The frequency-dependent dipole polarizabilities are calculated for the five lowest states 3(1)S; 4(1)S; 3(1)P; 3(3)P and 4(3)S of Mg by using our time-dependent gauge invariant method (TDGI). Estimations of the long-range dispersion coefficients for all the first-molecular states dissociations of Mg-2 are proposed. Accuracy of the results is checked through the calculations obtained from a length, a velocity and a mixed approach in the formulation of the oscillator strengths and the corresponding dynamic dipole polarizabilities. In all cases, the length results appear as a reference for the comparison with some previous works concerning the ground state. The long-range coefficients reported for almost all the low-lying states are new and predict a repulsive interaction between the 4(1)S states.