`CH_(3)CH_(2)OH overset(cocn. H_(2)SO_(4)) underset(413 K) to A'A` will be:

Options

A. `CH_(2)=CH_(2)`
B. `C_(2)H_(5)OCH_(3)`
C. `(C_(2)H_(5))_(2)O`
D. `CH_(3)CH_(2)CH_(2)CH_(3)`

Answer

To solve the question `CH₃CH₂OH overset(cocn. H₂SO₄) underset(413 K) to A'A`, we need to analyze the reaction of ethanol (CH₃CH₂OH) with concentrated sulfuric acid (H₂SO₄) at a temperature of 413 K.

### Step-by-Step Solution:

1. **Identify the Reactants**:
The reactant is ethanol (CH₃CH₂OH), and we are using concentrated sulfuric acid (H₂SO₄) as a catalyst.

2. **Understand the Reaction Conditions**:
The temperature given is 413 K. This temperature is crucial because it determines the pathway of the reaction. At lower temperatures (like 413 K), the reaction favors the formation of ethers rather than alkenes.

3. **Protonation of Alcohol**:
When ethanol is mixed with concentrated sulfuric acid, the first step is the protonation of the hydroxyl group (-OH) of ethanol. The sulfuric acid donates a proton (H⁺) to the oxygen atom in the hydroxyl group, forming an oxonium ion (CH₃CH₂OH₂⁺).

4. **Formation of Carbocation**:
The protonated ethanol (oxonium ion) is unstable and can lose a water molecule (H₂O), leading to the formation of a carbocation (CH₃CH₂⁺).

5. **Nucleophilic Attack**:
At 413 K, instead of elimination to form an alkene, the carbocation can react with another ethanol molecule. The ethyl group (CH₃CH₂) acts as a nucleophile and attacks the positively charged oxygen of the carbocation.

6. **Formation of Ether**:
The resulting product from this nucleophilic attack is diethyl ether (CH₃CH₂OCH₂CH₃). This is because the nucleophile (ethanol) donates a pair of electrons to bond with the carbocation, resulting in the formation of an ether.

7. **Final Product**:
Therefore, the final product A'A is diethyl ether (CH₃CH₂OCH₂CH₃).

### Conclusion:
The reaction of ethanol with concentrated sulfuric acid at 413 K leads to the formation of diethyl ether (CH₃CH₂OCH₂CH₃).

### Answer:
The product A'A will be diethyl ether (CH₃CH₂OCH₂CH₃).

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