3. Explain the mechanism for the formation of ethane $$ \left(\mathrm{CH}_{3}-\mathrm{CH}_{3}\right) $$ as a by product during chlorination of methane $$ \left(\mathrm{CH}_{4}\right) $$. Show all the steps involved. (10)

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During the chlorination of methane ($$\mathrm{CH}_4$$), ethane ($$\mathrm{CH}_3\text{-CH}_3$$) can form as a byproduct through a free radical mechanism. This process involves three main stages: **Initiation**, **Propagation**, and **Termination**. Below are the detailed steps explaining the formation of ethane:

### 1. Initiation

The reaction begins with the homolytic cleavage of a chlorine ($$\mathrm{Cl}_2$$) molecule to generate two chlorine radicals ($$\mathrm{Cl}^\bullet$$):
$$
\mathrm{Cl}_2 \xrightarrow{\text{heat/light}} 2\, \mathrm{Cl}^\bullet
$$
*This step requires energy (usually UV light) to break the $$\mathrm{Cl-Cl}$$ bond.*

### 2. Propagation

The chlorine radicals initiate a chain reaction by abstracting a hydrogen atom from methane, forming hydrogen chloride (HCl) and a methyl radical ($$\mathrm{CH}_3^\bullet$$):
$$
\mathrm{Cl}^\bullet + \mathrm{CH}_4 \rightarrow \mathrm{HCl} + \mathrm{CH}_3^\bullet
$$

The newly formed methyl radical then reacts with another chlorine molecule to produce chloromethane ($$\mathrm{CH}_3\text{Cl}$$) and regenerates a chlorine radical:
$$
\mathrm{CH}_3^\bullet + \mathrm{Cl}_2 \rightarrow \mathrm{CH}_3\text{Cl} + \mathrm{Cl}^\bullet
$$

*These propagation steps sustain the chain reaction by regenerating chlorine radicals.*

### 3. Termination

Besides forming the primary product ($$\mathrm{CH}_3\text{Cl}$$), side reactions can occur where two methyl radicals combine to form ethane:
$$
\mathrm{CH}_3^\bullet + \mathrm{CH}_3^\bullet \rightarrow \mathrm{CH}_3\text{-CH}_3 \ (\text{Ethane})
$$

Other termination steps include:
$$
\mathrm{CH}_3^\bullet + \mathrm{Cl}^\bullet \rightarrow \mathrm{CH}_3\text{Cl}
$$
$$
\mathrm{Cl}^\bullet + \mathrm{Cl}^\bullet \rightarrow \mathrm{Cl}_2
$$

*These termination steps remove radicals from the reaction mixture, thereby ending the chain reaction.*

### Summary of Ethane Formation

- **Generation of Methyl Radicals:** During the propagation step, methyl radicals ($$\mathrm{CH}_3^\bullet$$) are continuously produced.
- **Combination of Methyl Radicals:** Two methyl radicals can collide and combine to form ethane ($$\mathrm{CH}_3\text{-CH}_3$$) as a side product.

### Overall Reaction Scheme

1. **Initiation:**
   $$
   \mathrm{Cl}_2 \xrightarrow{\text{light}} 2\, \mathrm{Cl}^\bullet
   $$
2. **Propagation:**
   $$
   \mathrm{Cl}^\bullet + \mathrm{CH}_4 \rightarrow \mathrm{HCl} + \mathrm{CH}_3^\bullet
   $$
   $$
   \mathrm{CH}_3^\bullet + \mathrm{Cl}_2 \rightarrow \mathrm{CH}_3\text{Cl} + \mathrm{Cl}^\bullet
   $$
3. **Termination (Ethane Formation):**
   $$
   \mathrm{CH}_3^\bullet + \mathrm{CH}_3^\bullet \rightarrow \mathrm{CH}_3\text{-CH}_3
   $$

Through this mechanism, while the primary product of methane chlorination is chloromethane, ethane is formed as a byproduct via the combination of two methyl radicals during the termination step.
Ethane is formed during methane chlorination when two methyl radicals combine, resulting in the formation of ethane as a byproduct.

3. Explain the mechanism for the formation of ethane \( \left(\mathrm{CH}_{3}-\mathrm{CH}_{3}\right) \) as a by product during chlorination of methane \( \left(\mathrm{CH}_{4}\right) \). Show all the steps involved. (10)

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