DAT Organic Chemistry: Radical Chain Mechanisms

DAT High-Yield Concept

Homolytic Cleavage: Symmetrical bond breaking where each atom receives one electron, driven by heat ( $\Delta$ ) or light ( $h\nu$ ).
Single-Barbed Arrows: Fishhook curved arrows depict the movement of single electrons, whereas double-barbed arrows depict electron pairs.
Chain Reaction Steps: Initiation generates net radicals; propagation maintains net radical count to form major products; termination destroys radicals.
Peroxide Effect: Adding peroxides ( $\ce{ROOR}$ ) to $\ce{HBr}$ addition alters the pathway from Markovnikov ionic addition to anti-Markovnikov radical addition.

Homolytic Bond Cleavage and Single-Electron Bookkeeping

Chemical bonds break in two primary ways: heterolytically or homolytically. In heterolytic cleavage, both electrons in a covalent bond move to one atom, generating an ion pair (cation and anion). In homolytic bond cleavage, the two electrons in a single covalent bond divide equally between the two bonded atoms, generating two neutral species with unpaired electrons known as free radicals.

To keep track of single-electron movement during homolytic processes, chemists use single-barbed curved arrows (often called fishhook arrows). A standard double-barbed arrow indicates the shift of an electron pair, while a single-barbed fishhook arrow represents the transfer of exactly one electron.

Homolysis: single-electron (fishhook) arrows — Homolytic cleavage sends one electron to each atom, so each arrow carries a single barb rather than a full head. Two chlorine radicals result.

Feature	Homolytic Cleavage	Heterolytic Cleavage
Electron Distribution	Equal split (1 electron to each fragment)	Unequal split (2 electrons to one fragment)
Arrow Type	Single-barbed (fishhook) arrows	Double-barbed standard arrows
Products Formed	Neutral free radicals ( $\ce{A\cdot + B\cdot}$ )	Cation and anion ( $\ce{A^+ + B^-}$ )
Initiation Drivers	Heat ( $\Delta$ ), light ( $h\nu$ ), radical initiators	Polar solvents, acids, bases, electrophiles

Key Definition: Free Radical
A molecular fragment or atom containing one or more unpaired valence electrons. Alkyl radicals are neutral species with

sp^2

hybridization and a trigonal planar geometry containing an unhybridized

p

orbital with a single electron.

Worked Example 1: Single-Electron Arrow Bookkeeping

Question: Write the balanced chemical equation and describe the curved-arrow movement for the thermal homolysis of a chlorine molecule ( $\ce{Cl2}$ ).

Reasoning: When energy is supplied (photons of light $h\nu$ or thermal energy $\Delta$ ), the weak $\ce{Cl-Cl}$ single bond undergoes homolytic scission. One single-barbed arrow originates from the $\ce{Cl-Cl}$ bond center toward the left chlorine atom, and a second single-barbed arrow originates from the same bond toward the right chlorine atom.

Balanced Reaction: $\ce{Cl2 ->[h\nu] 2Cl\cdot}$

DAT Exam Trap: Students often mistakenly draw a single double-barbed arrow for homolysis or forget to balance the atom count on both sides of the radical equation.

Free Radical Chain Mechanism Steps

A classic radical substitution reaction proceeds through a self-sustaining three-stage chain mechanism: initiation, propagation, and termination.

Initiation: Non-radical species are converted into radical intermediates via homolytic bond cleavage. This step creates a net increase in free radicals (0 radicals $\rightarrow$ 2 radicals).
Propagation: A radical reacts with a non-radical molecule to form a product and a new radical species. Propagation steps repeat hundreds or thousands of times because the net count of radicals remains constant (1 radical $\rightarrow$ 1 radical). The sum of all propagation steps gives the net chemical reaction equation.
Termination: Any two radical species collide and combine to form a covalent bond. This step decreases the net count of free radicals (2 radicals $\rightarrow$ 0 radicals) and ends the chain process.

Mnemonic for Radical Chain Phases: IPT
Initiation = Increase radicals (0 → 2)
Propagation = Preserve radicals (1 → 1)
Termination = Truncate radicals (2 → 0)

Worked Example 2: Identifying Chain Mechanism Steps

Question: Classify the following step in alkane chlorination and write the overall net propagation sum: $\ce{\cdot CH3 + Cl2 -> CH3Cl + Cl\cdot}$ .

