A Linear Free Energy Relationship of the type in the title is applied to sorption of numerous compounds to polyethylene and three soils for which sorption to natural organic matter (NOM) is presumed dominant. It provides fractional contributions to the Gibbs free energy of sorption corresponding to hydrophobic effects, dipolar/polarizability (D/P) effects in excess of the reference state, and the sum of possible specific forces such as H-bonding and pi-pi electron donor-acceptor (pi-pi EDA) interactions in excess of the reference state. Minimal inputs are the isotherm, the n-hexadecane-water partition coefficient representing hydrophobic effects, and the Abraham pi_i parameter representing D/P effects, which combines the effects of dipole moment and electron polarizability. Sorption of all compounds to polyethylene can be modeled by considering hydrophobic effects and ignoring all others. Sorption of a calibration set of apolar compounds (aromatic and aliphatic hydrocarbons and chlorinated hydrocarbons) to the natural sorbents is well-modeled by a combination of hydrophobic and D/P effects. For the apolar set, the excess Gibbs free energy of D/P interactions with NOM contributes ~15-40% (2-8% for cyclohexane) of the total free energy of sorption. D/P effects increase with the degree of chlorination for aliphatic compounds. For aromatic compounds D/P effects increase with fused ring size but do not vary with degree of chlorination and chlorine substitution pattern. The excess free energy of H-bonding interaction with NOM contributes substantially to sorption of alcohols—similarly so for 2-nonanol and 2,4-dichlorophenol (33%-44%). pi-pi EDA forces between phenanthrene and p-acceptor functional groups on NOM contribute to sorption in one case. The influence of concentration, sorbent aromaticity (based on literature NMR), and sorbent polarity (based on (O+N)/C) on hydrophobic and D/P contributions evaluated for all compounds indicate the following. i) Molecules fill sites of progressively greater hydrophilic character; ii) the energy penalty for cavity formation in the solid decreases with concentration due to plasticization and greater intermolecular contact; iii) sorbent aromatic content, more than sorbent polarity, controls D/P interactions. Basing free energy on an inert electrostatic chemical environment afforded by n-hexadecane permits an evaulation of direct electrostatic forces in NOM that contribute to sorption.