How many different alcohol (not including optical isomers) are possible with the molecular formula : `C_(4)H_(10)O`?

Options

A. 3
B. 4
C. 5
D. 6

Answer

To determine how many different alcohols (not including optical isomers) are possible with the molecular formula \( C_4H_{10}O \), we can follow these steps:

### Step 1: Determine the Degree of Unsaturation
The degree of unsaturation (or double bond equivalent) can be calculated using the formula:

\[ \text{Degree of Unsaturation} = \frac{(2C + 2 - H)}{2} \]

Where \( C \) is the number of carbon atoms and \( H \) is the number of hydrogen atoms. For \( C_4H_{10}O \):

\[ \text{Degree of Unsaturation} = \frac{(2 \times 4 + 2 - 10)}{2} = \frac{(8 + 2 - 10)}{2} = \frac{0}{2} = 0 \]

This indicates that the compound is a saturated molecule (an alkane) with no double or triple bonds.

**Hint:** Use the formula for degree of unsaturation to find out if there are any rings or multiple bonds in the molecule.

### Step 2: Identify the Possible Alcohol Structures
Since we are looking for alcohols, we need to place the hydroxyl group (-OH) on different carbon atoms in the carbon skeleton. The possible structures can be derived by varying the position of the -OH group and the carbon chain.

1. **Butan-1-ol**:
- Structure: \( CH_3-CH_2-CH_2-CH_2OH \)

2. **Butan-2-ol**:
- Structure: \( CH_3-CH(OH)-CH_2-CH_3 \)

3. **Isobutanol (2-methylpropan-1-ol)**:
- Structure: \( (CH_3)_2CH-CH_2OH \)

4. **Tert-butanol (2-methylpropan-2-ol)**:
- Structure: \( (CH_3)_3C-OH \)

### Step 3: Count the Unique Alcohols
Now, we will count the unique structures we have identified:

1. Butan-1-ol
2. Butan-2-ol
3. Isobutanol (2-methylpropan-1-ol)
4. Tert-butanol (2-methylpropan-2-ol)

Thus, we have a total of **4 different alcohols**.

### Final Answer
The total number of different alcohols possible with the molecular formula \( C_4H_{10}O \) is **4**.

---