The number of different chain isomers for \( \text{C}_7\text{H}_{16} \) is ______.
Correct Answer: 9
Approach Solution - 1
For a hydrocarbon with the molecular formula \( C_7H_{16} \), which is an alkane, we can determine the possible chain isomers by drawing all unique structures with the same molecular formula.
The chain isomers for \( C_7H_{16} \) are as follows:
Straight Chain (Heptane):
\[ \text{CH}_3 - \text{CH}_2 - \text{CH}_2 - \text{CH}_2 - \text{CH}_2 - \text{CH}_2 - \text{CH}_3 \]
Branched Chains (Various Isomers):
- 2-Methylhexane
- 3-Methylhexane
- 2,2-Dimethylpentane
- 2,3-Dimethylpentane
- 2,4-Dimethylpentane
- 3,3-Dimethylpentane
- 3-Ethylpentane
- 2,2,3-Trimethylbutane
Each of these structures represents a distinct arrangement of carbon atoms, satisfying the molecular formula \( C_7H_{16} \).
Conclusion:
There are a total of 9 different chain isomers for \( C_7H_{16} \).
Approach Solution -2
We are asked to find the number of different chain isomers possible for the molecular formula \( \text{C}_7\text{H}_{16} \).
Step 2: Concept of chain isomerism.
Chain isomerism arises due to different arrangements of the carbon atoms in the main carbon chain. The molecular formula remains the same, but the structure (connectivity of carbon atoms) differs.
For alkanes (\( \text{C}_n\text{H}_{2n+2} \)), the number of chain isomers increases rapidly with the number of carbon atoms because the possibilities for branching increase.
Step 3: Listing all isomers for \( \text{C}_7\text{H}_{16} \).
1. n-Heptane
2. 2-Methylhexane
3. 3-Methylhexane
4. 2,2-Dimethylpentane
5. 2,3-Dimethylpentane
6. 2,4-Dimethylpentane
7. 3,3-Dimethylpentane
8. 3-Ethylpentane
9. 2,2,3-Trimethylbutane
Step 4: Counting unique structures.
The total number of unique chain isomers formed = 9.
Step 5: Final Answer.
\[ \boxed{9} \] Hence, there are 9 different chain isomers possible for \( \text{C}_7\text{H}_{16} \).
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