The total number of structural isomers possible for an amine with molecular formula `C_(4)H_(11)N` is

Options

A. 6
B. 5
C. 7
D. 8

Answer

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

### Step 1: Identify the Degree of Unsaturation
The formula to calculate the degree of unsaturation (DU) is:
\[ DU = \frac{C + 1 - H + X - N}{2} \]
Where:
- \( C \) = number of carbon atoms
- \( H \) = number of hydrogen atoms
- \( X \) = number of halogens (none in this case)
- \( N \) = number of nitrogen atoms

For \( C_4H_{11}N \):
- \( C = 4 \)
- \( H = 11 \)
- \( N = 1 \)

Substituting these values into the formula:
\[ DU = \frac{4 + 1 - 11 - 0 - 1}{2} = \frac{-7}{2} = 0 \]
This indicates that there are no rings or double bonds in the structure.

### Step 2: Classify the Amines
Amines can be classified as:
- Primary amines (1°)
- Secondary amines (2°)
- Tertiary amines (3°)

### Step 3: Determine Structural Isomers for Primary Amines
For primary amines, the general structure is \( RNH_2 \):
1. **Straight-chain structure**:
- Butylamine: \( CH_3(CH_2)_2CH_2NH_2 \) (1 structure)

2. **Branched structures**:
- Isobutylamine: \( (CH_3)_2CHCH_2NH_2 \) (1 structure)
- Sec-butylamine: \( CH_3CH(CH_3)CH_2NH_2 \) (1 structure)
- Tert-butylamine: \( (CH_3)_3CNH_2 \) (1 structure)

Total primary amine structures = 4.

### Step 4: Determine Structural Isomers for Secondary Amines
For secondary amines, the general structure is \( R_2NH \):
1. **Possible combinations**:
- Ethylmethylamine: \( CH_3CH_2NHCH_3 \) (1 structure)
- Dimethylamine: \( (CH_3)_2NH \) (1 structure)
- Isopropylamine: \( (CH_3)CH(CH_2)NH(CH_3) \) (1 structure)

Total secondary amine structures = 3.

### Step 5: Determine Structural Isomers for Tertiary Amines
For tertiary amines, the general structure is \( R_3N \):
1. **Possible combinations**:
- Trimethylamine: \( (CH_3)_3N \) (1 structure)
- Ethylmethylamine: \( CH_3CH_2N(CH_3)CH_3 \) (1 structure)

Total tertiary amine structures = 2.

### Step 6: Calculate Total Isomers
Now, we can sum the total number of structural isomers:
- Primary amines = 4
- Secondary amines = 3
- Tertiary amines = 2

Total structural isomers = \( 4 + 3 + 2 = 9 \).

### Final Answer
The total number of structural isomers possible for an amine with the molecular formula \( C_4H_{11}N \) is **9**.

---