Understand that ΔH°rxn represents the standard enthalpy change of a reaction, while ΔH°f represents the standard enthalpy of formation, which is the enthalpy change when one mole of a compound is formed from its elements in their standard states.
Identify that for a reaction to have ΔH°rxn = ΔH°f, the reaction must represent the formation of one mole of a compound from its elements in their standard states.
Examine each given reaction to determine if it forms exactly one mole of a compound from its elements in their standard states. The standard states are: C (s, graphite) for carbon, H2 (g) for hydrogen, and O2 (g) for oxygen.
Check the stoichiometry of each reaction. The correct reaction should have coefficients that result in the formation of exactly one mole of the compound, CH3OH (l), from its elements.
Identify the correct reaction: C (s, graphite) + 2 H2 (g) + ½ O2 (g) → CH3OH (l), as it forms one mole of methanol from its elements in their standard states, thus ΔH°rxn = ΔH°f.