A given type of fuel cell produces electrical energy W by...

A given type of fuel cell produces electrical energy $W$ by the interaction of $\mathrm{O}_2$ fed into one electrode and $\mathrm{H}_2$ to the other. These gases are fed in at 1 atmosphere pressure and 298 K , and react isothermally and isobarically to form water. Assuming that the reaction occurs reversibly and that the internal resistance of the cell is negligible, calculate the e.m.f. of the cell. Given: one Faraday $=96,500$ coulombs/g mole. Enthalpies in joules/g mole at 1 atmospheric and 298 K for oxygen, hydrogen, and water are respectively $17,200,8,100$ and $-269,300$. Entropies in joules/mole- K at 1 atmosphere and 298 K for oxygen, hydrogen, and water are respectively 201, 128 and 66.7 .

A given type of fuel cell produces electrical energy $W$ by the interaction of $\mathrm{O}_2$ fed into one electrode and $\mathrm{H}_2$ to the other. These gases are fed in at 1 atmosphere pressure and 298 K , and react isothermally and isobarically to form water. Assuming that the reaction occurs reversibly and that the internal resistance of the cell is negligible, calculate the e.m.f. of the cell. Given: one Faraday $=96,500$ coulombs/g mole.

Enthalpies in joules/g mole at 1 atmospheric and 298 K for oxygen, hydrogen, and water are respectively $17,200,8,100$ and $-269,300$.

Entropies in joules/mole- K at 1 atmosphere and 298 K for oxygen, hydrogen, and water are respectively 201, 128 and 66.7 .

Key Concepts

Fuel Cell Operation

Fuel cells convert chemical energy directly into electrical energy through redox reactions. The operation of a fuel cell relies on the reversible reaction between its fuel and oxidant under controlled thermodynamic conditions, ensuring that the energy change is efficiently converted into electrical work. Understanding the underlying chemical and thermodynamic principles is key to analyzing and optimizing fuel cell performance.

Faraday Constant

The Faraday constant (F) represents the charge of one mole of electrons (approximately 96,500 coulombs per mole). It is a fundamental constant used in electrochemistry to relate the amount of electrical charge transferred in a reaction to the number of moles of electrons involved, thereby linking the chemical change to the electrical energy produced.

Relationship Between Gibbs Energy and Cell Potential

The electromotive force (e.m.f.) of an electrochemical cell is directly related to the change in Gibbs free energy through the equation ?G = -nFE, where n is the number of moles of electrons transferred in the reaction, F is the Faraday constant, and E is the cell potential. This relationship is central to calculating the voltage produced by a fuel cell based on its chemical reaction.

Thermodynamics of Chemical Reactions

Thermodynamic analysis of chemical reactions involves evaluating changes in enthalpy (?H) and entropy (?S) to predict the behavior of the system under given conditions. In the context of a fuel cell operating isothermally (constant temperature) and isobarically (constant pressure), these parameters help determine the Gibbs free energy change, which in turn is used to calculate the cell's efficiency and generated electrical energy.

Gibbs Free Energy

Gibbs free energy (?G) is the thermodynamic potential that measures the maximum reversible work that may be performed by a chemical process at constant temperature and pressure. It is calculated using the relation ?G = ?H - T?S, where ?H is the change in enthalpy, T is the temperature in Kelvin, and ?S is the change in entropy. This concept is crucial in determining the spontaneity of a reaction and the amount of energy that can be harnessed in a fuel cell.

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