Hess's Law Application to Formation Enthalpy

Steps:

• Apply Hess's law: ΔH_rxn = [ΔH_f(Ca(OH)2(s)) + ΔH_f(H2(g))] - [ΔH_f(Ca(s)) + 2ΔH_f(H2O(l))].
• Set ΔH_f(Ca(s)) = 0 and ΔH_f(H2(g)) = 0, as they are elements in standard states.
• Simplify to ΔH_rxn = ΔH_f(Ca(OH)2(s)) - 2ΔH_f(H2O(l)).
• Solve for ΔH_f(Ca(OH)2(s)) = ΔH_rxn + 2ΔH_f(H2O(l)); requires ΔH_f(H2O(l)).

Why D is correct:

• D supplies ΔH_f[H2O(l)], the missing term in the rearranged formation equation per Hess's law.

Why the others are wrong:

• A: ΔH_f[Ca(OH)2(s)] is the value being calculated, creating circular reasoning.
• B: ΔH_f[H2(g)] = 0 by definition for diatomic hydrogen in standard state.
• C: Ionization energies of Ca pertain to gas-phase atomic processes, unrelated to this bulk reaction enthalpy.

Final answer: D