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We derive an expression for the chemical potential of an associating solutein a solvent relative to the value in a reference fluid using the quasichemicalorganization of the potential distribution theorem. The fraction of times thesolute is not associated with the solvent, the monomer fraction, is expressedin terms of (a) the statistics of occupancy of the solvent around the solute inthe reference fluid and (b) the Widom factors that arise because of turning onsolute-solvent association. Assuming pair-additivity, we expand the Widomfactor into a product of Mayer f-functions and the resulting expression isrearranged to reveal a form of the monomer fraction that is analogous to thatused within the statistical associating fluid theory (SAFT). The presentformulation avoids all graph-theoretic arguments and provides a fresh, moreintuitive, perspective on Wertheim's theory and SAFT. Importantly, multi-bodyeffects are transparently incorporated into the very foundations of the theory.We illustrate the generality of the present approach by considering examples ofmultiple solvent association to a colloid solute with bonding domains thatrange from a small patch on the sphere, a Janus particle, and a solute whoseentire surface is available for association.

Quasichemical theory and the description of associating fluids relative to a reference: Multiple bonding of a single site solute