How many tetriary alcohols of formula `C_(5)H_(12)O` are possible ?

Options

A. 1
B. 2
C. 3
D. 4

Explanation

To determine how many tertiary alcohols of the formula \( C_5H_{12}O \) are possible, we can follow these steps:

### Step 1: Understand the structure of tertiary alcohols
A tertiary alcohol is defined as an alcohol in which the hydroxyl group (-OH) is attached to a carbon atom that is bonded to three other carbon atoms. This means that the carbon with the -OH group must be a tertiary carbon.

### Step 2: Analyze the molecular formula
The molecular formula given is \( C_5H_{12}O \). We need to ensure that we can create a structure that fits this formula while also satisfying the conditions for a tertiary alcohol.

### Step 3: Calculate the degree of unsaturation
The degree of unsaturation can be calculated using the formula:
\[ \text{Degree of Unsaturation} = \frac{C + 1 - H + X - N}{2} \]
Where:
- \( C \) = number of carbons (5)
- \( H \) = number of hydrogens (12)
- \( X \) = number of halogens (0)
- \( N \) = number of nitrogens (0)

Substituting the values:
\[ \text{Degree of Unsaturation} = \frac{5 + 1 - 12 + 0 - 0}{2} = \frac{-6}{2} = -3 \]
Since the degree of unsaturation is 0, this means there are no double bonds, triple bonds, or rings in the structure.

### Step 4: Construct the structure
Since we need to create a tertiary alcohol, we can start with a carbon skeleton of 5 carbons. The structure must be such that one of the carbons is attached to the -OH group and is also bonded to three other carbons.

A possible structure for a tertiary alcohol with 5 carbons is:
- Place the -OH group on a carbon that is connected to three other carbons.

### Step 5: Draw the structure
One possible structure is:
```
CH3
|
CH3 - C - OH
|
CH2 - CH3
```
This structure shows a tertiary carbon (the central carbon) that is bonded to three other carbon groups (two methyl groups and one ethyl group).

### Step 6: Count the possible structures
In this case, there is only one way to arrange the five carbons while ensuring that one of them is a tertiary carbon with the -OH group attached. Therefore, there is only **one possible tertiary alcohol** with the formula \( C_5H_{12}O \).

### Final Answer
Thus, the number of tertiary alcohols of the formula \( C_5H_{12}O \) is **1**.

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