Calculate the enthalpy change ($\Delta H$) for the combustion of 1 mole of methane ($\mathrm{CH}_4$) given the reaction:
$$
\mathrm{CH}_4(g) + 2 \mathrm{O}_2(g) \rightarrow \mathrm{CO}_2(g) + 2 \mathrm{H}_2 \mathrm{O}(l)
$$
Given bond energies: C–H = 413 kJ/mol, O=O = 498 kJ/mol, C=O = 803 kJ/mol, O–H = 467 kJ/mol.