An experimental fuel cell has been designed that uses carbon...

An experimental fuel cell has been designed that uses carbon monoxide as fuel. The overall reaction is $$2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)$$ The two half-cell reactions are $$\begin{array}{l}\mathrm{CO}+\mathrm{O}^{2-} \longrightarrow \mathrm{CO}_{2}+2 \mathrm{e}^{-} \\\mathrm{O}_{2}+4 \mathrm{e}^{-} \longrightarrow 2 \mathrm{O}^{2-} \end{array}$$ The two half-reactions are carried out in separate compartments connected with a solid mixture of $\mathrm{CeO}_{2}$ and $\mathrm{Gd}_{2} \mathrm{O}_{3} .$ Oxide ions can move through this solid at high temperatures (about $800^{\circ} \mathrm{C}$ ). $\Delta G$ for the overall reaction at $800^{\circ} \mathrm{C}$ under certain concentration conditions is $-380 \mathrm{~kJ} .$ Calculate the cell potential for this fuel cell at the same temperature and concentration conditions.

An experimental fuel cell has been designed that uses carbon monoxide as fuel. The overall reaction is
$$2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)$$
The two half-cell reactions are
$$\begin{array}{l}\mathrm{CO}+\mathrm{O}^{2-} \longrightarrow \mathrm{CO}_{2}+2 \mathrm{e}^{-} \\\mathrm{O}_{2}+4 \mathrm{e}^{-} \longrightarrow 2 \mathrm{O}^{2-}
\end{array}$$
The two half-reactions are carried out in separate compartments connected with a solid mixture of $\mathrm{CeO}_{2}$ and $\mathrm{Gd}_{2} \mathrm{O}_{3} .$ Oxide ions can move through this solid at high temperatures (about $800^{\circ} \mathrm{C}$ ). $\Delta G$ for the overall reaction at $800^{\circ} \mathrm{C}$ under certain concentration conditions is $-380 \mathrm{~kJ} .$ Calculate the cell potential for this fuel cell at the same temperature and concentration conditions.

Key Concepts

Gibbs Free Energy and Electrochemical Work

The Gibbs free energy change (?G) for a reaction is a thermodynamic quantity that tells us whether a reaction can do work. In electrochemistry, the relationship ?G = -nFE_cell connects the chemical energy change with the electrical energy produced, where n is the number of moles of electrons transferred in the reaction and F is Faraday’s constant. This fundamental concept allows one to calculate the cell potential knowing the free energy change, thereby linking thermodynamics and electromotive force.

Electrochemical Cell Potential

The cell potential, or electromotive force (E_cell), is the measure of the voltage produced by an electrochemical cell. It is determined by the difference in potential between the two electrodes where oxidation and reduction reactions occur. Understanding how to compute E_cell, particularly using the relationship with Gibbs free energy, is essential in evaluating the performance and feasibility of fuel cells and other similar electrochemical devices.

Electron Transfer Stoichiometry

In electrochemical reactions, the number of electrons transferred (n) plays a crucial role in determining the relationship between chemical and electrical energy changes. The stoichiometry of the half-cell reactions must be balanced so that the overall reaction accounts for the correct number of electrons. This concept is key in applying the ?G = -nFE_cell equation accurately and is fundamental in the design and analysis of fuel cells.

Faraday’s Constant

Faraday’s constant (F) is a physical constant that represents the charge of one mole of electrons, approximately 96485 coulombs per mole. It provides the necessary conversion factor between the amount of charge transferred in an electrochemical process and the electrical energy associated with that transfer. In computations involving cell potentials and free energy changes, Faraday’s constant is indispensable for translating chemical reaction information into electrical terms.

Fuel Cell Operation and Ionic Conduction

Fuel cells convert chemical energy directly into electrical energy through redox reactions, operating efficiently and often at high temperatures. In certain fuel cells, such as solid oxide fuel cells, ion-conducting materials are used to transport specific ions (like oxide ions) between the electrodes. This ability to conduct ions while maintaining separation of the fuel and oxidant is critical to the overall performance and design of advanced fuel cell systems.

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