Total number of isomers having molecular formula `C_(4)` ` H_(8)`

Options

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

Explanation

To determine the total number of isomers for the molecular formula \( C_4H_8 \), we can follow these steps:

### Step 1: Determine the Degree of Unsaturation
The degree of unsaturation (DU) can be calculated using the formula:
\[ DU = \frac{(2C + 2 + N - H - X)}{2} \]
For \( C_4H_8 \):
- \( C = 4 \)
- \( H = 8 \)
- \( N = 0 \) (no nitrogen)
- \( X = 0 \) (no halogens)

Plugging in the values:
\[ DU = \frac{(2(4) + 2 - 8)}{2} = \frac{(8 + 2 - 8)}{2} = \frac{2}{2} = 1 \]
This indicates that there is one degree of unsaturation, which could be a double bond or a ring.

### Step 2: Identify Possible Structures
Given that we have one degree of unsaturation, we can have:
1. Alkenes (with a double bond)
2. Cycloalkenes (with a ring)

### Step 3: Draw the Isomers
1. **Isobutene (2-methylpropene)**:
\[ CH_2=C(CH_3)CH_3 \]

2. **1-Butene**:
\[ CH_2=CH-CH_2-CH_3 \]

3. **Cyclic structure (Cyclobutene)**:
\[ \text{Cyclobutene: } C_4H_8 \text{ in a ring structure} \]

4. **Cis-2-butene**:
\[ CH_3-CH=CH-CH_3 \text{ (with both methyl groups on the same side)} \]

5. **Trans-2-butene**:
\[ CH_3-CH=CH-CH_3 \text{ (with methyl groups on opposite sides)} \]

### Step 4: Count the Isomers
After drawing the structures, we find the following isomers:
1. Isobutene (2-methylpropene)
2. 1-Butene
3. Cyclobutene
4. Cis-2-butene
5. Trans-2-butene

### Conclusion
Thus, the total number of isomers for the molecular formula \( C_4H_8 \) is **5**.