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 step by step, we will analyze the information provided about the unknown compound \( A \) with the molecular formula \( C_8H_{10}O_3 \).

### Step 1: Calculate the Molecular Weight of Compound A
The molecular formula of compound \( A \) is \( C_8H_{10}O_3 \). We can calculate its molecular weight as follows:

\[ \text{Molecular Weight} = (12 \times 8) + (1 \times 10) + (16 \times 3) \]
\[ = 96 + 10 + 48 = 154 \]

**Hint:** Remember to multiply the number of each type of atom by its atomic weight and sum them up.

### Step 2: Determine the Increase in Molecular Weight After Acetylation
When compound \( A \) undergoes acetylation with \( CH_3COCl \), it forms an acetyl derivative with a molecular weight of 280. The increase in molecular weight due to the acetylation can be calculated as:

\[ \text{Increase in Molecular Weight} = 280 - 154 = 126 \]

**Hint:** Subtract the original molecular weight from the new molecular weight to find the increase.

### Step 3: Calculate the Number of Acetyl Groups Introduced
Each acetyl group contributes an increase of 42 units to the molecular weight (as calculated from the acetylation process). Therefore, the number of acetyl groups introduced can be calculated as:

\[ \text{Number of Acetyl Groups} = \frac{126}{42} = 3 \]

**Hint:** Divide the total increase in molecular weight by the increase per acetyl group to find how many groups were added.

### Step 4: Relate the Number of Hydroxyl Groups to the Acetyl Groups
The acetylation can occur on both phenolic and alcoholic hydroxyl groups. Since we found that a total of 3 acetyl groups were introduced, we can conclude that the total number of hydroxyl groups (both phenolic and alcoholic) in compound \( A \) is also 3.

Let \( X \) be the number of phenolic hydroxyls and \( Y \) be the number of alcoholic hydroxyls. Thus, we have:

\[ X + Y = 3 \]

**Hint:** The total number of hydroxyl groups that can be acetylated equals the number of acetyl groups introduced.

### Step 5: Conclusion
The sum of \( X \) (phenolic hydroxyls) and \( Y \) (alcoholic hydroxyls) is:

\[ X + Y = 3 \]

Thus, the answer to the question is:

\[ \boxed{3} \]