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

Explanation

The electronic configuration of `1s^(2),2s^(2),2p^(6),3s^(1)` and Mg is `1s^(2) 2s^(2) 2p^(6) 3s^(2)` respectively. To remove first electron from sodium, it is to be removed from `3s^(1)` and after the loss of that electron it will acquire noble gas configuration. However in case of Mg it is to be removed from completely filled `3s^(2)` stable orbital and after loss of one electron it will not acquire noble gas configuration. So the I.E. of Mg is higher than that of sodium., In order to remove 2nd electron from sodium it is to be removed from completely filled second orbital which is very difficult, whereas in magnesium it is to be removed from `3s^(1)`., from.which it can easily losse. So second I.E. of Mg smaller then that of sodium.