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

Options

A. 2
B. 3
C. 4
D. 6

Explanation

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

### Step 1: Calculate the Degree of Unsaturation
The degree of unsaturation can be calculated using the formula:
\[ \text{Degree of Unsaturation} = \frac{(2C + 2 + N - H - X)}{2} \]
Where:
- \( C \) = number of carbon atoms
- \( H \) = number of hydrogen atoms
- \( N \) = number of nitrogen atoms
- \( X \) = number of halogens (F, Cl, Br, I)

For \( C_4H_8 \):
- \( C = 4 \)
- \( H = 8 \)
- \( N = 0 \)
- \( X = 0 \)

Plugging in the values:
\[ \text{Degree of Unsaturation} = \frac{(2 \times 4 + 2 + 0 - 8 - 0)}{2} = \frac{(8 + 2 - 8)}{2} = \frac{2}{2} = 1 \]
This indicates that there is one degree of unsaturation, which corresponds to one double bond.

### Step 2: Identify Possible Alkene Structures
Since we have one double bond, we can create different structural isomers. The possible structures for \( C_4H_8 \) are:

1. **But-1-ene**:
\[ CH_2=CH-CH_2-CH_3 \]

2. **But-2-ene**: This can exist in two geometric isomers:
- **Cis-But-2-ene**:
\[ CH_3-CH=CH-CH_3 \quad (\text{cis form}) \]
- **Trans-But-2-ene**:
\[ CH_3-CH=CH-CH_3 \quad (\text{trans form}) \]

3. **Isobutylene (2-methylpropene)**:
\[ CH_2=C(CH_3)-CH_3 \]

### Step 3: Count the Isomers
Now, we can summarize the structures:
- But-1-ene
- Cis-But-2-ene
- Trans-But-2-ene
- Isobutylene (2-methylpropene)

Thus, the total number of distinct alkene isomers for \( C_4H_8 \) is **4**.

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

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