[Law_C.K.] Combustion physics

74 Chemical Kinetics
the dependence on internal energy in the manner of the RRK theory can be readily
conducted.
Chemically activated reactions are usually encountered for medium- to large-size
reactants. For example, the important methyl self-reaction
and the CO oxidation reaction
CH 3 + CH 3 → C 2 H 6
→ C 2 H 5 + H,
CO + OH → HOCO
→ CO 2 + H
belong to this class of reactions. The existence of these reactions adds yet another
dimension of difficulty in the identification of elementary reaction steps and the
determination of their rate constants.
2.4. CHAIN REACTION MECHANISMS
In most reaction mechanisms there are present small concentrations of highly reactive
intermediate species that participate and are regenerated in a sequence of reactions.
It is through the participation of these species, called the chain carriers, that the
reactants are converted to the products. Chain reactions can be further classified into
straight-chain and branched-chain reactions, which are now separately discussed.
2.4.1. Straight-Chain Reactions: The Hydrogen–Halogen System
We consider straight-chain reactions via the example of the hydrogen–halogen system,
which has a direct reaction path of
k 0
H 2 + X 2 → 2HX,
(X0)
with a production rate of HX given by
d[HX]
= 2k 0 [H 2 ][X 2 ], (2.4.1)
dt
where X 2 is the halogen molecule F 2 ,Cl 2 ,Br 2 ,orI 2 .Ithas been found, however, that
the reaction between H 2 and X 2 to produce HX actually follows a more complex
scheme consisting of the following five major steps:
X 2 + M k 1, f
→ X + X + M Chain initiation (X1f )
k 2, f
X + H 2 → HX + H Chain carrying (X2f )
k 3, f
H + X 2 → HX + X Chain carrying (X3f )
X + X + M k 1,b
→ X 2 + M Chain termination (X1b)
H + HX k 2,b
→ X + H 2 Chain carrying. (X2b)