Question

What mass of natural gas (CH₄) must you burn to emit 267 kJ of heat?

CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(g)
ΔH₀rxn = -802.3 kJ

Answer 1

To emit 267 kJ of heat, 4.812 g of methane (CH4) must be burned, which is calculated using stoichiometry and the molar enthalpy of combustion for methane.

Step-by-step explanation:

Stoichiometric Calculations of Methane Combustion

To determine the mass of natural gas (CH4) that must be burned to emit 267 kJ of heat, we use stoichiometry and the provided thermochemical equation for methane combustion. According to the given information, the combustion of 1 mole of methane (CH4) releases 890.4 kJ of heat. We calculate the amount of methane needed to produce 267 kJ of heat by setting up a proportion based on the molar enthalpy change.

Calculation Steps

Start with the given thermochemical equation: CH4(g) + 2 O2(g) → CO2(g) + 2 H2O(g), ΔH = -890.4 kJ.

Divide the desired heat release (267 kJ) by the heat released per mole of methane (890.4 kJ/mol): (267 kJ) / (890.4 kJ/mol) = 0.3 mol.

Find the molar mass of methane (CH4): C (12.01 g/mol) + 4 H (4 × 1.008 g/mol) = 16.04 g/mol.

Multiply the moles of methane by its molar mass to find the mass: 0.3 mol × 16.04 g/mol = 4.812 g.

Therefore, to emit 267 kJ of heat, 4.812 g of CH4 must be burned.