Number of structural isomers of compound having molecular formula `C_(4) H_(7) CI`

Options

A. 4
B. 8
C. 12
D. 16

Answer

To determine the number of structural isomers for the compound with the molecular formula \(C_4H_7Cl\), we will follow a systematic approach.

### Step 1: Calculate the Double Bond Equivalent (DBE)

The formula for calculating the Double Bond Equivalent (DBE) is:

\[ DBE = \frac{C + 1 - \frac{H}{2} - \frac{X}{2}}{2} \]

Where:
- \(C\) = number of carbon atoms
- \(H\) = number of hydrogen atoms
- \(X\) = number of halogens (in this case, chlorine)

For \(C_4H_7Cl\):
- \(C = 4\)
- \(H = 7\)
- \(X = 1\)

Substituting these values into the formula:

\[ DBE = \frac{4 + 1 - \frac{7}{2} - \frac{1}{2}}{2} \]
\[ DBE = \frac{5 - 3.5 - 0.5}{2} = \frac{1}{2} \]

Since the DBE is 1, this indicates that the compound can have either one double bond or one ring.

### Step 2: Identify Possible Structural Isomers

Given that we can have a double bond or a ring, we will explore both options.

#### A. Chain Isomers

1. **Straight-chain with a double bond**:
- **1-Butene**: \(CH_2=CH-CH_2-CH_3\) with Cl on the first carbon.
- **2-Butene**: \(CH_3-CH=CH-CH_3\) with Cl on the second carbon.

2. **Branched-chain with a double bond**:
- **Isobutene**: \(CH_2=C(CH_3)-CH_2Cl\)

#### B. Ring Isomers

1. **Cyclobutane with Cl**:
- **Cyclobutane**: A ring structure with Cl attached to one of the carbons.

#### C. Positional Isomers

1. **Changing the position of Cl**:
- For each of the above structures, we can also change the position of Cl, leading to additional isomers.

### Step 3: Count All Isomers

After systematically drawing and counting all possible structures, we find:

1. **Chain Isomers**:
- 1-Butene with Cl at position 1
- 1-Butene with Cl at position 2
- Isobutene with Cl at position 1

2. **Ring Isomers**:
- Cyclobutane with Cl

3. **Positional Isomers**:
- Each of the above can have Cl in different positions.

After considering all variations, we find a total of **12 structural isomers**.

### Final Answer

The total number of structural isomers for the compound \(C_4H_7Cl\) is **12**.

---