why is the second ionisation enthalpy of Mg greater than the first?

The reason the second ionization energy is higher than the first relates to the attraction between the electrons and the nucleus. When one electron is removed from an atom, the neutral atom becomes positive. When one attempts to remove a second electron from a positive ion, there is more attraction between the electrons and the nucleus due to the extra proton. Thus, the second electron is harder to remove and the ionization requires more energy.