  We consider the reversible adsorption of dimers on a regular lattice, where
adsorption occurs on a finite fraction of sites selected randomly. By comparing
this system to the pure system where all sites are available for adsorption, we
show that when the activity goes to infinity, there exists a mapping between
this model and the pure system at the same density. By examining the
susceptibilities, we demonstrate that there is no mapping at finite activity.
However, when the site density is small or moderate, this mapping exists up to
second order in site density. We also propose and evaluate approximate
approaches that may be applied to systems where no analytic result is known.
