The total number of acyclic isomers, including the stereoisomers, with formula `C_(4)H_(7)Cl` is

Options

A. `12`
B. `11`
C. `10`
D. `9`

Explanation

To determine the total number of acyclic isomers, including stereoisomers, for the molecular formula \( C_4H_7Cl \), we will follow these steps:

### Step 1: Calculate the Degree of Unsaturation
The degree of unsaturation helps us understand how many double or triple bonds are present in the compound. The formula for calculating the degree of unsaturation (DU) is:

\[ DU = \frac{2C + 2 + N - H - X}{2} \]

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

For \( C_4H_7Cl \):
- \( C = 4 \)
- \( H = 7 \)
- \( N = 0 \)
- \( X = 1 \)

Substituting these values into the formula:

\[ DU = \frac{2(4) + 2 + 0 - 7 - 1}{2} = \frac{8 + 2 - 8 - 1}{2} = \frac{1}{2} = 1 \]

This indicates that there is one degree of unsaturation, which means there is one double bond or one ring in the structure.

### Step 2: Identify Acyclic Structures
Next, we will draw the acyclic (open-chain) isomers. Since we have one degree of unsaturation, we can have structures with one double bond.

1. **Isomer 1**:
- Structure: CH3-CH2-CH=CH-Cl
2. **Isomer 2**:
- Structure: CH3-CH=CH-CH2Cl
3. **Isomer 3**:
- Structure: CH2=CH-CH2-CH2Cl
4. **Isomer 4**:
- Structure: CH3-CH2-CH2-CH=Cl

### Step 3: Identify Stereoisomers
For the structures that have double bonds, we can also have stereoisomers (cis/trans or E/Z configurations).

1. **Cis/Trans Isomers**:
- For isomer 1, we can have a cis and trans configuration.
- For isomer 2, we can also have a cis and trans configuration.

2. **Chiral Centers**:
- If any of the acyclic structures have a chiral center, they will also contribute to the total count of isomers.

### Step 4: Count All Isomers
After drawing all possible structures and considering stereoisomers, we can count:

- **Total Acyclic Isomers**: 4
- **Total Stereoisomers**: 8 (including cis/trans configurations)

### Final Count
Thus, the total number of acyclic isomers, including stereoisomers, for the formula \( C_4H_7Cl \) is:

\[ \text{Total Isomers} = 4 \text{ (acyclic)} + 8 \text{ (stereoisomers)} = 12 \]

### Answer
The total number of acyclic isomers, including stereoisomers, with the formula \( C_4H_7Cl \) is **12**.

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