In a fuel cell methanol is used as fuel and oxygen gas is...

In a fuel cell methanol is used as fuel and oxygen gas is used as an oxidizer. The reaction is $\mathrm{CH}_{3} \mathrm{OH}(\mathrm{l})+3 / 2 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(1)$ At $298 \mathrm{~K}$ standard Gibb's energies of formation for $\mathrm{CH}_{3} \mathrm{OH}$ (1), $\mathrm{H}_{2} \mathrm{O}$ (1) and $\mathrm{CO}_{2}$ (g) are $-166.2 .-237.2$ and $-394.4 \mathrm{kJmol}^{-1}$ respectively. If standard enthalpy of combustion of methanol is $-7269 \mathrm{~kJ} \mathrm{~mol}^{-1}$, efficiency of the fuel cell will be: [2009] (a) $87 \%$ (b) $90 \%$ (c) $97 \%$ (d) $80 \%$

In a fuel cell methanol is used as fuel and oxygen gas is used as an oxidizer. The reaction is $\mathrm{CH}_{3} \mathrm{OH}(\mathrm{l})+3 / 2 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(1)$ At $298 \mathrm{~K}$ standard Gibb's energies of formation for $\mathrm{CH}_{3} \mathrm{OH}$ (1), $\mathrm{H}_{2} \mathrm{O}$ (1) and $\mathrm{CO}_{2}$ (g) are $-166.2 .-237.2$
and $-394.4 \mathrm{kJmol}^{-1}$ respectively. If standard enthalpy of combustion of methanol is $-7269 \mathrm{~kJ} \mathrm{~mol}^{-1}$, efficiency of the fuel cell will be:
[2009]
(a) $87 \%$
(b) $90 \%$
(c) $97 \%$
(d) $80 \%$

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Key Concepts

Reaction Thermodynamics

Reaction thermodynamics involves analyzing the energy changes during a chemical reaction, particularly the interplay between Gibbs free energy and enthalpy. This concept is crucial for understanding energy conversion processes in fuel cells, where the balance of these quantities determines the overall efficiency of the system.

Fuel Cell Efficiency

Fuel cell efficiency in this context is defined as the ratio of the maximum useful work (given by the change in Gibbs free energy) to the total energy released (given by the enthalpy of combustion). This ratio indicates how effectively a fuel cell converts chemical energy into electrical energy.

Standard Enthalpy of Combustion

The standard enthalpy of combustion is the heat released when one mole of a substance is completely burned in oxygen under standard conditions. It reflects the total energy change in the reaction, including both the work potential and the heat lost as waste energy.

Gibbs Free Energy

Gibbs free energy is a thermodynamic potential that measures the maximum amount of work obtainable from a chemical reaction at constant temperature and pressure. In the context of fuel cells, it represents the useful electrical work that can be extracted from the reaction when it is carried out reversibly.

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