To explain why the first ionization enthalpy of sodium is lower than that of magnesium, but the second ionization enthalpy of sodium is higher than that of magnesium, we need to consider the electronic configuration and the stability of the resulting ions.

Sodium (Na) has an electronic configuration of 1s² 2s² 2p⁶ 3s¹, while magnesium (Mg) has an electronic configuration of 1s² 2s² 2p⁶ 3s². When sodium loses one electron to form Na⁺, it achieves a stable noble gas configuration, which is energetically favorable, leading to a lower first ionization enthalpy compared to magnesium, which requires more energy to remove one of its two outer electrons.

However, when we consider the second ionization enthalpy, for sodium, after losing one electron to form Na⁺, removing a second electron means taking it from a stable noble gas configuration (Ne), which requires significantly more energy. In contrast, magnesium's second ionization involves removing an electron from a positively charged ion (Mg⁺), which is less stable than a noble gas configuration, resulting in a lower second ionization enthalpy compared to sodium.

• First ionization enthalpy of sodium is lower because it achieves a stable configuration upon losing one electron.
• Second ionization enthalpy of sodium is higher due to the stability of the Na⁺ ion compared to the Mg⁺ ion.

The differences in ionization enthalpy between sodium (Na) and magnesium (Mg) can be understood by examining their electronic configurations and the stability of the ions formed.

First Ionization Enthalpy

Sodium has the electronic configuration of 1s² 2s² 2p⁶ 3s¹, while magnesium is configured as 1s² 2s² 2p⁶ 3s². When sodium loses one electron to form Na⁺, it reaches a stable noble gas configuration similar to neon. This stability makes it easier for sodium to lose its outer electron, resulting in a lower first ionization enthalpy compared to magnesium, which has to remove one of its two outer electrons.

Second Ionization Enthalpy

After sodium forms Na⁺, removing a second electron means taking it from a stable noble gas configuration (Ne). This process requires a significant amount of energy, leading to a higher second ionization enthalpy for sodium. In contrast, magnesium's second ionization involves removing an electron from the Mg⁺ ion, which is less stable than a noble gas configuration. Therefore, it requires less energy compared to sodium's second ionization.

• First Ionization: Sodium loses one electron easily due to stability.
• Second Ionization: Sodium's second ionization is harder due to its stable Na⁺ state.

In summary, sodium's first ionization enthalpy is lower because it achieves stability upon losing one electron, while its second ionization enthalpy is higher due to the stability of the Na⁺ ion compared to the Mg⁺ ion.