Chlorination of `CH_(4)` involves following steps :
(i) `Cl_(2)rarr2overset(.)(C)l`
(ii) `CH_(4)+overset(.)(C)lrarroverset(.)(C)H_(3)+HCl`
(iii) `overset(.)(C)H_(3)+overset(.)(C)lrarrCH_(3)Cl`
Which of the following is rate determining ?

Options

A. Step (i)
B. Step (ii)
C. Step (iii)
D. Step (ii) & (iii) both

Explanation

To determine the rate-determining step in the chlorination of methane (CH₄), we will analyze the provided steps in detail.

### Step-by-Step Solution:

1. **Identify the Steps of the Reaction:**
- Step (i): \( \text{Cl}_2 \xrightarrow{light} 2 \overset{.}{\text{Cl}} \)
- This is the initiation step where chlorine radicals are formed from chlorine gas in the presence of light.
- Step (ii): \( \text{CH}_4 + \overset{.}{\text{Cl}} \rightarrow \overset{.}{\text{CH}}_3 + \text{HCl} \)
- This is the first propagation step where methane reacts with a chlorine radical to form a methyl radical and hydrochloric acid.
- Step (iii): \( \overset{.}{\text{CH}}_3 + \overset{.}{\text{Cl}} \rightarrow \text{CH}_3\text{Cl} \)
- This is the second propagation step where the methyl radical reacts with another chlorine radical to form chloromethane (CH₃Cl).

2. **Determine the Rate-Determining Step:**
- The rate-determining step is the slowest step in a reaction mechanism that controls the overall rate of the reaction.
- In this case, the first propagation step (Step ii) is generally considered to be the rate-determining step because it involves the formation of the methyl radical, which is an endothermic process.
- The formation of the methyl radical requires significant energy input, leading to a higher activation energy and thus a slower reaction rate.

3. **Conclusion:**
- Based on the analysis, the rate-determining step in the chlorination of methane is Step (ii): \( \text{CH}_4 + \overset{.}{\text{Cl}} \rightarrow \overset{.}{\text{CH}}_3 + \text{HCl} \).

### Final Answer:
The rate-determining step is Step (ii).

---