How many structures are possible for `C_(5)H_(8)` with one triple bond?

Options

A. 4
B. 3
C. 2
D. 1

Explanation

To determine how many structures are possible for the hydrocarbon \( C_5H_8 \) with one triple bond, we can follow these steps:

### Step 1: Calculate the Degree of Unsaturation (DU)
The degree of unsaturation can be calculated using the formula:
\[ DU = \frac{1}{2} \left( 2C + 2 - H \right) \]
where \( C \) is the number of carbon atoms and \( H \) is the number of hydrogen atoms.

For \( C_5H_8 \):
\[ DU = \frac{1}{2} \left( 2 \times 5 + 2 - 8 \right) = \frac{1}{2} \left( 10 + 2 - 8 \right) = \frac{1}{2} \times 4 = 2 \]

### Step 2: Understand the Implications of DU
A degree of unsaturation of 2 indicates that there are either:
- Two double bonds, or
- One triple bond, or
- One double bond and one ring, or
- Two rings.

Since we are looking for structures with one triple bond, we will focus on that.

### Step 3: Identify Possible Structures with One Triple Bond
1. **Structure 1**:
- **Linear structure**: \( CH \equiv C - CH_2 - CH_2 - CH_3 \)
- This structure has the triple bond between the first and second carbon.

2. **Structure 2**:
- **Linear structure**: \( CH_2 - C \equiv C - CH_2 - CH_3 \)
- This structure has the triple bond between the second and third carbon.

3. **Structure 3**:
- **Branched structure**: \( CH_3 - CH_2 - C \equiv C - CH_3 \)
- This structure has the triple bond between the third and fourth carbon.

### Step 4: Check for Identical Structures
- The first and second structures are unique due to the position of the triple bond.
- The third structure is also unique as it has a branched configuration.

### Step 5: Conclusion
After analyzing the structures, we find that there are **three distinct structures** for \( C_5H_8 \) with one triple bond.

### Final Answer
Thus, the number of structures possible for \( C_5H_8 \) with one triple bond is **3**.

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