We study the principles behind specific ion effects of alkali and halide ions in various protic and aprotic solvents by means of a conceptual density functional theory (DFT) approach. The results of our calculations are in good agreement with experimental data and underline the crucial role of frontier molecular orbital energies. Further analysis reveals that the electronegativities and chemical hardness values of the considered ion and solvent species provide a molecular rationale for specific ion effects and the law of matching water affinities. Based on the analytical expressions and DFT calculations, we show that solvent affinities and the occurrence of specific ion effects, among other molecular mechanisms and interactions, are mainly due to electronegativity differences between the ions and the surrounding solvent molecules.