Which of the following is the balanced chemical equation used to calculate the standard enthalpy of formation (ΔH_f^∘) of CaCO_3(s)?

• A. Ca(s) + CO_2(g) + O_2(g) → CaCO_3(s)
• B. CaO(s) + CO_2(g) → CaCO_3(s)
• C. CaCO_3(s) → CaO(s) + CO_2(g)
• D. Ca(s) + C(s) + 1.5 O_2(g) → CaCO_3(s)

Answer: (D)

Verified step by step guidance

1. Understand that the standard enthalpy of formation (\( \Delta H_f^\circ \)) of a compound is defined as the enthalpy change when one mole of the compound is formed from its elements in their standard states.
2. Identify the elements that make up \( \text{CaCO}_3 \): calcium (Ca), carbon (C), and oxygen (O). Each must be in its standard elemental form on the reactant side.
3. Write the reactants as the elements in their standard states: solid calcium (Ca(s)), solid carbon (C(s), usually graphite), and oxygen gas (\( \text{O}_2(g) \)).
4. Balance the equation so that one mole of \( \text{CaCO}_3(s) \) is produced from these elements. This involves ensuring the number of atoms of each element is the same on both sides, including balancing oxygen atoms by using \( 1.5 \text{O}_2(g) \) molecules.
5. The balanced chemical equation for the standard enthalpy of formation of \( \text{CaCO}_3(s) \) is therefore: \n\n\$\$ \text{Ca}(s) + \text{C}(s) + \frac{3}{2} \text{O}_2(g) \rightarrow \text{CaCO}_3(s) \n\$\$