How many 5 membered parent chain alkane are possible for `C_7H_16`?

Explanation

To determine how many five-membered parent chain alkanes are possible for the molecular formula \( C_7H_{16} \), we will follow these steps:

### Step 1: Understand the Molecular Formula
The molecular formula \( C_7H_{16} \) indicates that we have 7 carbon atoms and 16 hydrogen atoms. We are specifically looking for alkanes, which are saturated hydrocarbons with the general formula \( C_nH_{2n+2} \).

### Step 2: Identify the Parent Chain
A five-membered parent chain means that we will have a straight chain of 5 carbon atoms. The remaining 2 carbon atoms will be used as substituents (branches) on this chain.

### Step 3: Draw the Five-Carbon Parent Chain
The five-carbon parent chain can be represented as follows:
```
C1 - C2 - C3 - C4 - C5
```
Here, C1 to C5 represent the five carbon atoms in the main chain.

### Step 4: Add the Remaining Carbon Atoms
Since we have 2 additional carbon atoms (from \( C_7 \)), we can attach these to the main chain. The two carbon atoms can be added as substituents in various positions.

### Step 5: Identify Different Isomers
We can systematically consider the different ways to place the two additional carbon atoms:
1. Both carbon atoms as substituents on the same carbon in the chain (e.g., C2).
2. One carbon atom as a substituent on C2 and the other on C3.
3. One carbon atom as a substituent on C3 and the other on C4.
4. Both carbon atoms as substituents on different carbons in the chain.

### Step 6: Count the Unique Structures
After considering the different combinations, we can identify the unique structures:
1. **2,2-Dimethylpentane**
2. **2,3-Dimethylpentane**
3. **2,4-Dimethylpentane**
4. **3,3-Dimethylpentane**
5. **3,4-Dimethylpentane**

### Conclusion
Thus, there are a total of **5 unique five-membered parent chain alkanes** possible for \( C_7H_{16} \).