The number of unbranched isomers (including stereoisomers) of `C_(6)H_(12)` are

Answer

To find the number of unbranched isomers (including stereoisomers) of the molecular formula \( C_6H_{12} \), we can follow these steps:

### Step 1: Identify the Type of Compound
The molecular formula \( C_6H_{12} \) indicates that we are dealing with a hydrocarbon that can be either a cycloalkane or an alkene. In this case, we will focus on alkenes since they can have geometric (cis-trans) isomers.

### Step 2: Draw the Straight-Chain Structure
The simplest straight-chain structure for \( C_6H_{12} \) is hexene. The structure can be represented as:
- **Hexene**: \( CH_3-CH_2-CH_2-CH_2-CH=CH_2 \)

### Step 3: Identify Possible Geometric Isomers
For alkenes, we can have cis and trans isomers. The double bond in hexene can lead to geometric isomers:
- **Cis-hexene**: The two substituents on the double bond are on the same side.
- **Trans-hexene**: The two substituents on the double bond are on opposite sides.

### Step 4: Explore Other Isomeric Structures
We can also create other structural isomers by varying the position of the double bond:
1. **1-Hexene**: \( CH_3-CH_2-CH_2-CH_2-CH=CH_2 \) (no geometric isomer)
2. **2-Hexene**: \( CH_3-CH_2-CH=CH-CH_2-CH_3 \) (has both cis and trans forms)
3. **3-Hexene**: \( CH_3-CH=CH-CH_2-CH_2-CH_3 \) (has both cis and trans forms)

### Step 5: Count the Total Isomers
Now, let's summarize the isomers:
1. **1-Hexene**: 1 isomer
2. **2-Hexene**: 2 isomers (cis and trans)
3. **3-Hexene**: 2 isomers (cis and trans)

Adding these up:
- Total = 1 (from 1-hexene) + 2 (from 2-hexene) + 2 (from 3-hexene) = 5 isomers.

### Conclusion
The total number of unbranched isomers (including stereoisomers) of \( C_6H_{12} \) is **5**.

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