A compound with molecular mass 180 is acylated with `CH_(3)COCl` to get a compound with molecular mass 390. the number of amino groups present per molecule of the former compound is-

Answer

To solve the problem, we need to determine the number of amino groups present in a compound with a molecular mass of 180 after it is acylated with acetic chloride (CH₃COCl) to yield a compound with a molecular mass of 390.

### Step-by-Step Solution:

1. **Identify the Initial and Final Molecular Masses**:
- The initial compound has a molecular mass of 180 g/mol.
- After acylation with CH₃COCl, the final compound has a molecular mass of 390 g/mol.

2. **Calculate the Change in Molecular Mass**:
- The change in molecular mass due to acylation can be calculated as:
\[ \text{Change in mass} = \text{Final mass} - \text{Initial mass} = 390 \, \text{g/mol} - 180 \, \text{g/mol} = 210 \, \text{g/mol} \]

3. **Determine the Mass Increase per Amino Group**:
- When an amino group (NH₂) is acylated, it is converted to an acylated amino group (NHCOCH₃). The mass change for one NH₂ group can be calculated as follows:
- Mass of NH₂ = 14 (N) + 2 (H) = 16 g/mol
- Mass of NHCOCH₃ = 14 (N) + 1 (C) + 3 (H from CH₃) + 16 (O) = 58 g/mol
- Therefore, the increase in mass per acylation is:
\[ \text{Increase} = \text{Mass of NHCOCH₃} - \text{Mass of NH₂} = 58 \, \text{g/mol} - 16 \, \text{g/mol} = 42 \, \text{g/mol} \]

4. **Calculate the Number of Amino Groups**:
- Now, we can find the number of amino groups (n) in the original compound by dividing the total mass increase by the mass increase per amino group:
\[ n = \frac{\text{Total mass increase}}{\text{Mass increase per amino group}} = \frac{210 \, \text{g/mol}}{42 \, \text{g/mol}} = 5 \]

5. **Conclusion**:
- Therefore, the number of amino groups present per molecule of the former compound is **5**.