The long-standing question whether the chemical concept of molecular association has a place in a rigorous statistical mechanical theory is addressed. This topic received renewed attention during the recent discussion of the criticality of ionic fluids and solutions. Whereas in the chemical approach associates, such as ion pairs are presumed to exist in a chemical equilibrium with monomers that is described by a mass-action law, the central quantity of interest in the physical approach is the partition function of the system. The partition function is based on the molecular interactions among the particles comprising the system, i.e., among the monomers; this approach is expected to offer a complete description of the thermodynamic behavior. In a previous paper by one of the authors [W. Schröer, J. Mol. Liq. 164 (2011) 3–10], it was demonstrated that, for a one-dimensional system of particles interacting by a square-well potential, the exact solution and the chemical formulation of an equilibrium between a bound state and a non-bound (free) state are thermodynamically equivalent. The maximum term of the polynomial representing the complete solution yields the mass-action law. In this work, the approach is extended to a three-dimensional system of spherical particles interacting by a square-well potential. The exact solution being unknown, we limit ourselves to evaluating all graphs consisting of N vertices representing the particles in which each particle is connected by a Mayer f-bond to at most one other particle. As in the one-dimensional case, the maximum term of this series is of the form that describes the equilibrium between free particles (monomers) and bound particles (dimers, in this case), where the Mayer cluster integral b2 (the negative of the 2nd virial coefficient B2) is the equilibrium constant. The equilibrium formulation is, once again, equivalent to the complete series in the thermodynamic limit. The fact, that b2 is a sum of the excluded volume and a part determined by the attractive potential, suggests separating these two parts and describing the association equilibrium by the attractive contribution to the Mayer f-function alone. The mass-action law obtained in this way includes a selection of graphs from the complete partition function involving b2 and higher powers of it. The density expansion of the free energy yields the contributions of pure powers of b2 to all order of the density, not just to the second virial coefficient.