Pseudo-first-order reactions and the fall-off range

PSEUDO-FIRST-ORDER REACTIONS AND THE FALL-OFF RANGE 

As mentioned earlier, practically all reactions are initiated by bimolecular collisions however, certain bimolecular reactions exhibit first-order kinetics. Whether a reaction is first- or second-order is particularly important in combustion because of the presence of large radicals that decompose into a stable species and a smaller radical (primarily the hydrogen atom). A prominent combustion example is the decay of a paraffinic radical to an olefin and an H atom. The order of such reactions, and hence the appropriate rate constant expression, can change with the pressure. Thus, the rate expression developed from one pressure and temperature range may not be applicable to another range. This question of order was first addressed by Lindemann [4], who proposed that first-order processes occur as a result of a two-step reaction sequence in which the reacting molecule is activated by collisional processes, after which the activated species decomposes to products. Similarly, the activated molecule could be deactivated by another collision before it decomposes. If A is considered the reactant molecule and M its nonreacting collision partner, the Lindemann scheme can be represented as follows  

Applying the steady-state assumption to the activated species equation gives 

Many systems fall in a region of pressures (and temperatures) between the high- and low-pressure limits. This region is called the fall-off range, and 

For a pressure (or concentration) in the center of the fall-off range, (kdiss()/ diss,a ) = 1 and 

---