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 (OH) groups in the unknown compound A with the molecular formula \( C_9H_8O_5 \) based on the information given about its methylation.

### Step-by-step Solution:

1. **Identify the Molecular Weight of Compound A**:
- The molecular formula of compound A is \( C_9H_8O_5 \).
- To calculate the molecular weight (MW) of compound A:
- Carbon (C): \( 9 \times 12 = 108 \)
- Hydrogen (H): \( 8 \times 1 = 8 \)
- Oxygen (O): \( 5 \times 16 = 80 \)
- Total molecular weight of compound A:
\[ MW = 108 + 8 + 80 = 196 \]

2. **Identify the Molecular Weight of the Methyl Derivative**:
- The molecular weight of the methyl derivative formed after methylation is given as 210.

3. **Calculate the Difference in Molecular Weight**:
- The difference in molecular weight between the methyl derivative and compound A:
\[ \Delta MW = 210 - 196 = 14 \]

4. **Determine the Change in Weight Due to Methylation**:
- When a hydroxyl group (OH) is methylated, it is replaced by a methoxy group (OCH3).
- The molecular weight of OH is \( 17 \) (16 for O and 1 for H).
- The molecular weight of OCH3 is \( 31 \) (16 for O and 15 for CH3).
- The change in molecular weight when one OH is replaced by one OCH3:
\[ \text{Change} = 31 - 17 = 14 \]

5. **Conclusion on the Number of Hydroxyl Groups**:
- Since the change in molecular weight (14) corresponds to the replacement of one hydroxyl group with one methoxy group, we can conclude that there is **only one hydroxyl group** in compound A.

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

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