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Overview:
The general
form of the Williamson ether synthesis mechanism is as follows:
Placing
an alcohol in sodium metal forms the alcoxide plus hydrogen
gas (because it forms hydrogen, keep this away from any flame
or it will explode!).

The alcoxide
can then be added to a suitable alkyl halide (primary or secondary)
to form the ether via an SN2 mechanism.
An example
of the Williamson ether synthesis:

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