The equivalence of the thermodynamic description of a system comprised of interacting particles by a collection of non-interacting clusters of these particles has been a long-standing issue in statistical mechanics since the pioneering work of Frenkel, Band, and Mayer. Woolley derived the association constants for the postulated chemical reactions of individual particles (monomers) to dimers, trimers, and so on, by matching the pressure of the mixture of non-interacting clusters of different sizes to the virial expansion of the interacting (but non-associating) original particles. The association constants determined in this way, however, turn out to become negative in certain temperature ranges, leading to negative concentrations of clusters. Hill subsequently resolved this problem by introducing the additional requirement that the kinetic energy had to be less than the potential energy in order to have a bound state; with this definition of a cluster, association constants remain strictly positive. Here, we present an alternative approach to avoid negative association constants by correctly incorporating the excluded volume of a cluster that results in a reduction of the space available to the non-interacting clusters of particles, without the need to define bound states. For concreteness, we study the cases of square-well fluids in one, two, and three dimensions. The mass-action laws that govern the association reactions among ideal gases formulated by Woolley are thus augmented by activity coefficients for hard rods, disks, and spheres, respectively, which account for the residual interactions caused by the excluded volume of the particles. We thereby identify the condition for obtaining a formally exact theory of geometrical clusters.