Final answer:
The formation of ethane as a by-product in the radical bromination of methane occurs when two methyl radicals (•CH₃) produced in the reaction combine. The first step of this mechanism, the initiation stage, involves the homolytic cleavage of molecular bromine into bromine radicals.
Step-by-step explanation:
The question involves the mechanism by which radical bromination of methane can lead to the formation of by-products such as ethane. The first step in this mechanism is the initiation stage, where a homolytic cleavage occurs due to the energy provided by heat or light, producing two bromine radicals (Br•).
The chemical equation for this initiation step can be depicted as:
Br₂ → 2Br•
Each bromine atom now has an unpaired electron. This bromine radical can then abstract a hydrogen atom from methane (CH₄), leading to the formation of methyl radical (•CH₃) and hydrobromic acid (HBr), as shown below:
•Br + CH₄ → •CH₃ + HBr
The methyl radical can then react with another bromine molecule to form methyl bromide (CH₃Br). However, two methyl radicals can also combine to form ethane (C₂H₆) as a side product in the following reaction:
•CH₃ + •CH₃ → C₂H₆