In a fuel cell (a device for producing electricity directly...

In a fuel cell (a device for producing electricity directly from chemical reaction), methanol is used as fuel and oxygen gas is used as an oxidizer. The reaction is, $$ \mathrm{CH}_{3} \mathrm{OH}_{(\mathrm{l})}+3 / 2 \mathrm{O}_{2(\mathrm{~g})} \longrightarrow \mathrm{CO}_{2(\mathrm{~g})}+2 \mathrm{H}_{2} \mathrm{O}_{(\mathrm{l})} $$ Calculate the standard Gibbs energy change for the reaction that can be converted into electrical work. If standard enthalpy of combustion for methanol is $-726 \mathrm{~kJ} \mathrm{~mol}^{-1}$, calculate the efficiency of conversion of Gibbs energy into useful work. $\left(\Delta_{1} G^{\circ}\right.$ for $\mathrm{CO}_{2}, \mathrm{H}_{2} \mathrm{O}, \mathrm{CH}_{3} \mathrm{OH}, \mathrm{O}_{2}$ are $-394.36,-237.13,-166.27$ and zero respectively.)

In a fuel cell (a device for producing electricity directly from chemical reaction), methanol is used as fuel and oxygen gas is used as an oxidizer. The reaction is,
$$
\mathrm{CH}_{3} \mathrm{OH}_{(\mathrm{l})}+3 / 2 \mathrm{O}_{2(\mathrm{~g})} \longrightarrow \mathrm{CO}_{2(\mathrm{~g})}+2 \mathrm{H}_{2} \mathrm{O}_{(\mathrm{l})}
$$
Calculate the standard Gibbs energy change for the reaction that can be converted into electrical work. If standard enthalpy of combustion for methanol is $-726 \mathrm{~kJ} \mathrm{~mol}^{-1}$, calculate the efficiency of conversion of Gibbs energy into useful work. $\left(\Delta_{1} G^{\circ}\right.$ for $\mathrm{CO}_{2}, \mathrm{H}_{2} \mathrm{O}, \mathrm{CH}_{3} \mathrm{OH}, \mathrm{O}_{2}$ are $-394.36,-237.13,-166.27$ and
zero respectively.)

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Key Concepts

Gibbs Free Energy

Gibbs free energy is a thermodynamic potential that represents the maximum amount of non-expansion work obtainable from a process at constant temperature and pressure. It indicates the spontaneity of a reaction and is calculated using the chemical potentials of the reactants and products in their standard states.

Enthalpy of Combustion

The enthalpy of combustion is the heat released when a substance undergoes complete combustion with oxygen under standard conditions. It provides a measure of the energy content in a fuel and is used to compare the energy outputs of different fuels.

Efficiency of Energy Conversion

Efficiency in the context of energy conversion, such as in a fuel cell, is the ratio of the useful work output (related to the change in Gibbs free energy) to the total energy released (related to the enthalpy change). This efficiency quantifies how effectively the chemical energy is converted into electrical energy.

Standard Thermodynamic Data

Standard thermodynamic data, such as standard Gibbs energies and standard enthalpies of formation or combustion, are used to calculate the overall energy changes in a reaction under standard conditions. These values provide a baseline for comparing the energetic properties of different reactions and are crucial for designing and analyzing energy conversion systems.

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