How would you explain the fact that the first ionsiation enthalpy of sodium is lower than that of magnesium but its second ionisation enthalpy is higher than that of magnesium?

Explanation

The electronic configurations of Na and Mg are as follows:
`Na(Z=11):1s^(2)2s^(2)2p^(6)3s^(1)`
`Mg(Z=12) : 1s^(2)2s^(2)2p^(6)3s^(2)`
Since sodium possesses a smaller nuclear charge (+11) as compared to that of magnesium ( + 12), the first ionization enthalpy of sodium is lower than that of magnesium. After the removal of first electron, Na changes to `Na^(+)` ion and Mg to `Mg^(+)` ion. Their electronic configurations are as follows :
`Na^(+) : 1s^(2)2s^(2)2p^(6)`
`Mg^(+) : 1s^(2)2s^(2)2p^(6)3s^(1)`
`Na^(+)` ion possesses a very stable electronic configuration similar to that of neon. Therefore, it will require a greater amount of energy to remove an electron from `Na^(+)` as compared to that from `Mg^(+)` ion. This is why the second ionisation enthalpy of Na is higher than that of Mg.