An analysis is outlined that utilizes electrode potential-dependent measurements of the intramolecular vibrational frequency (nu (c)) for chemisorbates, specifically carbon monoxide and nitric oxide, at ordered Pt-group metal-solution interfaces (i.e., the electrochemical Stark effect), in comparison with corresponding vibrational frequencies at the metal-ultrahigh vacuum (UHV) interfaces, as a means of assessing the role of local versus average surface potentials in the former systems. For saturated adlayers featuring the same (or similar) binding-site configurations in the aqueous electrochemical and UHV environments, adjusting the electrode potential, E-eq, to the point where nu (c) equals that measured at the corresponding metal-UHV interface yields E-eq, values that are closely concordant with the work function, Phi, for the latter surfaces. This E-eq - Phi correlation, which also yields an "absolute potential" of the reference electrode consistent with literature estimates, indicates that the average surface potential exerts a dominant influence upon v, for uniform saturated adlayers. Interestingly, a closely similar E-eq - Phi correlation is also obtained for dilute CO or NO adlayers (i.e., for isolated solvated chemisorbed molecules) that again feature the same binding sites (and coverages) in the electrochemical and UHV environments, despite the dominant presence of inner-layer solvent. These results are used to deduce that the "local" surface potentials sensed by the chemisorbate molecules within dilute electrochemical adlayers are closely similar to (within ca. 0.05-0.1 V of) the average values. This simple finding suggests, perhaps unexpectedly, that the dipolar fields generated in the vicinity of the nonpolar chemisorbates CO and NO by the double-layer environment do not differ significantly from the average values across the solvated inner layer.