# 4.2: Chain Reactions

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##### Learning Objectives
• Explain the mechanisms of chain reactions in terms of elementary steps.
• Define these terms: radical, chain carrier.
• Classify elementary steps as initiation, chain propagation, chain branching, chain inhibition, and chain termination.

Chain reactions usually consist of many repeating elementary steps, each of which has a chain carrier. Once started, chain reactions continue until the reactants are exhausted. Fire and explosions are some of the phenomena associated with chain reactions. The chain carriers are some intermediates that appear in the repeating elementary steps. These are usually free radicals.

Once initiated, repeating elementary steps continue until the reactants are exhausted. When repeating steps generate more chain carriers, they are called chain branching reactions, which leads to explosions. If the repeating elementary steps do not lead to the formation of new product, they are called chain inhibition reactions. Addition of other materials in the reaction mixture can lead to the inhibition reaction to prevent the chain propagation reaction. When chain carriers react with one another forming stable product, the elementary steps are called chain termination reactions.

Explosions, polymerizations, and food spoilage often involve chain reactions. The chain reaction mechanism is involved in nuclear reactors; in this case the chain carriers are neutrons. The mechanisms describing chain reactions are useful models for describing chemical reactions. Most chemical chain reactions have very reactive intermediates called free radicals. The intermediate that maintains the chain reaction is called a chain carrier. These atoms or fragments are usually derived from stable molecules due to photo- or heat-dissociation.

Usually, a free radical is marked by a dot beside the symbol ($$\ce{*}$$), which represents an odd electron exists on the species. This odd electron makes the intermediate very reactive. For example, the oxygen, chlorine and ethyl radicals are represented by $$\ce{O*}$$, $$\ce{Cl*}$$, and $$\ce{C2H5*}$$, respectively. The $$\ce{Cl*}$$ radicals can be formed by the homolytic photodissociation reaction:

$\ce{Cl2 + h\nu \rightarrow Cl* + *Cl} \nonumber$

## Mechanism of Chain Reactions

The elementary steps used for mechanisms of chain reactions can be grouped into the following categories:

• initiation step
• chain propagation steps
• chain branching steps
• chain inhibition steps
• chain termination steps

For example, the chlorination of ethane is a chain reaction, and its mechanism is explained in the following way.

If we mix chlorine, $$\ce{Cl2}$$, and ethane, $$\ce{CH3CH3}$$, together at room temperature, there is no detectable reaction. However, when the mixture is exposed to light, the reaction suddenly initiates, and explodes. To explain this, the following mechanism is proposed.

### Initiation Step

Light ($$\ce{h\nu}$$) can often be used to initiate chain reactions since they can generate free radical intermediates via a photodissociation reaction. The initiation step can be written as:

$\ce{Cl2 + h\nu \rightarrow Cl* + *Cl} \nonumber$

### Chain Propagation Step

Elementary steps in which the number of free radicals consumed is equal to the number of free radicals generated are called chain propagation steps. Once initiated, the following chain propagation steps repeat indefinitely or until the reactants are exhausted:

$\ce{Cl* +\; H3CCH3 \rightarrow ClH2CCH3 +\; H*} \nonumber$

$\ce{Cl* +\; H3CCH3 \rightarrow H3CCH2* +\; HCl} \nonumber$

$\ce{H* +\; Cl_2 \rightarrow HCl + Cl*} \nonumber$

and many other possibilities.

In each of these steps, a radical is consumed, and another radical is generated. Thus, the chain reactions continue, releasing heat and light. The heat and light cause more radicals to form. Thus, the chain propagation steps cause chain branching reactions.

### Chain Branching Steps

Branching reactions are elementary steps that generate more free radicals than they consume. Branching reactions result in an explosion. For example, in the reaction between hydrogen and oxygen, the following reaction may take place:

$\ce{H* +\; O2 \rightarrow HO* + *O*} \nonumber$

where $$\ce{*O*}$$ is a di-radical, because the $$\ce{O}$$ atom has an electronic configuration 2s2 2px2 2py1 2pz1. In this elementary step, three radicals are generated, whereas only one is consumed.

