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:

We need to find the number of hydroxyl groups in compound X.

Molar mass of compound X: 122 g/mol

Molar mass of acetylated product: 290 g/mol

During acetylation with acetic anhydride, each -OH group is converted to -OCOCH₃. In this process:

Each -OH (mass = 17) is replaced by -OCOCH₃ (mass = 59), so the increase in molar mass per -OH group is:

$$\Delta M = 59 - 17 = 42 \text{ g/mol per OH group}$$

Total increase in molar mass:

$$290 - 122 = 168 \text{ g/mol}$$

Number of OH groups:

$$n = \frac{168}{42} = 4$$

Therefore, the number of hydroxyl groups present in compound X is Option 2: 4.