We determined the partial molar volumes and adiabatic compressibilities of N-acetyl amino acid amides, N-acetyl amino acid methylamides, N-acetyl amino acids, and short oligoglycines as a function of urea concentration. We analyze these data within the framework of a statistical thermodynamic formalism to determine the association constants for the reaction in which urea binds to the glycyl unit and each of the naturally occurring amino acid side chains replacing two waters of hydration. Our determined association constants, k, range from 0.04 to 0.39M. We derive a general equation that links k with changes in free energy, Delta G(tr), accompanying the transfer of functional groups from water to urea. In this equation, Delta G(tr) is the sum of a change in the free energy of cavity formation, Delta Delta G(C), and the differential free energy of solute-solvent interactions, Delta Delta G(I), in urea and water. The observed range of affinity coefficients, k, corresponds to the values of Delta Delta G(I) ranging from highly favorable to slightly unfavorable. Taken together, our data support a direct interaction model in which urea denatures a protein by concerted action via favorable interactions with a wide range of protein groups. Our derived equation linking k to Delta G(tr) suggests that Delta Delta G(I) and, hence, the net transfer free energy, Delta G(tr) are both strongly influenced by the concentration of a solute used in the experiment. We emphasize the need to exercise caution when two solutes differing in solubility are compared to determine the Delta G(tr) contribution of a particular functional group. (C) 2010 Wiley Periodicals, Inc. Biopolymers 93: 866-879, 2010.