\(IE_1\) and \(IE_2\) of Mg(g) are \(178\,\mathrm{kcal\,mol^{-1}}\) and \(348\,\mathrm{kcal\,mol^{-1}}\), respectively. The energy required for the reaction \(\mathrm{Mg(g)}\rightarrow\mathrm{Mg}^{2+}\mathrm{(g)}+2e^{-}\) is