Free Radical Halogenation of Alkanes

1. Concept: Alkanes undergo substitution reactions with halogens in the presence of ultraviolet light ($$h\nu$$) or high temperature ($$250\text{--}400^\circ\text{C}$$). A hydrogen atom of the alkane is replaced by a halogen atom via a free radical chain mechanism.

2. General Reaction Equation

$$\text{R--H} + \text{X}_2 \xrightarrow{h\nu \text{ or } \Delta} \text{R--X} + \text{HX}$$

3. Reaction Mechanism (3-Step Process)

Step 1: Chain Initiation

Homolytic cleavage: $$\text{X--X} \xrightarrow{h\nu} 2\text{X}\cdot$$

Step 2: Chain Propagation

$$\text{R--H} + \text{X}\cdot \to \text{R}\cdot + \text{HX}$$

$$\text{R}\cdot + \text{X}_2 \to \text{R--X} + \text{X}\cdot$$

Step 3: Chain Termination

$$\text{X}\cdot + \text{X}\cdot \to \text{X}_2$$

$$\text{R}\cdot + \text{R}\cdot \to \text{R--R}$$

$$\text{R}\cdot + \text{X}\cdot \to \text{R--X}$$

4. Reactivity Trends

$$\text{F}_2 > \text{Cl}_2 > \text{Br}_2 > \text{I}_2$$

• $$\text{F}_2$$: Explosive and violent; requires dilution with inert gas ($$\text{N}_2$$).
• $$\text{Cl}_2$$ & $$\text{Br}_2$$: Smooth and useful under laboratory conditions.
• $$\text{I}_2$$: Reversible and extremely slow. Requires an oxidizing agent like $$\text{HNO}_3$$ or $$\text{HIO}_3$$ to consume $$\text{HI}$$ and drive the equilibrium forward.

4. Reactivity Order of Hydrogens ( $$\text{C--H}$$ Bonds)

$$3^\circ > 2^\circ > 1^\circ > \text{CH}_4$$

(Reason: Relative stability of intermediate free radicals due to hyperconjugation and inductive effects)