Unknown compound A `C_9H_8O_5` on methylation with `(CH_3)SO_4//NaOH` forms methyl derivative whose MW is 210. The number of hydroxyl groups is A is

Options

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

Answer

To solve the problem, we need to determine the number of hydroxyl groups in the unknown compound A with the molecular formula \( C_9H_8O_5 \) based on the information provided about its methylation and the molecular weight of the resulting derivative.

### Step-by-Step Solution:

1. **Identify the Molecular Weight of Compound A**:
- The molecular formula of compound A is \( C_9H_8O_5 \).
- Calculate the molecular weight (MW) of compound A:
\[ \text{MW} = (9 \times 12) + (8 \times 1) + (5 \times 16) = 108 + 8 + 80 = 196 \]

2. **Determine the Molecular Weight of the Methyl Derivative**:
- The methyl derivative formed after methylation has a molecular weight of 210.

3. **Calculate the Change in Molecular Weight**:
- The change in molecular weight due to methylation is:
\[ \text{Change} = 210 - 196 = 14 \]

4. **Understand the Methylation Process**:
- Methylation occurs at hydroxyl groups (–OH). When an –OH group is converted to an –OCH₃ group, the change in molecular weight can be calculated as follows:
- The molecular weight of an –OH group is 17 (16 for oxygen + 1 for hydrogen).
- The molecular weight of an –OCH₃ group is 15 (12 for carbon + 3 for hydrogen).
- Therefore, the change in molecular weight when one –OH is converted to –OCH₃ is:
\[ \text{Change} = 15 - 17 = -2 \]
- However, since we are adding a methyl group and removing a hydrogen, the overall change in molecular weight is:
\[ \text{Change} = 15 - 1 = 14 \]

5. **Determine the Number of Hydroxyl Groups**:
- Since the change in molecular weight is 14, and we know that each hydroxyl group contributes to a change of 14 when methylated, we can conclude that there is only one hydroxyl group in compound A.
- Therefore, the number of hydroxyl groups in compound A is 1.

### Final Answer:
The number of hydroxyl groups in compound A is **1**.