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What determines the chain length in a chemical chain reaction?

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A graph showing a potential energy curve for a chemical reaction, with the y-axis labeled potential energy and the x-axis labeled progress of reaction. The curve rises from the initial state (reactants) to a peak labeled transition state (activated complex), indicating activation energy, then drops to the final state (products). — chemical kinetics In the Arrhenius equation, the activation energy (E) represents the minimum amount of energy required to transform reactants into products in a chemical reaction. On a potential energy curve, the value of the activation energy is equivalent to the difference in potential energy between particles in an intermediate configuration (known as the activated complex, or transition state) and particles of reactants in their initial state. The activation energy thus can be visualized as a barrier that must be overcome by reactants before products can be formed.

In a chemical chain reaction, the chain length—the number of product molecules formed per single act of initiation—is determined by the competition between the propagation steps and the termination steps.12

A chain reaction consists of three primary stages:
* Initiation: A reactive intermediate (such as an atom or free radical) is formed through the action of heat, light, or a catalyst.34
* Propagation: The intermediate reacts with original reactants to produce stable products while simultaneously regenerating a new reactive intermediate, allowing the cycle to repeat.34
* Termination: The chain is broken when reactive intermediates are consumed or recombine, preventing further propagation.34

The chain length is essentially a measure of how many times the propagation cycle repeats before a termination event occurs. If the propagation steps are highly efficient and the concentration of substances that cause termination (such as inhibitors or antioxidants) is low, the chain length increases. Conversely, if the containing vessel or the introduction of inhibitors causes chain carriers to recombine or be removed rapidly, the chain length is shortened. In many cases, the reaction continues until the reactants are exhausted or the intermediates are destroyed.23