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 $$ \mathrm{CH}_3 \mathrm{OH}(\mathrm{l})+3 / 2 \mathrm{O}_2(\mathrm{~g}) \longrightarrow \mathrm{CO}_2(\mathrm{~g})+2 \mathrm{H}_2 \mathrm{O}(\mathrm{l}) $$ At 298 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

$$
\mathrm{CH}_3 \mathrm{OH}(\mathrm{l})+3 / 2 \mathrm{O}_2(\mathrm{~g}) \longrightarrow \mathrm{CO}_2(\mathrm{~g})+2 \mathrm{H}_2 \mathrm{O}(\mathrm{l})
$$

At 298 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

Gibbs Free Energy

Gibbs free energy is the thermodynamic potential that measures the maximum reversible work obtainable from a chemical reaction at constant temperature and pressure. It plays a central role in determining whether a reaction will occur spontaneously and, in the context of fuel cells, it represents the maximum useful electrical work that can be extracted from the reaction.

Enthalpy of Reaction

The enthalpy of reaction is a measure of the heat released or absorbed during a chemical process at constant pressure. In combustion and fuel cell reactions, it indicates the total energy change, including both useful work and heat losses, arising from the breaking and formation of chemical bonds.

Fuel Cell Efficiency

Fuel cell efficiency is defined as the ratio of the useful electrical work output (represented by the change in Gibbs free energy) to the total energy released in the reaction (represented by the change in enthalpy). This ratio shows how effectively the fuel cell converts the chemical energy of the fuel into electrical energy, highlighting the role of thermodynamic limits in energy conversion.

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