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Step 1: The standard enthalpy change of reaction is given by Hess's law using enthalpies of formation. H^_rxn = n H^_f (products) - n H^_f (reactants) where n is the stoichiometric coefficient. Step 2: Identify enthalpies of formation with units (all in kJ mol^-1 at 298 K): H^_f (CO2(g)) = -393.5 H^_f (H2O(l)) = -285.8 H^_f (CH4(g)) = -74.8 H^_f (O2(g)) = 0 Step 3: Calculate sum for products. Products: 1 · CO2(g) + 2 · H2O(l) n H^_f (products) = [1 × (-393.5)] + [2 × (-285.8)] \, kJ \, mol^-1 = -393.5 + 2 × (-285.8) \, kJ \, mol^-1 = -393.5 - 571.6 \, kJ \, mol^-1 = -965.1 \, kJ \, mol^-1 Step 4: Calculate sum for reactants. Reactants: 1 · CH4(g) + 2 · O2(g) n H^_f (reactants) = [1 × (-74.8)] + [2 × 0] \, kJ \, mol^-1 = -74.8 + 0 \, kJ \, mol^-1 = -74.8 \, kJ \, mol^-1 Step 5: Subtract sums. H^_rxn = [-965.1] - [-74.8] \, kJ \, mol^-1 = -965.1 + 74.8 \, kJ \, mol^-1 = -890.3 \, kJ \, mol^-1 -890 kJ mol^-1