A particular natural gas consists, in mole percents, of 83.0...

A particular natural gas consists, in mole percents, of $83.0 \% \mathrm{CH}_{4}, 11.2 \% \mathrm{C}_{2} \mathrm{H}_{6,}$ and $5.8 \% \mathrm{C}_{3} \mathrm{H}_{8} .$ A $385 \mathrm{L}$ sam- ple of this gas, measured at $22.6^{\circ} \mathrm{C}$ and $739 \mathrm{mm} \mathrm{Hg}$, is burned at constant pressure in an excess of oxygen gas. How much heat, in kilojoules, is evolved in the combustion reaction?

A particular natural gas consists, in mole percents, of $83.0 \% \mathrm{CH}_{4}, 11.2 \% \mathrm{C}_{2} \mathrm{H}_{6,}$ and $5.8 \% \mathrm{C}_{3} \mathrm{H}_{8} .$ A $385 \mathrm{L}$ sam-
ple of this gas, measured at $22.6^{\circ} \mathrm{C}$ and $739 \mathrm{mm} \mathrm{Hg}$, is burned at constant pressure in an excess of oxygen gas. How much heat, in kilojoules, is evolved in the combustion reaction?

Key Concepts

Ideal Gas Law

The Ideal Gas Law (PV = nRT) is fundamental in relating the pressure, volume, temperature, and number of moles of a gas. In problems like this, it is used to calculate the moles of gas present from the measured conditions, facilitating the subsequent stoichiometric calculations for the chemical reactions involved.

Mole Percent Composition

Mole percent composition is a way to express the relative amounts of components in a gas mixture. It allows one to determine the number of moles of each individual gas from the total moles of the mixture, which is essential when dealing with multi-component combustion reactions.

Combustion Reaction Stoichiometry

Combustion reaction stoichiometry involves balancing the chemical equations for the combustion of fuels with oxygen. This step is crucial to determine how much oxygen is required and the amount of products formed, as well as linking the moles of the fuel consumed to the heat evolved during the reaction.

Reaction Enthalpy

Reaction enthalpy, specifically the heat of combustion, measures the energy released when a substance burns in oxygen. It is a critical concept as it quantifies the exothermic nature of combustion reactions and is used to calculate the total heat evolved based on the moles of fuel combusted.

Weighted Average Calculation

When a fuel is composed of multiple components, each with its own heat of combustion, a weighted average based on the mole percentages of each component is used to determine the overall heat release. This approach integrates the individual contributions of each hydrocarbon to find the net enthalpy change for the mixture.

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