20. The enthalpy change under standard conditions for which of the reactions below would be equal to the \( \Delta H_{\mathrm{f}}^{\circ} \) of \( \mathrm{NaOH}(s) \) ? (A) \( \mathrm{Na}(s)+\mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{NaOH}(s)+1 / 2 \mathrm{H}_{2}(g) \) (B) \( \mathrm{Na}(s)+1 / 2 \mathrm{O}_{2}(g)+1 / 2 \mathrm{H}_{2}(g) \rightarrow \mathrm{NaOH}(s) \) (C) \( \mathrm{Na}(s)+1 / 2 \mathrm{H}_{2} \mathrm{O}_{2}(l) \rightarrow \mathrm{NaOH}(s) \) (D) \( \mathrm{Na}^{+}(a q)+\mathrm{OH}^{-}(a q) \rightarrow \mathrm{NaOH}(s) \)

The enthalpy change under standard conditions for reaction (B) \( \mathrm{Na}(s)+1 / 2 \mathrm{O}_{2}(g)+1 / 2 \mathrm{H}_{2}(g) \rightarrow \mathrm{NaOH}(s) \) directly results in the formation of solid sodium hydroxide (\( \mathrm{NaOH}(s) \)) from its elemental components, and thus corresponds to the standard enthalpy of formation \( \Delta H_{\mathrm{f}}^{\circ} \) of \( \mathrm{NaOH}(s) \). The other options either involve decomposing sodium hydroxide, producing hydrogen gas, or consist of already formed ions, which don’t align with the definition of the standard enthalpy of formation as a reaction starting from elements in their standard states.