1. Mechanism of Some Typical Complex Reactions

2. §11.9 1 Chain Reaction 1.1 basic concepts of chain reaction:
chain-initiating step
chain-propagating steps
chain-terminating step
The chain-initiating step is usually a reaction in which a molecule is decomposed by thermal collision or radiation. In some cases, a molecule named as initiator, which can readily decompose and produces radicals, is introduced into the system. Some activated species, such as free atoms, radicals, carbonium ions, act as chain initiating species, which is usually called chain carriers.

3. chain-propagating steps
A chain reaction is one in which some intermediates are consumed and regenerated in a cycle of reactions the net result of which is to carry forward the overall reaction.
Owing to the participation of active intermediate, the activation energy of chain reactions, usually ranging between 0 ~ 40 kJ mol-1, is much lower than that of other kinds of reactions of 40 ~ 400 kJ mol-1. Therefore, chain reactions can proceed rapidly.

4. Basic characteristics of chain reaction:
1) with active radicals participating;
2) low activation energy of chain propagation
3) wide existence
Examples for Chain reactions:
1) H2 + Cl2 ; H2 + Br2 ;
2) Pyrolysis (thermal decomposition) of many organic molecules.
3) polymerization:

5. 1.2 rate equation of chain reaction
Polymerization initiated by initiator
X-X X
X + RCH=CH2  XRCH-CH2
XRCH-CH2 + RCH=CH2  XRCH-CH2-RCH-CH2  ……
XR(CH-CH2)n-1CH-CH2 + RCH=CH2  XR(CH-CH2)nCH-CH2 k2
XR(CH-CH2)nCH-CH2 +X   XR(CH-CH2)nCH-CH2X k3
XR(CH-CH2)n + XR(CH-CH2)m   XR(CH-CH2)n (CH-CH2) mRX
Just likes that of H2+Cl2 

6. 1.3 Branched chain reactions and explosion
According to Arrhenius equation:
the rate constant of the reaction increases exponentially with temperature.
If an exothermic reaction is constrained to take place in a limited volume and the heat cannot be dissipated, temperature will increase. The higher temperature will, in turn, accelerate the reaction and produce more heat, which causes a still higher temperature. This will finally result in a catastrophe-an explosion, which is named as thermal explosion.

7. Explosion of H2-O2 mixture
The most extensively studied branched chain reaction is the formation of water.
2 H2(g) + O2(g)  2 H2O (g)
It was found that, the rate of the reaction is highly dependent on the surface of container, temperature, and pressure. p1 p2 p3
explosion limit;
region of explosion;
region of normal reaction.

8. Stable peninsula Explosion peninsula
pressure
temperature
600 oC
Stable peninsula
Explosion peninsula
The complete mechanism for the reaction is still not unambiguously established. One simple sequence consists of the following elementary steps was proposed:

9. Initiation:
Propagation:
Branching:
gaseous termination:
Wall termination:

10. For certain reaction under appropriate conditions, propagating steps occur in which the loss of a single propagator is overcompensated for by the production of two or more other propagating species, such chain reaction is branched chain reaction.

11. Initiation:
Propagation:
gaseous termination:
Wall termination:
Under low pressure, the free range of molecules is large, the wall termination is dominate, therefore, the explosion depends on the volume and the nature of the vessel.
At high pressure, the free range of molecules is small, the gaseous termination is dominate, therefore, the explosion does not depend on the volume and the nature of the vessel.

12. When  = 1, the denominator (kw + kg) has certain value, and the reaction will take place at a moderate rate.
When  > 1, i.e., branched chain reaction, k2[A](1-) is of minus value, if k2[A](1-) + kw + kg  0, the reaction rate  , and explosion occurs.