  It is now well-established that the elemental abundance patterns of stars
holds key clues not only to their formation but also to the assembly histories
of galaxies. One of the most exciting possibilities is the use of stellar
abundance patterns as "chemical tags" to identify stars that were born in the
same molecular cloud. In this paper we assess the prospects of chemical tagging
as a function of several key underlying parameters. We show that in the
fiducial case of $10^4$ distinct cells in chemical space and $10^5-10^6$ stars
in the survey, one can expect to detect $\sim 10^2-10^3$ groups that are $\ge
5\sigma$ overdensities in the chemical space. However, we find that even very
large overdensities in chemical space do not guarantee that the overdensity is
due to a single set of stars from a common birth cloud. In fact, for our
fiducial model parameters, the typical $5\sigma$ overdensity is comprised of
stars from a wide range of clusters with the most dominant cluster contributing
only 25% of the stars. The most important factors limiting the identification
of disrupted clusters via chemical tagging are the number of chemical cells in
the chemical space and the survey sampling rate of the underlying stellar
population. Both of these factors can be improved through strategic
observational plans. While recovering individual clusters through chemical
tagging may prove challenging, we show, in agreement with previous work, that
different CMFs imprint different degrees of clumpiness in chemical space. These
differences provide the opportunity to statistically reconstruct the slope and
high mass cutoff of CMF and its evolution through cosmic time.
