Total number of `2^(@)` amine isomers of `C_(4)H_(11)N` would be (only structural)

Options

A. 4
B. 3
C. 5
D. 2

Answer

To determine the total number of structural isomers of secondary amines for the molecular formula \( C_4H_{11}N \), we can follow these steps:

### Step 1: Identify the Degree of the Amine
We are looking for secondary amines, which have the general structure \( NHR_1R_2 \), where \( R_1 \) and \( R_2 \) are hydrocarbon groups.

### Step 2: Calculate the Double Bond Equivalent (DBE)
The formula for DBE is given by:
\[ \text{DBE} = \frac{(C - H + N + 1)}{2} \]
For \( C_4H_{11}N \):
- Number of Carbon atoms (C) = 4
- Number of Hydrogen atoms (H) = 11
- Number of Nitrogen atoms (N) = 1

Substituting these values into the formula:
\[ \text{DBE} = \frac{(4 - 11 + 1 + 1)}{2} = \frac{-5}{2} = 0 \]
A DBE of 0 indicates that there are no double bonds or rings in the structure.

### Step 3: Construct Possible Isomers
Since we need to create secondary amines, we will consider different combinations of hydrocarbon groups \( R_1 \) and \( R_2 \) while ensuring that the total number of carbon atoms remains 4.

1. **Isomer 1**:
- Let \( R_1 = \text{N-propyl} \) (3 carbons) and \( R_2 = \text{methyl} \) (1 carbon).
- Structure: \( \text{N(CH}_2\text{CH}_2\text{CH}_3)(\text{CH}_3) \)

2. **Isomer 2**:
- Let \( R_1 = \text{isopropyl} \) (3 carbons) and \( R_2 = \text{methyl} \) (1 carbon).
- Structure: \( \text{N(CH}_3\text{CH}(\text{CH}_3))(\text{CH}_3) \)

3. **Isomer 3**:
- Let \( R_1 = \text{ethyl} \) (2 carbons) and \( R_2 = \text{ethyl} \) (2 carbons).
- Structure: \( \text{N(CH}_2\text{CH}_3)(\text{CH}_2\text{CH}_3) \)

### Step 4: Count the Isomers
From the constructions above, we have identified three distinct structural isomers of secondary amines for the formula \( C_4H_{11}N \).

### Conclusion
The total number of structural isomers of secondary amines for \( C_4H_{11}N \) is **3**.

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