Step 1: Understanding the Question:
The question asks us to identify the major organic product R after a sequence of three reactions starting with acetylene.
Step 2: Key Formula or Approach:
1. Cyclic polymerization: Passing acetylene through a red-hot iron tube at $873\ \text{K}$ causes trimerization to form benzene.
2. Electrophilic chlorination: Benzene reacts with $\text{Cl}_2/\text{AlCl}_3$ to produce chlorobenzene.
3. Wurtz-Fittig reaction: Reaction of an aryl halide and an alkyl/arylalkyl halide with sodium metal leads to a coupling product.
Step 3: Detailed Explanation:
• Step 1: When acetylene gas ($\text{HC}\equiv\text{CH}$) is passed through a red-hot iron tube at $873\ \text{K}$, it undergoes cyclic trimerization to form benzene as product P:
\[ 3\ \text{C}_2\text{H}_2 \xrightarrow{\text{Fe, } 873\text{ K}} \text{C}_6\text{H}_6 \text{ (Benzene)} \]
• Step 2: Benzene (P) undergoes electrophilic aromatic substitution when treated with chlorine gas ($\text{Cl}_2$) in the presence of anhydrous aluminium chloride ($\text{AlCl}_3$). This produces chlorobenzene as product Q:
\[ \text{C}_6\text{H}_6 + \text{Cl}_2 \xrightarrow{\text{AlCl}_3} \text{C}_6\text{H}_5\text{Cl} + \text{HCl} \]
• Step 3: Chlorobenzene (Q) is mixed with benzyl chloride ($\text{C}_6\text{H}_5\text{CH}_2\text{Cl}$) and treated with sodium metal (Na).
• This is a classic Wurtz-Fittig reaction.
• The sodium metal acts as a reducing agent, transferring electrons to the carbon-chlorine bonds to form highly reactive radical or carbanion intermediates from both chlorobenzene and benzyl chloride.
• These intermediates couple together to form a new carbon-carbon single bond:
\[ \text{C}_6\text{H}_5\text{-Cl} + 2\text{Na} + \text{Cl-CH}_2\text{-C}_6\text{H}_5 \rightarrow \text{C}_6\text{H}_5\text{-CH}_2\text{-C}_6\text{H}_5 + 2\text{NaCl} \]
• The coupled product consists of a central methylene group ($\text{-CH}_2-$) bonded to two phenyl rings, which is diphenylmethane (R).
Step 4: Final Answer:
Therefore, the major product R is diphenylmethane (Option A).