Which of the following reactions represents the standard enthalpy of formation (ΔH_f^∘) for water (H_2O(l))?

• A. H_2(g) + O_2(g) → H_2O_2(l)
• B. 2H_2(g) + O_2(g) → 2H_2O(l)
• C. H_2(g) + rac{1}{2}O_2(g) → H_2O(l)
• D. H_2O(l) → H_2(g) + rac{1}{2}O_2(g)

Answer: (C)

Verified step by step guidance

1. Understand that the standard enthalpy of formation (ΔH_f^∘) of a compound is defined as the enthalpy change when one mole of the compound is formed from its elements in their standard states under standard conditions.
2. Identify the elements involved in forming water (H_2O). These are hydrogen (H_2) and oxygen (O_2), both in their standard states as diatomic gases.
3. Write the balanced chemical equation that forms exactly one mole of liquid water (H_2O(l)) from its elements in their standard states. This means the equation should have H_2 and O_2 as reactants and H_2O(l) as the product, with coefficients adjusted to produce one mole of water.
4. Recall that the oxygen molecule (O_2) must be halved to provide the correct stoichiometric amount of oxygen atoms for one mole of water, resulting in the equation: \(\mathrm{H_2(g) + \frac{1}{2}O_2(g) \rightarrow H_2O(l)}\).
5. Confirm that the other given reactions either produce more than one mole of water or form a different compound (like hydrogen peroxide), so they do not represent the standard enthalpy of formation for water.