The other possible case would be that the second step is slow and rate-determining, meaning that it is slower than the first step in the reverse direction: r ≪ r. In this hypothesis, r − r ≈ 0, so that the first step is (almost) at equilibrium. The overall rate is determined by the second step: r = r ≪ r, as very few molecules that react at the first step continue to the second step, which is much slower.  Such a situation in which an intermediate (here ) forms an equilibrium with reactants prior to the rate-determining step is described as a pre-equilibrium For the reaction of  and CO, this hypothesis can be rejected, since it implies a rate equation that disagrees with experiment.
#  +  → NO +  (fast step)
#  + CO →  +  (slow step, rate-determining)
If the first step were at equilibrium, then its equilibrium constant expression permits calculation of the concentration of the intermediate  in terms of more stable (and more easily measured) reactant and product species:
The overall reaction rate would then be
which disagrees with the experimental rate law given above, and so disproves the hypothesis that the second step is rate-determining for this reaction. However, some other reactions are believed to involve rapid pre-equilibria prior to the rate-determining step, as shown below.