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Ethanol with `H_(2)SO_(4)` at 443 K forms ethene while at 413 K it forms ethoxy ethane. Explain the mechanism .

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Case-I : Ethanol reacts with Conc. `H_(2)SO_(4)` at 443 K forms ethene
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Case-II : Ethanol reacts with Conc. `H_(2)SO_(4)` at 413 K to form ethoxy ethane.
`2C_(2)H_(5)OH underset(413K) overset("Conc." H_(2)SO_(4))to C_(2)H_(5)OC_(2)H_(5)`
Mechanism :
In the above reaction ether formation is a `SN^(2)` reaction. This involve attack of alcohol molecules on a protonated alcohol.
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