Major product of the following `S_N1` reaction is :
`H_3C-underset(Br)underset(|)(CH)-underset(CH_3)underset(|)(CHCH_3)+bar(O)C_2H_4rarr`

Options

A. `H_3C-underset(OC_2H_5)underset(|)(CH)-overset(CH_3)overset(|)(CH)-CH_3`
B. `H_3C-underset(CH_3)underset(|)(CH)-CH_2CH_2OC_2H_5`
C. `CH_3CH_2-underset(OC_2H_5)underset(|)overset(CH_3)overset(|)("CCH"_3)`
D. `CH_3CH=overset(CH_3)overset(|)("CCH"_5)`

Explanation

To determine the major product of the given SN1 reaction, we will follow a systematic approach:

### Step 1: Identify the Reactant
The reactant is given as:
\[ \text{H}_3\text{C}-\text{Br}-\text{C}(\text{CH}_3)-\text{C}(\text{CH}_3) \]

### Step 2: Mechanism of SN1 Reaction
The SN1 reaction proceeds in two steps:
1. Formation of a carbocation.
2. Nucleophilic attack on the carbocation.

### Step 3: Carbocation Formation
In the first step, the bromine atom (leaving group) will leave, resulting in the formation of a carbocation. The structure will look like this:
\[ \text{H}_3\text{C}-\text{C}^+(\text{CH}_3)-\text{C}(\text{CH}_3) \]

### Step 4: Determine the Stability of the Carbocation
The carbocation formed is a secondary carbocation because it is attached to two carbon atoms. Secondary carbocations can rearrange to form more stable carbocations if possible.

### Step 5: Rearrangement of Carbocation
To achieve a more stable tertiary carbocation, a hydride shift can occur. A hydrogen atom from the adjacent carbon can shift to the carbocation carbon, resulting in:
\[ \text{H}_3\text{C}-\text{C}(\text{CH}_3)-\text{C}^+(\text{CH}_3) \]
This results in a tertiary carbocation:
\[ \text{C}^+(\text{CH}_3)-\text{C}(\text{CH}_3)-\text{C}(\text{H}_3) \]

### Step 6: Nucleophilic Attack
The nucleophile, which is ethoxide (\( \text{O-C}_2\text{H}_5 \)), will now attack the positively charged carbon of the tertiary carbocation:
\[ \text{C}^+(\text{CH}_3)-\text{C}(\text{CH}_3)-\text{O-C}_2\text{H}_5 \]

### Step 7: Formation of the Product
The product formed will have the structure:
\[ \text{H}_3\text{C}-\text{C}(\text{CH}_3)-\text{C}(\text{O-C}_2\text{H}_5) \]
This product has a butane chain with the ethoxy group attached to one of the carbon atoms.

### Step 8: Identify the Major Product
Now, we compare the options provided in the question. The correct major product will be the one that has:
- A butane parent chain.
- The ethoxy group and the methyl group attached to the same carbon.

### Conclusion
Thus, the major product of the given SN1 reaction is option C.

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