circ_f(\text{products}) - \sum \Delta G^\circ_f(\text{reactants}) \).
4. Determine the number of moles of electrons transferred, \( n \), by balancing the redox reaction.
5. Solve for \( E^\circ_{\text{cell}} \) using the rearranged formula \( E^\circ_{\text{cell}} = -\frac{\Delta G^\circ}{nF} \).

Key Concepts

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. It indicates the spontaneity of a reaction; a negative ∆G value suggests that the reaction can occur spontaneously, while a positive value indicates non-spontaneity. In the context of fuel cells, understanding ∆G helps in evaluating the efficiency and feasibility of the chemical reactions involved.

Standard Gibbs Free Energy of Formation (∆Gf°)

The Standard Gibbs Free Energy of Formation (∆Gf°) is the change in Gibbs free energy when one mole of a compound is formed from its elements in their standard states. This value is crucial for calculating the overall Gibbs free energy change of a reaction by using the formula: ∆G° = Σ∆Gf°(products) - Σ∆Gf°(reactants). It provides insight into the stability of compounds and the energy changes during chemical reactions.

Electrochemical Cell Potential (Ec°ell)

Electrochemical Cell Potential (Ec°ell) is the measure of the voltage or electromotive force (EMF) generated by an electrochemical cell under standard conditions. It is related to the Gibbs free energy change of the reaction by the equation ∆G° = -nFEc°ell, where n is the number of moles of electrons transferred and F is Faraday's constant. Understanding this relationship is essential for evaluating the performance of fuel cells, such as those used in breathalyzers.