Give the number alcohol of isomer of `C_4H_9OH`

Options

A. 2
B. 3
C. 4
D. 5

Explanation

To determine the number of isomers of the alcohol with the molecular formula \( C_4H_9OH \), we can follow these steps:

### Step 1: Understand the Molecular Formula
The molecular formula \( C_4H_9OH \) can be rewritten as \( C_4H_{10}O \). This indicates that we have 4 carbon atoms, 10 hydrogen atoms, and 1 oxygen atom.

### Step 2: Calculate the Degree of Unsaturation
The degree of unsaturation (or double bond equivalence) can be calculated using the formula:
\[ \text{DBE} = \frac{(2C + 2 - H)}{2} \]
Where \( C \) is the number of carbon atoms and \( H \) is the number of hydrogen atoms.
For \( C_4H_{10}O \):
- \( C = 4 \)
- \( H = 10 \)

Calculating DBE:
\[ \text{DBE} = \frac{(2 \times 4 + 2 - 10)}{2} = \frac{(8 + 2 - 10)}{2} = \frac{0}{2} = 0 \]
This indicates that there are no double bonds or rings in the structure, meaning it is a saturated alcohol.

### Step 3: Identify Possible Alcohol Structures
Since we have a saturated alcohol, we can identify the possible structural isomers by varying the position of the hydroxyl group (-OH) and the arrangement of carbon atoms.

1. **1-Butanol**: The hydroxyl group is on the first carbon.
\[ CH_3-CH_2-CH_2-CH_2OH \]

2. **2-Butanol**: The hydroxyl group is on the second carbon.
\[ CH_3-CH(OH)-CH_2-CH_3 \]

3. **Tertiary Alcohol (2-Methyl-2-Propanol)**: The hydroxyl group is on a carbon that is bonded to three other carbon atoms.
\[ (CH_3)_3C-OH \]

4. **Isobutanol (2-Methyl-1-Propanol)**: The hydroxyl group is on the end carbon of a branched chain.
\[ CH_3-CH(CH_3)-CH_2OH \]

### Step 4: Count the Isomers
From the structures identified, we have:
1. 1-Butanol
2. 2-Butanol
3. 2-Methyl-2-Propanol (Tertiary)
4. 2-Methyl-1-Propanol (Isobutanol)

Thus, there are a total of **4 isomers** of \( C_4H_9OH \).

### Conclusion
The number of isomers of alcohol \( C_4H_9OH \) is **4**.

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