To solve this problem, we need to understand the reaction mechanism of the hydration of alkynes.$\\$The reaction given is: $H_3C-C \equiv CH \xrightarrow[HgSO_4]{H_2O, H_2SO_4}$ Intermediate $A \rightarrow$ Product $B. \\$This is an example of the hydration of an alkyne, specifically acetylene, in the presence of $\\$mercury(II) sulfate and sulfuric acid, which leads to the formation of a ketone.$\\$Step-by-step mechanism:$\\$1. Formation of the enol (Intermediate A):$\\$• The alkyne reacts with water in the presence of $HgSO_4$ and $H_2SO_4. \\$• This leads to the formation of an enol, which is an alcohol with a double bond.$\\$• The enol formed is unstable and quickly tautomerizes to a ketone.$\\$2. Tautomerization to form the ketone (Product B):$\\$• The enol undergoes keto-enol tautomerism, where the hydroxyl group (OH) and the double bond $\\$ rearrange to form a carbonyl group (C=O).$\\$• This results in the formation of acetone, a ketone.$\\$Analyzing the options:$\\$• Option 1: The intermediate is an enol, but the product is incorrect.$\\$• Option 2: The intermediate is a ketone, which is incorrect.$\\$• Option 3: The intermediate is an enol, and the product is a ketone (acetone). This is correct.$\\$• Option 4: The intermediate is incorrect.$\\$Therefore, the correct option is Option 3.$\\$Intermediate A: $H_3C-C(OH)=CH_2 \\$Product B: $H_3C-C(=O)-CH_3 \\$