We compare upper and lower bounds for the rate of the reversible, cooperative adsorption of hard particles from a reservoir at constant activity to a lattice surface where the only cooperative effect is excluded volume. The adsorption rate is proportional to the density of groups of unoccupied lattice sites: holes, large enough to accommodate a particle. The bounds on the rate of adsorption are then bounds on the density of holes. The upper bound for particles that are infinitely mobile on the surface is obtained from the equilibrium Mayer activity series for the pressure, while the lower bound is obtained from the extensive exact series calculated by Gan and Wang [J. Chem. Phys. 108, 3010 (1998)] for the case of irreversible random sequential adsorption where the particles are immobile once adsorbed. In all cases the bounds coincide at low densities. For the one-dimensional lattice with nearest-neighbor exclusion (where the bounds are known exactly! the upper and lower bounds are very close for all densities below the limit of random close packing as they are for the adsorption of hard dimers on two-dimensional lattices. Thus in these cases equilibrium statistical mechanics can give useful information about the kinetics of cooperative processes.