The double-layer region impedance of polycrystalline Pt/Perchloric acid solutions interfaces was measured to determine the influence of electrode surface roughness and solution electrolyte concentration on the fractional power n of the constant phase element cpe associated to frequency dispersion in the impedance behaviour of this system. The surface roughness factor was obtained through the adsorption charge of hydrogen from cyclic voltammograms. The solution electrolyte concentration was found to have a significant effect on the cpe only when smaller than 0.5 mol l-1. On the other hand, the frequency dispersion was found to depend directly on the surface roughness. An empirical linear relationship was found between the exponent n and the inverse if the roughness factor, leading to a minimum value of 76 for the phase angle; this value contrasts to the theoretically predicted value of 45-degrees. From a general logarithmic relationship between roughness factor delta and the fractal dimension d of the electrode surface, derived from known equations, and the linear relationship between n and 1/delta, an empirical logarithmic relationship between n and d is obtained. This empirical relationship contrasts with linear relationships previously derived by other authors.