Density functional theory (DFT) calculations of energetic, geometric, vibrational, and electrostatic properties of different arrangements of CO and NO at quarter and half monolayer coverage on Pt(111) are presented. Differences in the extents of electron back-donation from the Pt surface to these molecules cause the low-coverage adsorbate dipoles to have opposite signs at atop and more highly coordinated bridge or fcc sites. These dipoles of opposite sign occupy adjacent positions in the experimentally observed atop-bridge or atop-fcc high -coverage arrangements, leading to attractive electrostatic interactions and concomitant changes in dipole moments, bond lengths, and vibrational frequencies. The interaction energies are estimated by charge partitioning to extract individual dipoles from the mixed arrangement and by calculations of field-dipole interactions. These estimated dipole interactions contribute significantly (20-60%) to the DFT-calculated relative stability of mixed arrangements over atop-, bridge-, or fcc-only arrangements and thus play an important role in coverage-dependent adsorption. We further extend these analyses to a range of molecules with varying dipole moments and show that the general nature of these interactions is not limited to CO and NO.