Reasoning: Notice the radical count: there is 1 radical on the reactant side ( $\ce{\cdot CH3}$ ) and 1 radical on the product side ( $\ce{Cl\cdot}$ ). Because radical count is conserved, this is a propagation step. Combining it with the other propagation step ( $\ce{CH4 + Cl\cdot -> \cdot CH3 + HCl}$ ) yields the overall balanced reaction: $\ce{CH4 + Cl2 -> CH3Cl + HCl}$ .

Peroxide and Light Initiation

Homolytic cleavage usually requires energy because breaking a $\sigma$ -bond homolytically has a significant endothermic bond dissociation energy. Light energy ( $h\nu$ , typically UV) or thermal heat ( $\Delta$ ) provides the energy required to cleave halogen bonds (e.g., $\ce{Cl-Cl}$ or $\ce{Br-Br}$ ).

Alternatively, radical initiators containing weak bonds with low bond dissociation energies are used to start radical reactions at lower temperatures. Dialkyl or diacyl peroxides ( $\ce{ROOR}$ ) contain a weak oxygen-oxygen single bond ( $\approx \pu{150 kJ/mol}$ ) that readily undergoes homolytic cleavage upon mild heating or irradiation.

Azobisisobutyronitrile (AIBN) is another common radical initiator; thermal cleavage releases stable $\ce{N2}$ gas as a thermodynamic driving force, leaving two tertiary cyanoalkyl radicals.

When $\ce{HBr}$ is added to an alkene in the presence of peroxides ( $\ce{ROOR}$ ), the reaction mechanism changes dramatically from an ionic electrophilic addition to a free-radical chain addition, leading to anti-Markovnikov regioselectivity.

In this radical addition mechanism, the alkoxy radical ( $\ce{RO\cdot}$ ) abstracts a hydrogen atom from $\ce{HBr}$ to yield an alcohol ( $\ce{ROH}$ ) and a bromine radical ( $\ce{Br\cdot}$ ). The bromine radical then adds to the alkene double bond first, placing the radical on the more substituted carbon atom to optimize intermediate radical stability. Subsequent hydrogen abstraction from $\ce{HBr}$ yields the anti-Markovnikov alkyl bromide product and regenerates $\ce{Br\cdot}$ . (Note: Carbon radical stability trends and halogen selectivity principles are covered in depth in their dedicated lesson.)

Worked Example 3: Radical Addition of $\ce{HBr}$ with Peroxides

Question: Predict the major organic product when 1-butene reacts with $\ce{HBr}$ in the presence of trace peroxides ( $\ce{ROOR}$ ) and heat.

Reasoning:
1. Peroxide homolysis generates $\ce{RO\cdot}$ , which reacts with $\ce{HBr}$ to produce $\ce{Br\cdot}$ : $\ce{RO\cdot + HBr -> ROH + Br\cdot}$ .
2. $\ce{Br\cdot}$ adds to 1-butene ( $\ce{CH3CH2CH=CH2}$ ). Adding $\ce{Br\cdot}$ to C1 yields a secondary carbon radical ( $\ce{CH3CH2\cdot CH-CH2Br}$ ), which is more stable than adding to C2.
3. The secondary alkyl radical abstracts H from $\ce{HBr}$ : $\ce{CH3CH2\cdot CH-CH2Br + HBr -> CH3CH2CH2CH2Br + Br\cdot}$ .

Product: 1-bromobutane ( $\ce{CH3CH2CH2CH2Br}$ ), the anti-Markovnikov product.

DAT Exam Trap: Peroxide initiation reverses regioselectivity for $\ce{HBr}$ additions only! $\ce{HCl}$ and $\ce{HI}$ do NOT undergo anti-Markovnikov radical addition with peroxides because one of their propagation steps is endothermic and kinetically unfavorable.

Critical Thinking & Application Questions

Why does the presence of a trace radical inhibitor (such as $\ce{O2}$ or hydroquinone) completely halt a radical chain reaction even when UV light is continuously supplied?
In radical halogenation, why does a single initiation event lead to the conversion of thousands of reactant molecules into products before termination occurs?
Explain why adding $\ce{HCl}$ to an alkene in the presence of peroxides still yields the Markovnikov alkyl chloride rather than the anti-Markovnikov product.

References

Sources returned by Google Search grounding during lesson verification.

Free Radical Initiation: Why Is "Light" Or "Heat" Required? — masterorganicchemistry.com
5.5. The Free-Radical Chain Reaction — chem.libretexts.org

Radical Chain Mechanisms

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