Final answer:
The enthalpy of combustion of methane (CH₄) at 298 K is ΔHₓₙ₈ = -890.4 kJ/mol, indicating an exothermic reaction where heat is released.
Step-by-step explanation:
To calculate the enthalpy of combustion of methane (CH₄) at 298 K according to the balanced chemical equation CH₄ + 2O₂ → CO₂ + 2H₂O(g), you need to utilize the provided thermochemical data. The combustion of 1 mol of methane releases 890.4 kJ. Therefore, the enthalpy of combustion of methane is ΔHₓₙ₈ = -890.4 kJ/mol.
The negative sign indicates that the reaction is exothermic, meaning heat is released during the combustion process. This calculation implies that for every mole of methane burned, 890.4 kilojoules of heat energy are liberated.