Match Organic Chemical Conversions with Suitable Reagent Sets

To determine the correct matching between the chemical transformations in List I and the reagent sets in List II, let us analyze each reaction individually:

1. Transformation P: $\text{Tertiary alkyl chloride } \big(\text{(CH}_3\text{)}_3\text{C-Cl}\big) \longrightarrow \text{Alkene } \big(\text{(CH}_3\text{)}_2\text{C=CH}_2\big)$ This transformation is an elimination reaction ($E2$) of a $3^\circ$ alkyl halide to yield an alkene. This requires a strong base such as sodium ethoxide ($\text{NaOEt}$). $\text{P} \rightarrow 2$

2. Transformation Q: $\text{Alkoxide } \big(\text{(CH}_3\text{)}_3\text{C-O}^-\text{Na}^+\big) \longrightarrow \text{Ether } \big(\text{(CH}_3\text{)}_3\text{C-O-Et}\big)$ This is the Williamson Ether Synthesis, where a nucleophilic alkoxide undergoes an $S_N2$ reaction with a primary alkyl halide such as ethyl bromide ($\text{Et-Br}$). $\text{Q} \rightarrow 3$

3. Transformation R: $\text{1-methylcyclopentene} \longrightarrow \text{1-methylcyclopentanol}$ This reaction represents the addition of water across the double bond following Markovnikov's rule without carbocation rearrangement. The suitable reagent set for oxymercuration-demercuration is: $\text{(i) } \text{Hg(OAc)}_2, \quad \text{(ii) } \text{NaBH}_4$ $\text{R} \rightarrow 1$

4. Transformation S: $\text{1-methylcyclopentene} \longrightarrow \textit{trans}\text{-2-methylcyclopentanol}$ This conversion represents an anti-Markovnikov addition of water with syn-stereospecificity to give the trans alcohol. The appropriate process for this transformation is Hydroboration-Oxidation, utilizing: $\text{(i) } \text{BH}_3, \quad \text{(ii) } \text{H}_2\text{O}_2/\text{NaOH}$ $\text{S} \rightarrow 4$

Comparing these matches with the given options: $\text{P} \rightarrow 2, \quad \text{Q} \rightarrow 3, \quad \text{R} \rightarrow 1, \quad \text{S} \rightarrow 4$

Thus, the correct option is A.