`CH_(3)CH_(2)-underset(CH_(3))underset(|)overset(CH_(3))overset(|)(C)-underset(OH)underset(|)(C)H-CH_(3) underset(heat)overset(H_(2)SO_(4))tounderset("Major")P`
What is the major product P in the above reactions?

Options

A. `overset(CH_(3))overset(|)(C)H_(2)-CH_(2)-overset(CH_(3))overset(|)(C)-CH=CH_(2)`
B. `CH_(3)-overset(CH_(3))overset(|)(C)H-overset(CH_(3))overset(|)(C)H-CH=CH_(3)`
C. `CH_(3)CH_(2)-underset(CH_(3))underset(|)overset(CH_(3))overset(|)(C)-CH=CH_(2)`
D. `CH_(3)CH_(2)-overset(H_(3)C)overset(|)(C)=overset(CH_(3))overset(|)(C)-CH_(3)`

Explanation

To determine the major product P from the given reaction, we will analyze the steps involved in the dehydration of the alcohol using sulfuric acid (H₂SO₄) as a catalyst.

### Step-by-Step Solution:

1. **Identify the Starting Material**:
The starting material is an alcohol with the structure:
\[ CH_3CH_2C(CH_3)(OH)CH_3 \]
This is a tertiary alcohol due to the presence of the hydroxyl (-OH) group attached to a carbon that is bonded to three other carbon atoms.

2. **Protonation of the Alcohol**:
When the alcohol is treated with sulfuric acid (H₂SO₄), the hydroxyl group (-OH) gets protonated to form a better leaving group, water (H₂O):
\[ CH_3CH_2C(CH_3)(OH)CH_3 + H^+ \rightarrow CH_3CH_2C(CH_3)(OH_2^+)CH_3 \]
This results in the formation of a protonated alcohol.

3. **Formation of Carbocation**:
The protonated alcohol loses water (H₂O), leading to the formation of a carbocation:
\[ CH_3CH_2C^+(CH_3)CH_3 \]
This carbocation is a tertiary carbocation, which is relatively stable.

4. **Carbocation Rearrangement**:
The carbocation can undergo rearrangement to form a more stable carbocation. In this case, a methyl group (CH₃) can migrate from the adjacent carbon to the carbocation carbon:
\[ CH_3CH_2C^+(CH_3)CH_3 \rightarrow CH_3CH_2C(CH_3)CH_2^+ \]
This results in a more stable tertiary carbocation.

5. **Elimination of Beta Hydrogen**:
The next step involves the elimination of a beta hydrogen (H) to form a double bond. The beta hydrogens can be removed from either of the adjacent carbons:
- From the carbon adjacent to the carbocation.
- From the other adjacent carbon.

The elimination leads to the formation of an alkene:
\[ CH_3CH_2C(CH_3)=CH_2 \]

6. **Identify the Major Product**:
The major product of this dehydration reaction is:
\[ CH_3CH_2C(CH_3)=CH_2 \]
This compound has a double bond between the carbons, and due to the stability of the formed alkene, this is the major product.

### Final Answer:
The major product P is:
\[ \text{CH}_3\text{CH}_2\text{C}(\text{CH}_3)=\text{CH}_2 \]