A compound with molecular formula `C_(6)H_(10)O_(4)` on acylation with acetic anhydride gives a compound with molecular formula `C_(12)H_(18)O_(8)`. How many hydroxyl groups are present in the compound?

Options

A. one
B. two
C. three
D. four

Answer

To determine the number of hydroxyl groups present in the compound with the molecular formula \( C_6H_{10}O_4 \), we will analyze the acylation reaction that occurs when it reacts with acetic anhydride.

### Step-by-Step Solution:

1. **Identify the Initial Compound**:
The initial compound has the molecular formula \( C_6H_{10}O_4 \).

2. **Understand Acylation**:
Acylation with acetic anhydride (\( CH_3CO_2O \)) involves the replacement of a hydrogen atom from the hydroxyl group (-OH) with an acetyl group (\( CH_3CO \)).

3. **Determine the Change in Molecular Formula**:
During the acylation process, the molecular formula changes as follows:
- The hydroxyl group (-OH) contributes \( H \) and \( O \).
- When acylated, the hydrogen from -OH is replaced by an acetyl group, resulting in the loss of one hydrogen atom and the addition of an acetyl group.
- Therefore, the change in molecular formula can be represented as:
\[ \text{Change} = C_2H_2O \]
This means that for each hydroxyl group that undergoes acylation, the molecular formula increases by \( C_2H_2O \).

4. **Calculate the Change in Molecular Formula**:
The final compound after acylation has the molecular formula \( C_{12}H_{18}O_8 \). We can find the difference in molecular formulas:
\[ C_{12}H_{18}O_8 - C_{6}H_{10}O_{4} = C_{6}H_{8}O_{4} \]

5. **Relate the Change to Hydroxyl Groups**:
Since the change in molecular formula is \( C_6H_8O_4 \), we can analyze how many hydroxyl groups contributed to this change:
- Each hydroxyl group contributes \( C_2H_2O \) upon acylation.
- To find the number of hydroxyl groups (\( n \)), we can set up the equation:
\[ n \times C_2H_2O = C_6H_8O_4 \]
- This can be broken down into:
- Carbon: \( 2n = 6 \) → \( n = 3 \)
- Hydrogen: \( 2n = 8 \) → \( n = 4 \)
- Oxygen: \( n = 4 \)
- The consistent value across all calculations indicates that there are **4 hydroxyl groups** in the compound.

### Conclusion:
The number of hydroxyl groups present in the compound \( C_6H_{10}O_4 \) is **4**.