To solve this question, we need to identify the reagents (X, Y, Z) used in the transformation of \(C_2H_5Cl\) into different compounds. Let's analyze each part of the reaction scheme:
- X: Transformation to \(C_2H_5F\)
- The conversion of \(C_2H_5Cl\) to \(C_2H_5F\) can be carried out using a fluoride source. The most suitable reagent from the options provided is \(Hg_2F_2\), which facilitates the halogen exchange reaction.
- Y: Transformation to \(CH_2 = CH_2\)
- This step involves dehydrohalogenation of \(C_2H_5Cl\) to form ethylene \((CH_2 = CH_2)\). Alcoholic KOH is commonly used for such elimination reactions.
- Z: Transformation to \(C_4H_{10}\)
- The conversion of \(C_2H_5Cl\) to butane \((C_4H_{10})\) can occur via the Wurtz reaction, involving the coupling of alkyl halides. This reaction uses sodium in dry ether as the reagent.
Based on the above analysis, the correct choice of reagents for X, Y, and Z are \(Hg_2F_2\), alcoholic KOH, and Na in dry ether, respectively.
Conclusion: The correct answer is \(Hg_2F_2\), alcoholic KOH, Na in dry ether.