Q.IE₁ and IE₂ of Mg are 179 and 348 kcal mol⁻¹ respectively. The energy required for the reaction Mg → Mg²⁺ + 2 e⁻ is

Ionisation enthalpy (ionisation energy) is the minimum energy needed to remove the most loosely bound electron from an isolated, neutral, gaseous atom in its ground state: $M_{(g)} + IE_1 \rightarrow M^+_{(g)} + e^-$. Removing further electrons from the resulting cations defines successive ionisation energies ($IE_2, IE_3,\ldots$), which always increase, $IE_1 < IE_2 < IE_3 < \ldots$, since each successive electron is removed from a progressively more positively charged (and so more tightly binding) species.

Across a period, ionisation enthalpy generally increases left to right, since the effective nuclear charge on the valence shell grows steadily (same mechanism as the atomic-radius trend). Two well-known exceptions occur where losing an electron takes a stable filled or half-filled subshell into an unstable partially-filled one, or vice versa: Be ($2s^2$, filled) has a higher IE1 than B ($2s^2 2p^1$), and N ($2p^3$, half-filled) has a higher IE1 than O ($2p^4$). …