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How is diethyl ether prepared from ethyl alcohol?

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How is diethyl ether prepared from ethyl alcohol?  

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Ethyl alcohol is first treated with sodium to form sodium ethoxide C2H5OH + Na C2H5O– Na+ + H2 

Sodium ethoxide is then treated with ethyl halide to form di ethyl ether. 

SN² C2H5O Na + — C2H5X → C2H5O C2H5 + NaX (Williamson synthesis)  

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