A theory is presented which allows us to accurately calculate the surface tensions and the surface potentials of electrolyte solutions. Both the ionic hydration and the polarizability are taken into account. We find a good correlation between the Jones-Dole viscosity B coefficient and the ionic hydration near the air-water interface. The kosmotropic anions such as fluoride, iodate, sulfate, and carbonate are found to be strongly hydrated and are repelled from the interface, The chaotropic anions such as perchlorate, iodide, chlorate, and bromide are found to be significantly adsorbed to the interface. Chloride and bromate anions become weakly hydrated in the interfacial region. The sequence of surface tensions and surface potentials is found to follow the Hofmeister ordering. The theory quantitatively accounts for the surface tensions of 10 sodium salts or which there is experimental data