Fast equilibria, such as ionic dissociations within cloud drops and the establishment of Henry's law at the air-liquid interface between dissolved chemical species and the corresponding vapour pressure, may occur under special conditions. The main advantage of making equilibrium assumptions is to allow the calculation of some chemical species concentrations using simple equilibrium relations at any time without the need for time integration. The other advantage of these assumptions is the elimination of stiffness and thus the saving of CPU time which is important for three dimensional models. An existing algorithm is used to scale the system of Ordinary Differential Equations (ODE) describing a chemical box-model and the computation of the exact lumping of species. Such a scaling analysis allows us to evaluate whether an equilibrium assumption can be made without loosing accuracy. Furthermore, the algorithm determines the exact lumping of species to be introduced in order to keep the model valid while assuming equilibrium. The resulting reduced model consists of a set of ODEs and a set of algebraic relations describing the equilibrium state. The results show that according to the magnitudes of the characteristic timescales, hierarchical underlying reduced models may exist where the computed lumpings of species are mainly related to the fast ionizations and Henry's law, but also some mixed lumpings. The study shows that equilibrium may or may not be valid for individual mass transfer and ionization/dissociation reactions under different conditions. The chemical mechanism examined here is an extension of the Regional Acid Deposition Mechanism (RADM2) including sulfur and transition metal chemistry.