The di-radical may react with a $$\ce{H2}$$ molecule to form two radicals.

$\ce{*O* +\, H2 \rightarrow HO* +\, H*} \nonumber$

Thus, together chain branching reactions increase the number of chain carriers. Branching reactions contribute to the rapid explosion of hydrogen-oxygen mixtures, especially if the mixtures have proper proportions.

### Chain Inhibition Steps

The steps not leading to the formation of products are called inhibition reactions or steps. For example, the following steps are inhibition reactions.

$\ce{Cl* +\; ClH2CCH3 \rightarrow H3CCH2* +\; Cl2} \nonumber$

$\ce{Cl* +\; HCl \rightarrow H* +\; Cl2} \nonumber$

$\ce{H* +\; ClH2CCH3 \rightarrow H3CCH3 + Cl*} \nonumber$

Furthermore, sometimes another reactive substance $$\ce{*A}$$ may be added to the system to reduce the chain carriers to inhibit the chain reactions.

$$\ce{Cl* + *A \rightarrow ClA\: (not\: reactive)}$$

The species $$\ce{A*}$$ is often called a radical scavenger. In food industry, radical scavengers are added to prevent spoilage due to oxidation; these are called biological oxidants.

The mechanisms in chain reactions are often quite complicated. When intermediates are detected, a reasonable mechanism can be proposed. Adding radical scavenger to prevent food spoilage is an important application in food chemistry. This application came from the application of the chain reaction model to natural phenomena.

### Chain Termination Steps

Chain termination steps are elementary steps that consume radicals. When reactants are exhausted, free radicals combine with one another to give stable molecules (since unpaired electrons become paired). These elementary steps are responsible for the chain reactions' termination:

$\ce{Cl* + *Cl \rightarrow Cl-Cl} \nonumber$

$\ce{H* + *H \rightarrow H-H} \nonumber$

$\ce{H* + *Cl \rightarrow H-Cl} \nonumber$

$\ce{H3CCH2* + *H2CCH3 \rightarrow CH3CH2-CH2CH3\: (forming\: a\: dimer)} \nonumber$

and other possibilities

In chain reactions, many products are produced.

## Questions

1. Is argon atom $$\ce{Ar}$$ a free radical? (yes/no)
2. $$\ce{Cl* +\, ClH2CCH3 \rightarrow H3CCH2* +\, Cl2}$$
1. initiation step
2. chain propagation step
3. chain branching step
4. chain inhibition reaction
5. chain termination step

Skill -
Identify steps for the names in the multiple choices.

3. Skill -
Predicting the intermediate from the nature of the reactants.
4. Which one of the following is not a chain propagation reaction in the chlorination of ethane?
1. $$\ce{Cl* +\; H3CCH3 \rightarrow ClH2CCH3 + H*}$$
2. $$\ce{Cl* +\; H3CCH3 \rightarrow H3CCH2* +\; HCl}$$
3. $$\ce{H* +\; Cl2 \rightarrow HCl + Cl*}$$
4. $$\ce{Cl* +\; HCl \rightarrow H* +\; Cl2}$$

## Solutions

1. No, argon atoms are monoatomic molecules.

Discussion -
Argon exists as a mono-atomic gas. All noble gases have mono-atomic molecules.

2. d.
3. $$\ce{Br*}$$
4. d.

Discussion -
The reactant $$\ce{HCl}$$ in the step is a product in the overall reaction. When $$\ce{HCl}$$ reacts with $$\ce{Cl*}$$, the reaction is retarded. $$\ce{Cl*}$$ attacked one of the product molecule $$\ce{HCl}$$ causing a reversal of the reaction.

4.2: Chain Reactions is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Chung (Peter) Chieh.