In this study, we investigate the thermodynamics of alkali nitrate salt solutions, especially the formation of contact ion pairs between alkali cation and nitrate anion. The ion-pairing propensity shows an order of LiNO3 < NaNO3 < KNO3. Such results explain the salt activity coefficients and suggest that the empirical "law of matching water affinity" is followed by these alkali nitrate salt solutions. The spatial patterns of contact ion pairs are different in the three salt solutions studied here: Li(+) forms the contact ion pair with only one oxygen of the nitrate while Na(+) and K(+) can also be shared by two oxygens of the nitrate. In reproducing the salt activity coefficient using Kirkwood-Buff theory, we find that it is essential to include electronic polarization for Li(+) which has a high charge density. The electronic continuum correction for nonpolarizable force field significantly improves the agreement between the calculated activity coefficients and their experimental values. This approach also improves the performance of the force field on salt solubility. From these two aspects, this study suggests that electronic continuum correction can be a promising approach to force-field development for ions with high charge densities.