IE₁ and IE₂ of Mg are 178 and 348 kcal mol^-1. The energy required for the reaction $\mathrm{Mg}\to {\mathrm{Mg}}^{2+}+2{\mathrm{e}}^{-}$ is __________.

$\text{ (i) }{\mathrm{Mg}}_{\left(\mathrm{g}\right)}⟶{{\mathrm{Mg}}^{\oplus }}_{\left(\mathrm{g}\right)}+e^{-},{\mathrm{IE}}_1=178 \mathrm{kcal} {\mathrm{mol}}^{-1}$

$\text{ (ii) }\underset{ }{{{\mathrm{Mg}}^{\oplus }}_{\left(g\right)}}⟶{{\mathrm{Mg}}^{2+}}_{\left(\mathrm{g}\right)}+e^{-},{\mathrm{IE}}_2=348\mathrm{kcal}{\mathrm{mol}}^{-1}$

Adding (i) and (ii), we have

$$\begin{gathered} ---------- \\ {\mathrm{Mg}}_{\left(\mathrm{g}\right)}⟶{{\mathrm{Mg}}^{2+}}_{\left(\mathrm{g}\right)}+2e^{-} \\ ---------- \end{gathered}$$

$\therefore$ E = IE₁ + IE₂ = 178 +348 =526 kcal