(Solved): Calculate the standard enthalpy of formation, \( \Delta \mathrm{H}_{\mathrm{f}}^{\mathrm{f}} \), i ...

Calculate the standard enthalpy of formation, \( \Delta \mathrm{H}_{\mathrm{f}}^{\mathrm{f}} \), in \( \mathrm{kJ} \mathrm{mol}^{-1} \), of solid \( \mathrm{Mg}(\mathrm{OH})_{2} \), given the following data: \[ \begin{array}{l} 2 \mathrm{Mg}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{MgO}(\mathrm{s}) \Delta \mathrm{H}^{\mathrm{O}}=-1203.6 \mathrm{~kJ} \\ \mathrm{Mg}(\mathrm{OH})_{2}(\mathrm{~s}) \rightarrow \mathrm{MgO}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(\mathrm{I}) \Delta \mathrm{H}_{2}^{\mathrm{o}}=+37.1 \mathrm{~kJ} \\ 2 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{H}_{2} \mathrm{O}(\mathrm{I}) \Delta \mathrm{H}_{3}=-571.7 \mathrm{~kJ} \\ \quad+924.7 \\ \quad-1849.5 \\ \quad-924.7 \\ \quad+1849.5 \\ \quad-462.3 \end{array} \]