Electron-transfer reactions of redox solutes at electrode/solution interfaces are facilitated when their formal potentials match, or are close to, the energy of an electronic state of the electrode. Metal electrodes have a continuum of electronic levels, and redox reactions occur without restraint over a wide span of electrode potentials. This paper shows that reactions on electrodes composed of films of metal nanoparticles do have constraints when the nanoparticles are sufficiently small and molecule-like so as to exhibit energy gaps, and resist electron transfers with redox solutes at potentials within the energy gap. When solute formal potentials are near the electronic states of the nanoparticles in the film, electron-transfer reactions can occur. The electronic states of the nanoparticle film electrodes are reflected in the formal potentials of the electrochemical reactions of the dissolved nanoparticles at naked metal electrodes. These ideas are demonstrated by voltammetry of aqueous solutions of the redox solutes methyl viologen, ruthenium hexammine, and two ferrocene derivatives at films on electrodes of 1.1 nm core diameter Au nanoparticles coated with protecting monolayers of phenylethanethiolate ligands. The methyl viologen solute is unreactive at the nanoparticle film electrode, having a formal potential lying in the nanoparticle's energy gap. The other solutes exhibit electron transfers, albeit slowed by the electron hopping resistance of the nanoparticle film. The nanoparticles are not linked together, being insoluble in the aqueous medium; a small amount of an organic additive (acetonitrile) facilitates observing the redox solute voltammetry.