(Solved): The enthalpy changes, \( \Delta H \), for three reactions are given. \[ \begin{array}{cl} \mathrm{H ...

The enthalpy changes, \( \Delta H \), for three reactions are given. \[ \begin{array}{cl} \mathrm{H}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) & \Delta H=-286 \mathrm{~kJ} / \mathrm{mol} \\ \mathrm{Ca}(\mathrm{s})+2 \mathrm{H}^{+}(\mathrm{aq}) \longrightarrow \mathrm{Ca}^{2}+(\mathrm{aq})+\mathrm{H}_{2}(\mathrm{~g}) & \Delta H=-544 \mathrm{~kJ} / \mathrm{mol} \\ \mathrm{CaO}(\mathrm{s})+2 \mathrm{H}^{+}(\mathrm{aq}) \longrightarrow \mathrm{Ca}^{2}+(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) & \Delta H=-193 \mathrm{~kJ} / \mathrm{mol} \end{array} \] Using Hess's law, calculate the heat of formation for \( \mathrm{CaO}(\mathrm{s}) \) using the reaction shown. \[ \mathrm{Ca}(\mathrm{s})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CaO}(\mathrm{s}) \] \[ \Delta H=\{\quad \mathrm{kJ} / \mathrm{mol} \]