Chain isomers of `C_7H_(16)` is :

Options

A. 3
B. 4
C. 9
D. 8

Answer

To determine the chain isomers of \( C_7H_{16} \), we will follow a systematic approach to identify the different structural arrangements of the carbon atoms while ensuring the molecular formula remains the same.

### Step-by-Step Solution:

1. **Understanding Chain Isomers**:
- Chain isomers are compounds that have the same molecular formula but differ in the arrangement of carbon atoms in the chain. For \( C_7H_{16} \), we need to find all possible arrangements of 7 carbon atoms.

2. **Longest Chain**:
- Start with the longest chain of 7 carbon atoms (n-heptane).
- Structure:
\[ CH_3-CH_2-CH_2-CH_2-CH_2-CH_2-CH_3 \]
- This is one isomer.

3. **Reducing the Chain**:
- Next, we can reduce the chain length by creating branches. Start with a chain of 6 carbons and add a methyl group (CH₃) to different positions:
- **1-Methylhexane**:
\[ CH_3-CH(CH_3)-CH_2-CH_2-CH_2-CH_3 \]
- **2-Methylhexane**:
\[ CH_3-CH_2-CH(CH_3)-CH_2-CH_2-CH_3 \]
- These give us two more isomers.

4. **Continuing with 5 Carbons**:
- Now, consider a chain of 5 carbons and add two methyl groups:
- **2,2-Dimethylpentane**:
\[ CH_3-C(CH_3)_2-CH_2-CH_2-CH_3 \]
- **2,3-Dimethylpentane**:
\[ CH_3-CH(CH_3)-CH(CH_3)-CH_2-CH_3 \]
- **3,3-Dimethylpentane**:
\[ CH_3-CH_2-C(CH_3)_2-CH_2-CH_3 \]
- **2,4-Dimethylpentane**:
\[ CH_3-CH(CH_3)-CH_2-CH(CH_3)-CH_3 \]

5. **Adding Ethyl Groups**:
- We can also create isomers by adding ethyl groups:
- **3-Ethylpentane**:
\[ CH_3-CH_2-CH(CH_2CH_3)-CH_2-CH_3 \]

6. **Final Count**:
- After systematically going through the possibilities, we find the following isomers:
1. n-Heptane
2. 2-Methylhexane
3. 3-Methylhexane
4. 2,2-Dimethylpentane
5. 2,3-Dimethylpentane
6. 3,3-Dimethylpentane
7. 2,4-Dimethylpentane
8. 3-Ethylpentane
9. 2,2,3-Trimethylbutane

- Thus, we have a total of **9 chain isomers** for \( C_7H_{16} \).

### Conclusion:
The total number of chain isomers for \( C_7H_{16} \) is **9**.