The ionization enthalpy increases across a period as the nuclear charge increases. Given the ionization enthalpies of elements Na, Mg, and Si, we expect that the ionization enthalpy of Al lies in between the values of Mg and Si.
Thus, for Al, the ionization enthalpy is approximately the average of those of Mg and Si:
\[
\text{Ionization Enthalpy of Al} = \frac{737 + 786}{2} = 761.5 \, \text{kJ mol}^{-1}
\]
But, the first ionization enthalpy of Al is slightly less than the average due to its slightly smaller size than Si. Therefore, the value of 575 kJ mol}^{-1} is the best estimate.
Thus, the first ionization enthalpy of Al is 575 kJ mol}^{-1}.