The 1^ st ionization enthalpy for Mg is +737 kJ/mol. The most...

Ionization enthalpy is the energy required to remove an electron from an isolated gaseous atom or ion. It is always an endothermic process, so its value is always positive.

The second ionization enthalpy is the energy required to remove an electron from a unipositive ion. Since the effective nuclear charge increases after the removal of the first electron, the remaining electrons are held more tightly by the nucleus. Thus, the second ionization enthalpy is always greater than the first ionization enthalpy ($IE_{2} > IE_{1}$).

Given the first ionization enthalpy of Mg is $+737$ kJ/mol, the second ionization enthalpy must be positive and greater than $+737$ kJ/mol.

Among the given options, only $+1450$ kJ/mol satisfies these conditions.

Answer: $+1450$ kJ/mol