DAT Organic Chemistry: Radical Stability

DAT High-Yield Concept

Radical Stability Hierarchy: Benzylic ≈ allylic > tertiary (3°) > secondary (2°) > primary (1°) > methyl > vinylic/aryl.
Formation at Most Substituted Carbon: Hydrogen abstraction occurs fastest at the most substituted carbon to produce the most stable radical intermediate.
Absence of Rearrangement: Free radicals do not undergo 1,2-hydride or 1,2-alkyl shifts, distinguishing them fundamentally from carbocations on the DAT.

Radical Stability Order and Electronic Stabilization

Free radicals are neutral, electron-deficient chemical species bearing an unpaired electron in an $sp^2$ -hybridized, unhybridized $p$ orbital with approximately $120^ \circ$ bond angles. Containing 7 valence electrons, radicals are stabilized by factors that donate electron density into the half-filled $p$ orbital.

The relative stability hierarchy of alkyl and resonance-stabilized radicals follows the order:

$\ce{benzylic}$ ≈ $\ce{allylic}$ > $\ce{3^ \circ}$ > $\ce{2^ \circ}$ > $\ce{1^ \circ}$ > $\ce{CH3^\bullet}$ > $\ce{vinylic/aryl}$

Radical stability: tertiary > secondary > primary > methyl — Left to right: methyl, primary, secondary, tertiary — stability rises with each added alkyl group, which donates electron density into the half-filled orbital through hyperconjugation, the same order that stabilizes carbocations. Bromine's preference for the most substituted position follows directly from this ladder.

Alkyl groups stabilize radical centers primarily through hyperconjugation—the delocalization of electron density from adjacent $\sigma$ bonds ( $\ce{C-H}$ or $\ce{C-C}$ ) into the singly occupied $p$ orbital. Consequently, tertiary radicals possess the greatest number of hyperconjugative interactions among un-conjugated alkyl radicals.

Resonance stabilization further enhances stability when the radical center is adjacent to a $\pi$ system (allylic or benzylic). Allylic and benzylic radicals delocalize the unpaired electron across multiple carbon atoms via $\pi$ -overlap. (Reagents like N-bromosuccinimide selectively functionalize these positions, covered in depth in its own lesson).

Key Concept: Electronic Effects in Radicals
Alkyl substitution donates electron density through hyperconjugation, while adjacent

\pi

systems delocalize the unpaired electron through resonance. Vinylic and aryl radicals hold the unpaired electron in an

sp^2

sp

hybrid orbital, holding it closer to the nucleus and rendering them extremely unstable.

Radical Formation at the Most Substituted Carbon

In radical substitution and addition reactions, hydrogen abstraction or radical addition preferentially proceeds through the transition state that generates the most stable radical intermediate. Because C-H bond dissociation energy (BDE) decreases as carbon substitution increases, abstracting a hydrogen atom from a tertiary carbon requires less energy than from a secondary or primary carbon.

Worked Example: Regioselective Bromination

Starting Material: Reaction of 2-methylbutane with $\ce{Br2}$ in the presence of light ( $h\nu$ ).

Reasoning: 2-Methylbutane contains primary, secondary, and tertiary hydrogen atoms. In the propagation step, bromine radical abstraction can occur at any position:

$\ce{(CH3)2CHCH2CH3 + Br^\bullet -> (CH3)2\dot{C}CH2CH3 + HBr}$

Abstraction at C2 generates a $3^\circ$ radical, which is significantly lower in energy than the alternative $2^\circ$ or $1^\circ$ radicals. Because bromination is endothermic in the hydrogen abstraction step, the transition state resembles the radical intermediate (Hammond Postulate), conferring high regioselectivity for the most substituted carbon.

Product: 2-bromo-2-methylbutane (>99% yield).

Common DAT Exam Trap: Assuming radical chlorination yields the same regioselectivity as bromination. Chlorination is exothermic with an early transition state, making $\ce{Cl^\bullet}$ unselective and yielding a complex mixture of regioisomers.

Absence of Radical Rearrangement

A critical distinction tested on the DAT between carbocation and radical intermediates is rearrangement behavior. Unlike carbocations, free radicals do not undergo 1,2-hydride or 1,2-alkyl shifts under standard organic reaction conditions due to the high activation barrier required for a radical 1,2-shift.

Worked Example: Radical Addition without Rearrangement

Starting Material: Reaction of 3,3-dimethyl-1-butene with $\ce{HBr}$ and peroxides ( $\ce{ROOR}$ ).

Reasoning: Initiation generates a bromine radical ( $\ce{Br^\bullet}$ ). Addition of $\ce{Br^\bullet}$ to the terminal C1 position generates a secondary radical at C2:

$\ce{(CH3)3C-CH=CH2 + Br^\bullet -> (CH3)3C-\dot{C}H-CH2Br}$

Although C3 is a quaternary carbon adjacent to the radical center, no 1,2-methyl shift occurs. The secondary radical directly abstracts a hydrogen atom from $\ce{HBr}$ in the next propagation step:

$\ce{(CH3)3C-\dot{C}H-CH2Br + HBr -> (CH3)3C-CH2-CH2Br + Br^\bullet}$

Product: 1-bromo-3,3-dimethylbutane (anti-Markovnikov addition).

Common DAT Exam Trap: Predicting a rearranged product (such as 2-bromo-2,3-dimethylbutane) due to carbocation habituation. Remember: radicals lock in place at the carbon where they are initially generated.

Comparing Intermediate Pathways

Property	Free Radicals	Carbocations
Valence Electrons	7 (Unpaired electron)	6 (Empty $p$ orbital)
Stability Trend	Benzylic ≈ Allylic > 3° > 2° > 1° > Methyl	Benzylic ≈ Allylic > 3° > 2° > 1° > Methyl
1,2-Rearrangements	No (Absence of 1,2-shifts)	Yes (Readily undergoes 1,2-hydride/alkyl shifts)
DAT Regioselective Reactions	Radical bromination, Peroxide $\ce{HBr}$ addition	$\text{S}_\text{N}1$ , $\text{E}1$ , Electrophilic addition of $\ce{HX}$

DAT Mnemonic: RADICALS
Resonance And Degree Increase Center Always, Lacks Shifts!
(Resonance and higher substitution increase radical stability; radicals never undergo 1,2-shifts.)

Critical Thinking Questions

Why is a vinylic radical ( $\ce{H2C=CH^\bullet}$ ) significantly less stable than a primary alkyl radical ( $\ce{CH3CH2^\bullet}$ )?
When ethylbenzene is treated with $\ce{Br2}$ under light, abstraction occurs exclusively at the benzylic carbon rather than the primary methyl carbon. What electronic effect accounts for this complete regioselectivity?
Predict the product formed when 3-methyl-1-butene is treated with (a) $\ce{HBr}$ alone vs. (b) $\ce{HBr}$ with $\ce{ROOR}$ . Why do their carbon skeletons differ or remain identical?

References

Sources returned by Google Search grounding during lesson verification.

3 Factors That Stabilize Free Radicals - Master Organic Chemistry — masterorganicchemistry.com
Radical Stability | Wizeprep — wizeprep.com

Radical Stability

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