Can a zeroth order reaction be reversible? After recently studying about chemical equilibrium, I was convinced that the forward and backward reaction rates meet each other at equilibrium.

However thinking about zeroth order reaction annoyed me a little, as I could not figure out how the rates would become equal, if at all, in cases where the rate remains static throughout. Here's what I guessed:


The backward reaction of a zeroth order reaction must not be a zeroth order reaction in itself, so that it may reach the reaction rate equivalence point at equilibrium.But then this generalization is difficult to digest (for me).  


or


A zeroth order reaction can not attain equilibrium (highly unlikely).
A zeroth order reaction does not achieve equilibrium as a zeroth order reaction.  Instead the kinetics will go away from zeroth order when we get close to the equilibrium condition.

Zeroth order kinetics is an approximation we get to when some aspect of the reaction approaches a saturation condition, for example the reaction mechanism may involve adsorption on a surface and there is enough reactant to saturate all the adsorption sites.  Such conditions are perforce relatively far from equilibrium; "saturation" and "reversibility" do not come about simultaneously.