For which one of the following reactions is the value of ΔH_rxn equal to ΔH_f for the product?

• A. C(s) + O_2(g) → CO_2(g)
• B. CO_2(g) + H_2O(l) → H_2CO_3(aq)
• C. N_2(g) + 3H_2(g) → 2NH_3(g)
• D. 2H_2(g) + O_2(g) → 2H_2O(l)

Answer: (A)

Verified step by step guidance

1. Recall the definition of the standard enthalpy of formation (\( \Delta H_f \)): it is the enthalpy change when one mole of a compound is formed from its elements in their standard states under standard conditions.
2. Identify the product in each reaction and check if the reactants are the elements in their standard states. The standard states are the most stable physical form of the element at 1 atm and 25°C (e.g., C as graphite or diamond solid, O_2 as gas, H_2 as gas, N_2 as gas).
3. For the reaction to represent \( \Delta H_f \) of the product, the reaction must form exactly one mole of the product from its elements in their standard states without any other products or reactants.
4. Analyze each reaction: - \( \text{C(s)} + \text{O}_2(g) \rightarrow \text{CO}_2(g) \): forms 1 mole of CO_2 from elemental carbon (solid) and oxygen gas, both standard states. - \( \text{CO}_2(g) + \text{H}_2\text{O}(l) \rightarrow \text{H}_2\text{CO}_3(aq) \): reactants are compounds, not elements. - \( \text{N}_2(g) + 3\text{H}_2(g) \rightarrow 2\text{NH}_3(g) \): forms 2 moles of NH_3, not 1 mole. - \( 2\text{H}_2(g) + \text{O}_2(g) \rightarrow 2\text{H}_2\text{O}(l) \): forms 2 moles of H_2O, not 1 mole.
5. Conclude that the reaction where \( \Delta H_{rxn} = \Delta H_f \) for the product is the one forming exactly one mole of product from its elements in their standard states, which is the first reaction: \( \text{C(s)} + \text{O}_2(g) \rightarrow \text{CO}_2(g) \).