For which one of the following reactions is the value of ΔH°_rxn equal to ΔH°_f for the product?

• A. CO2(g) → C(s) + O2(g)
• B. 2CO(g) + O2(g) → 2CO2(g)
• C. C(s) + O2(g) → CO2(g)
• D. C(s) + 1/2 O2(g) → CO(g)

Answer: (C)

Verified step by step guidance

1. Recall that the standard enthalpy of formation, \(\Delta H^\circ_f\), of a compound is defined as the enthalpy change for the formation of 1 mole of that compound from its elements in their standard states.
2. Identify the reaction that represents the formation of the product from its elements in their standard states. This means the reactants must be the elements in their standard forms, and the product is the compound of interest.
3. Examine each given reaction and determine whether the reactants are elements in their standard states and the product is a compound:
4. - For example, in \(\mathrm{C(s) + O_2(g) \rightarrow CO_2(g)}\), carbon (C) is a solid element in its standard state, oxygen (O2) is a diatomic gas in its standard state, and carbon dioxide (CO2) is the compound formed.
5. - Other reactions either involve compounds as reactants or do not form the product directly from elements in their standard states.
6. Conclude that the reaction where \(\Delta H^\circ_{rxn}\) equals \(\Delta H^\circ_f\) for the product is the one where the product is formed directly from its elements in their standard states.
7. Therefore, the reaction \(\mathrm{C(s) + O_2(g) \rightarrow CO_2(g)}\) fits the definition of a formation reaction, and its \(\Delta H^\circ_{rxn}\) corresponds to \(\Delta H^\circ_f\) of \(\mathrm{CO_2(g)}\).