Assume that 4.19 ×10^6 kJ of energy is needed to heat a...

Assume that $4.19 \times 10^{6} \mathrm{~kJ}$ of energy is needed to heat a home. If this energy is derived from the combustion of methane $\left(\mathrm{CH}_{4}\right)$, what volume of methane, measured at STP, must be burned? $\left(\Delta H_{\text {combustion }}^{\circ}\right.$ for $\mathrm{CH}_{4}=-891 \mathrm{~kJ} / \mathrm{mol}$ )

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Key Concepts

Energy Unit Consistency

Ensuring that all energy measurements are in consistent units is fundamental in thermochemical calculations. This involves carefully matching units between the total energy required and the energy per mole provided by the combustion process so that the conversion and stoichiometric calculations yield meaningful results.

Molar Volume at STP

At standard temperature and pressure, one mole of an ideal gas occupies a known volume. This allows the conversion of the calculated moles of methane into a volume measure. Understanding this concept is crucial for relating chemical quantities to real-world measurements of gas volumes.

Stoichiometric Conversion

This concept involves using the relationship between moles of a reactant and the energy produced by its combustion. By dividing the total required energy by the energy produced per mole, we obtain the number of moles of methane needed, which is a key step in linking the macroscopic energy requirement to molecular scale quantities.

Enthalpy of Combustion

This concept refers to the energy released when one mole of a substance (in this case methane) combusts completely in oxygen under standard conditions. It quantifies the exothermic nature of the reaction and is essential for determining how much fuel is required to produce a given amount of energy.

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