Alcohols, Phenols and Ethers Part 2

Concept:Acetylation of a hydroxyl group ($-\mathrm{OH}$) replaces it with an acetyl group ($-\mathrm{OCOCH}_3$), causing a fixed increase in molar mass of $42\ \mathrm{g\ mol}^{-1}$ per $-\mathrm{OH}$ group.Explanation:Let the number of hydroxyl groups in compound $X$ be $n$.Molar mass of $X$ is $122\ \mathrm{g\ mol}^{-1}$.After complete acetylation, the product has molar mass $290\ \mathrm{g\ mol}^{-1}$.The total increase in molar mass is $290 - 122 = 168\ \mathrm{g\ mol}^{-1}$.Each $-\mathrm{OH}$ group (mass $17\ \mathrm{g\ mol}^{-1}$) is converted to $-\mathrm{OCOCH}_3$ (mass $59\ \mathrm{g\ mol}^{-1}$), giving an increase of $59 - 17 = 42\ \mathrm{g\ mol}^{-1}$ per group.Therefore, $n = \frac{168}{42} = 4$.Answer:The number of hydroxyl groups is $4$, which corresponds to option B.