The fundamental equations of a Poisson-Boltzmann model to investigate the effects of a de-localized surface interaction energy on the ionic adsorption in a finite-length electrolytic cell are solved. Two distinct, physically plausible, forms of the interaction energy, having different decaying spatial behavior are explicitly analyzed. The surface and chemical potentials are evaluated in terms of the strengths of these van der Waals-like interactions characterizing the adsorption energy. A quantity playing the role of an integral double-layer capacitance of the cell is introduced and its behavior is investigated as a function of the parameters of the adsorption potentials.