It is well established that the electrical interactions between macroions in solution and colloidal suspension are altered when the ionic strength of the medium is varied. The ionic strength is usually couched in the form of the screening parameter, generally represented by the parameter kappa. By focusing on only that part of the Helmholtz free energy of the system that depends upon kappa, i.e., A(sys)(elec)(kappa), the following relationship with the "Gibbsian" free energy G(sys)(elec)(kappa) was obtained, G(sys)(elec)(kappa)=A(sys)(elec)(kappa) + (kappa/2)(partial derivative A(sys)(elec)(kappa)/partial derivative kappa), where, from thermodynamic arguments, (kappa/2)(partial derivative)A(sys)(elec)(kappa) is identified with an internal pressure. Application of the above relationship to A(elec)((2))(kappa), a repulsive pairwise interaction which has the standard screened Coulombic form, indicates that the resulting "Gibbsian" free energy, G(elec)((2))(kappa), exhibits an "attractive" minimum at a location which depends upon kappa. Although Sogami and Ise obtained similar results with different model assumptions, the present derivation has as the "source" term for the minimum a term different from that of the Sogami-Ise theory. Hence the "solvent correction" term of Overbeek to the Sogami-Ise theory does not apply to the present derivation. It is shown that G(elec)((2))(kappa) adequately describes recent digital video data on latex spheres that indicate either attractive or repulsive interactions without having to postulate interactions other than A(elec)((2))(kappa). Since G(elec)((2))(kappa)-->A(elec)((2))(kappa) as kappa-->0, one must perform experiments with added electrolyte to distinguish between these two forms of the pairwise free energy.