  Dissociative adsorption onto a surface introduces dynamic correlations
between neighboring sites not found in non-dissociative absorption. We study
surface coverage dynamics where reversible dissociative adsorption of dimers
occurs on a finite linear lattice. We derive analytic expressions for the
equilibrium surface coverage as a function of the number of reactive sites,
$N$, and the ratio of the adsorption and desorption rates. Using these results,
we characterize the finite size effect on the equilibrium surface coverage. For
comparable $N$'s, the finite size effect is significantly larger when $N$ is
even than when $N$ is odd. Moreover, as $N$ increases, the size effect decays
more slowly in the even case than in the odd case. The finite-size effect
becomes significant when adsorption and desorption rates are considerably
different. These finite-size effects are related to the number of accessible
configurations in a finite system where the odd-even dependence arises from the
limited number of accessible configurations in the even case. We confirm our
analytical results with kinetic Monte Carlo simulations. We also analyze the
surface-diffusion case where adsorbed atoms can hop into neighboring sites. As
expected, the odd-even dependence disappears because more configurations are
accessible in the even case due to surface diffusion.
