How many alkenes are possible with molecular formula `C_(4)H_(8)`?

Options

A. (a)2
B. (b)3
C. (c )4
D. (d)6

Explanation

To determine how many alkenes are possible with the molecular formula \( C_4H_8 \), we will follow these steps:

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

For \( C_4H_8 \):
- \( C = 4 \)
- \( H = 8 \)

Substituting the values:
\[ DU = \frac{(2 \times 4 + 2 - 8)}{2} = \frac{(8 + 2 - 8)}{2} = \frac{2}{2} = 1 \]

### Step 2: Identify Possible Structures
A DU of 1 indicates that there is one double bond in the structure. We can have different structural isomers based on the position of the double bond and the arrangement of carbon atoms.

1. **But-1-ene**:
- Structure: \( CH_3-CH_2-CH=CH_2 \)

2. **But-2-ene**:
- Structure: \( CH_3-CH=CH-CH_3 \)
- This can exist in two geometric isomers:
- **Cis-but-2-ene**: \( CH_3 \) groups on the same side.
- **Trans-but-2-ene**: \( CH_3 \) groups on opposite sides.

3. **Cyclobutene**:
- Structure: A four-membered ring with one double bond.

### Step 3: Count the Isomers
From the structures identified:
- **But-1-ene**: 1 isomer
- **But-2-ene**: 2 isomers (cis and trans)
- **Cyclobutene**: 1 isomer

Adding these together:
\[ 1 \text{ (But-1-ene)} + 2 \text{ (But-2-ene)} + 1 \text{ (Cyclobutene)} = 4 \text{ isomers} \]

### Final Answer
Thus, the total number of alkenes possible with the molecular formula \( C_4H_8 \) is **4**.

---