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

Options

A. 2
B. 5
C. 4
D. 6

Explanation

To solve the problem step by step, we will analyze the information given and perform the necessary calculations.

### Step 1: Understand the Reaction
The compound with a molecular mass of 180 is acylated with CH₃COCl (acetyl chloride). This reaction introduces an acetyl group (−COCH₃) to the amino groups (−NH₂) in the compound.

### Step 2: Determine the Increase in Molecular Mass
After acylation, the molecular mass of the new compound is 390. Therefore, we can calculate the increase in molecular mass due to the reaction:

\[ \text{Increase in mass} = \text{Final mass} - \text{Initial mass} = 390 - 180 = 210 \]

### Step 3: Calculate the Mass Increase per Amino Group
When an amino group (−NH₂) is acylated, it transforms into an amide (−NHCOCH₃). We need to calculate the mass difference between these two groups.

1. **Molecular mass of NH₂**:
- N: 14
- H: 1 × 2 = 2
- Total: 14 + 2 = 16

2. **Molecular mass of NHCOCH₃**:
- N: 14
- H: 3 (from CH₃)
- C: 12 (from CO)
- O: 16
- Total: 14 + 3 + 12 + 16 = 45

3. **Increase in mass per NH₂ unit**:
\[ \text{Increase} = \text{mass of NHCOCH₃} - \text{mass of NH₂} = 45 - 16 = 29 \]

### Step 4: Calculate the Number of Amino Groups
Now, we can find the number of amino groups in the original compound by dividing the total increase in mass by the increase in mass per amino group:

\[ \text{Number of NH₂ groups} = \frac{\text{Total increase in mass}}{\text{Increase in mass per NH₂ unit}} = \frac{210}{29} \]

Calculating this gives:
\[ \text{Number of NH₂ groups} = \frac{210}{29} \approx 7.24 \]

Since the number of amino groups must be a whole number, we round it down to 7.

### Final Answer
The number of amino groups present per molecule of the former compound is **7**.

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