An unknown compound `AC_(8)H_(10)O_(3)` on acetylation with `CH_(3)COCl//Py` forms acetyl derivative of A whose MW is 280. A on treat with `CH_(2)N_(2)` gives methyl etherof B having MW 182. If the number of phenolic hydroxyls and alcoholic hydroxyls in the compound A are X and Y respectively. Find the sum of `X+Y` here?,

Answer

To solve the problem, we need to analyze the unknown compound \( A \) with the molecular formula \( C_8H_{10}O_3 \) and determine the number of phenolic hydroxyls (denoted as \( X \)) and alcoholic hydroxyls (denoted as \( Y \)). We will then find the sum \( X + Y \).

### Step 1: Determine the number of hydroxyl groups in compound A using acetylation

1. **Acetylation Reaction**: When \( A \) is acetylated with \( CH_3COCl \) in the presence of pyridine, it forms an acetyl derivative with a molecular weight of 280.
2. **Molecular Weight of Acetyl Derivative**: The molecular weight of the acetyl derivative is given as 280.
3. **Molecular Weight of Compound A**: The molecular weight of compound \( A \) is 154 (calculated from \( C_8H_{10}O_3 \)).
4. **Formula for Hydroxyl Groups**: The number of hydroxyl groups can be calculated using the formula:
\[ \text{Number of hydroxyl groups} = \frac{(\text{Molecular weight of acetyl derivative} - \text{Molecular weight of compound A})}{42} \]
Here, 42 is the molecular weight of the acetyl group (C2H3O).

5. **Calculation**:
\[ \text{Number of hydroxyl groups} = \frac{(280 - 154)}{42} = \frac{126}{42} = 3 \]
Therefore, the total number of hydroxyl groups in compound \( A \) is 3.

### Step 2: Determine the number of phenolic and alcoholic hydroxyl groups

1. **Treatment with \( CH_2N_2 \)**: When \( A \) is treated with \( CH_2N_2 \), it forms a methyl ether \( B \) with a molecular weight of 182.
2. **Molecular Weight of Methyl Ether**: The molecular weight of the methyl ether \( B \) is given as 182.
3. **Formula for Hydroxyl Groups**: The number of alcoholic hydroxyl groups can be calculated using the formula:
\[ \text{Number of alcoholic hydroxyl groups} = \frac{(\text{Molecular weight of methyl ether} - \text{Molecular weight of compound A})}{14} \]
Here, 14 is the molecular weight of the \( CH_2 \) group introduced during the reaction.

4. **Calculation**:
\[ \text{Number of alcoholic hydroxyl groups} = \frac{(182 - 154)}{14} = \frac{28}{14} = 2 \]
Therefore, the number of alcoholic hydroxyl groups is 2.

### Step 3: Determine \( X \) and \( Y \)

1. **Total Hydroxyl Groups**: We found that the total number of hydroxyl groups is 3.
2. **Phenolic Hydroxyl Groups**: Since the number of alcoholic hydroxyl groups \( Y \) is 2, we can find the number of phenolic hydroxyl groups \( X \):
\[ X + Y = 3 \quad \text{and} \quad Y = 2 \]
\[ X = 3 - 2 = 1 \]

### Step 4: Calculate \( X + Y \)

Now we can find the sum \( X + Y \):
\[ X + Y = 1 + 2 = 3 \]

### Final Answer
The sum of \( X + Y \) is **3**.