Though the importance of chemisorption at the electrochemical interface is well recognized, an electronic level description for the same still remains in a nascent stage. The present work specifically addresses this problem. An appropriate model Hamiltonian based formalism is proposed for a random adsorbate layer with arbitrary coverage and the ensuing two-dimensional band formation by metallic adsorbates in the monolayer regime. The coherent potential approximation is employed to handle the randomness. The adsorbate self-energy is evaluated explicitly using the density of states for the substrate band. This takes us beyond the conventional wide-band approximation and removes the logarithmic divergence associated with the binding energy calculations. The formalism is applied to the electrosorption of copper ion on gold electrode, and the coverage dependence of adsorbate charge, binding energy, and adsorbate density of states are determined. The analysis predicts a unique charge configuration of copper adsorbate, having a net positive charge, in the high-coverage regime, and multiple charge states when the coverage is low. Though one of the charge configurations of copper is nearly neutral at small coverage, its positive charge state is the most stable in the entire coverage range. The transition from the relative neutral state of copper at low coverage to a positive charge configuration occurs sharply at the intermediate-coverage region. This transition is caused due to the progressive desolvation of copper adion with increasing coverage. The energy calculations show that copper s-orbital bonding contributes maximally toward the binding energy at the metal-vacuum interface, whereas it is the copper d-orbital bonding which makes chemisorption feasible at the gold electrode. Finally, our numerical results are compared with the relevant experimental studies.