We investigate the (surface) bonding of a class of industrially and biologically important molecules in which the chemically active orbital is a 2p electron lone pair located on an N or O atom bound via single bonds to H or alkyl groups. This class includes water, ammonia, alcohols, ethers, and amines. Using extensive density functional theory (DFT) calculations, we discover scaling relations (correlations) among molecular binding energies of different members of this class: the bonding energetics of a single member can be used as a descriptor for other members. We investigate the bonding mechanism for a representative (H2O) and find the most important physical surface properties that dictate the strength and nature of the bonding through a combination of covalent and noncovalent electrostatic effects. We describe the importance of surface intrinsic electrostatic, geometric, and mechanical properties in determining the extent of the lone-pair-surface interactions. We study systems including ionic materials in which the surface positive and negative centers create strong local surface electric fields, which polarize the dangling lone pair and lead to a strong "electrostatically driven bond". We emphasize the importance of noncovalent electrostatic effects and discuss why a fully covalent picture, common in the current first-principles literature on surface bonding of these molecules, is not adequate to correctly describe the bonding mechanism and energy trends. By pointing out a completely different mechanism (charge transfer) as the major factor for binding N- and O-containing unsaturated (radical) adsorbates, we explain why their binding energies can be tuned independently from those of the aforementioned species, having potential implications in scaling-driven catalyst discovery.