Q. A hydroxy compound (X) with molar mass 122 g mol⁻¹ is acetylated with acetic anhydride, using a large excess of the reagent ensuring complete acetylation of all hydroxyl groups. The product obtained has a molar mass of 290 g mol⁻¹. The number of hydroxyl groups present in compound (X) is:
Explanation
Acetylation of one hydroxyl (–OH) group replaces the hydrogen atom by an acetyl group (–COCH₃).
Increase in molar mass per hydroxyl group during acetylation is:
\[
\text{Mass of } (-\mathrm{COCH_3}) - \text{Mass of H} = 43 - 1 = 42 \, \text{g mol}^{-1}
\]
Given molar mass of compound (X):
\[
M_X = 122 \, \text{g mol}^{-1}
\]
Molar mass of acetylated product:
\[
M_{\text{product}} = 290 \, \text{g mol}^{-1}
\]
Increase in molar mass after acetylation:
\[
\Delta M = 290 - 122 = 168 \, \text{g mol}^{-1}
\]
If number of hydroxyl groups is \( n \), then:
\[
42n = 168
\]
\[
n = 4
\]
Therefore, compound (X) contains four hydroxyl groups.