A compound with molcular formula `C_(4)H_(10)O_(3)`. is converted by the action of acetyl chloride to a compound of molecular mass 190. The original compound `(C_(4)H_(10)O_(3))` has

Answer

To determine the number of -OH groups in the compound with the molecular formula \( C_4H_{10}O_3 \), we can follow these steps:

### Step 1: Calculate the molar mass of the original compound
The molecular formula is \( C_4H_{10}O_3 \). We can calculate the molar mass as follows:
- Carbon (C): 4 atoms × 12 g/mol = 48 g/mol
- Hydrogen (H): 10 atoms × 1 g/mol = 10 g/mol
- Oxygen (O): 3 atoms × 16 g/mol = 48 g/mol

Adding these together:
\[ \text{Molar mass of } C_4H_{10}O_3 = 48 + 10 + 48 = 106 \text{ g/mol} \]

### Step 2: Determine the molar mass of the product
The problem states that the compound is converted to a product with a molecular mass of 190 g/mol.

### Step 3: Calculate the mass difference
To find the mass difference between the product and the original compound:
\[ \text{Mass difference} = \text{Molar mass of product} - \text{Molar mass of original compound} \]
\[ \text{Mass difference} = 190 - 106 = 84 \text{ g/mol} \]

### Step 4: Understand the acetylation reaction
In the acetylation reaction, each -OH group is replaced by an acetyl group (\( CH_3CO \)). The mass of the acetyl group is 43 g/mol, and we lose 1 g/mol for the hydrogen atom from the -OH group. Therefore, the net gain in mass for each -OH group replaced is:
\[ \text{Net gain per -OH group} = 43 - 1 = 42 \text{ g/mol} \]

### Step 5: Calculate the number of -OH groups
To find the number of -OH groups in the original compound, we can divide the total mass difference by the net gain per -OH group:
\[ \text{Number of -OH groups} = \frac{\text{Mass difference}}{\text{Net gain per -OH group}} = \frac{84}{42} = 2 \]

### Conclusion
The original compound \( C_4H_{10}O_3 \) has **2 -OH groups**.

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