In situ STM and cyclic voltammetry are employed to investigate the adsorption of organic molecules with different functional groups on Cu(111) in a 0.1 M HClO4 solution. The molecules of cyanuric acid, cyanuric chloride, and 1,3,5-tribromo-benzene adsorb on the Cu(111) electrode surface and form well-defined adlayers with (3 x 3) structure in the double layer potential region. The STM image feature for each molecule is a set of three bright spots, suggesting a flat-lying orientation for the molecules. Structural models are proposed for the three adlayers. The results are compared with those obtained on aromatic and heterocyclic molecular adlayers.