$(i)\,2Fe(s)\, + \,\frac{3}{2}\,{O_2}\,(g)\, \to \,F{e_2}{O_3}\,(s)\,;$ $\Delta {H^\Theta }\, = \ \,-193.4\,kJ$
$(ii)\,Mg(s)\, + \,\,{O_2}\,(g)\, \to \,MgO\,(s)\,;$ $\Delta {H^\Theta }\, = \, - \,140.2\,kJ$
What is $\Delta {H^\Theta }$ of the reaction ?
$3Mg + Fe_2O_3 \to 3MgO + 2Fe$
.......$kJ$
$(i)$ $2 \mathrm{Fe}(\mathrm{s})+\frac{3}{2} \mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s})$ $\Delta {{\text{H}}^\Theta } = - 193.4\,{\mkern 1mu} {\text{kJ}}$
$(ii)$ $\mathrm{Mg}(\mathrm{s})+3 / 2 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow 3 \mathrm{MgO}(\mathrm{s})$ $\Delta \mathrm{H}=-420.6\,\mathrm{kJ}$
Subtracting $(i)$ from $(ii)$.
$3 \mathrm{Mg}(\mathrm{S})+\mathrm{Fe}_{2} \mathrm{O}_{3} \longrightarrow 3 \mathrm{MgO}+2 \mathrm{Fe}$
$\Delta {{\text{H}}^\Theta } = - 420.6 - ( - 193.4)$ $=\, -\,227.2\,\mathrm{kJ}$
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