Ch.7 - Thermochemistry

Problem 64

Chapter 7, Problem 64

What mass of natural gas (CH4) must burn to emit 352 kJ of heat? CH4( g) + 2 O2( g)¡CO2( g) + 2 H2O( g) ΔH °rxn = -802.3 kJ

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Identify the given values and the required value. Here, the heat emitted is 352 kJ and the heat of reaction (ΔH°rxn) for the combustion of methane (CH4) is -802.3 kJ/mol.

Understand that the negative sign of ΔH°rxn indicates that the reaction is exothermic, meaning it releases heat. The magnitude of ΔH°rxn tells us how much heat is released when 1 mole of CH4 reacts completely.

Set up a proportion to find the number of moles of CH4 needed to release 352 kJ of heat. Use the ratio: (moles of CH4) / 352 kJ = 1 mol CH4 / 802.3 kJ.

Calculate the moles of CH4 required by solving the proportion set up in the previous step.

Convert the moles of CH4 to mass using the molar mass of CH4. The molar mass of CH4 (methane) is approximately 16.04 g/mol. Multiply the moles of CH4 by this molar mass to find the mass in grams.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions. It involves using balanced chemical equations to determine the relationships between the quantities of substances consumed and produced. In this case, stoichiometry will help us relate the amount of CH4 burned to the heat emitted based on the reaction's enthalpy change.

Enthalpy Change (ΔH)

Enthalpy change (ΔH) is a measure of the heat absorbed or released during a chemical reaction at constant pressure. A negative ΔH indicates that the reaction is exothermic, meaning it releases heat. For the combustion of methane (CH4), the given ΔH of -802.3 kJ indicates that burning one mole of CH4 releases this amount of energy, which is crucial for calculating the mass needed to emit a specific amount of heat.

Molar Mass

Molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol). For CH4, the molar mass is approximately 16.04 g/mol. Knowing the molar mass is essential for converting between moles of CH4 and grams, allowing us to determine how much mass is required to produce the desired heat output based on the stoichiometric calculations.

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