The fuel in high-efficiency natural gas vehicles consists...

The fuel in high-efficiency natural gas vehicles consists primarily of methane $\left(\mathrm{CH}_{4}\right) .$ (a) How much heat is produced in burning 1 mol of $\mathrm{CH}_{4}(g)$ under standard conditions if reactants and products are brought to $298 \mathrm{~K}$ and $\mathrm{H}_{2} \mathrm{O}(l)$ is formed? (b) What is the maximum amount of useful work that can be accomplished under standard conditions by this system?

Key Concepts

Enthalpy Change

Enthalpy change is the measure of heat absorbed or released during a chemical reaction at constant pressure. In combustion reactions, the standard enthalpy change (?H°) indicates the overall heat released when fuel reacts (for example, when methane burns), and it is determined from the differences in enthalpy of the reactants and products under standard conditions.

Gibbs Free Energy

Gibbs free energy is a thermodynamic potential that combines enthalpy and entropy to indicate the maximum reversible work obtainable from a process at constant temperature and pressure. The change in Gibbs free energy (?G°) is crucial because it represents the portion of the reaction energy (from the total enthalpy change) that can be converted into useful work, aside from work done by pressure-volume expansion.

Standard Conditions

Standard conditions provide a reference state for thermodynamic calculations, typically defined as a pressure of 1 atm (or 1 bar in modern usage) and a temperature of 298 K. Under these conditions, measured thermodynamic properties like enthalpy and Gibbs free energy are standardized, making it easier to compare the energetics of different reactions such as the combustion of methane.

Second Law of Thermodynamics

The second law of thermodynamics states that energy transformations are not 100% efficient, as some energy is always lost as unusable heat due to entropy production. This principle explains why only a fraction of the total heat released in a combustion reaction (quantified by the enthalpy change) can be converted into maximum useful work—the Gibbs free energy—under ideal, reversible conditions.

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