  In its general definition, the law of mass action posits that, in systems
where multiple elements move randomly, the rate by which they physically
interact is proportional to the product of their densities. This law predicts
the rate of elementary chemical reactions and many other phenomena in biology,
physics, and social sciences. Using combinatorial mathematics, this study shows
that this law inherently overestimates the rate of homotypic interactions, i.e.
whereby identical elements interact with each other. This overestimation
depends on how many of them interact simultaneously (homointeractivity), and on
the difference between the density of interactants and homointeractivity. When
this difference is large, as in most systems, the rate expression given by the
law of mass action for any homotypic interaction is corrected by dividing it by
the factorial of homointeractivity. This modification should yield better
agreement between theoretical predictions and experimental determinations of
interaction rates in a wide range of natural phenomena.
