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How is 1-propoxypropane synthesised from...

How is 1-propoxypropane synthesised from propan-1-ol ? Write mechanism of the reaction.

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Two methods can be used for the sybnthesis of 1-propoxypropane from propan-1-ol
By Williamson's sybthesis
The halogen derivative such as bromoderivative and sodium salt of the alcohol take part in the Williamson's synthesis.
`3CH_(3)-underset("Propane-1-ol")(CH_(2)-CH_(2))-OH+PBr_(3)rarr3CH_(3)-underset("1-Bromopropane")(CH_(2)-CH_(2))-Br+H_(3)PO_(3)`
`3CH_(3)-underset("Propan-1ol")(CH_(2)-CH_(2))-OH+NararrCH_(3)-underset("Sod.propoxide")(CH_(2)-CH_(2))-overset(-)Ooverset(+)Na+1//2H_(2)`

By dehydration of propan-1ol with conc. `H_(2)SO_(4)` at 413 K
`CH_(3)-CH_(2)underset("Prpane-1-ol")(-CH_(2))-overset(* *)underset(* *)O-H+H^(+)hArrCH_(3)-CH_(2)-CH_(2)-underset("Protonated alcohol")underset(H)underset(|)overset(o+)overset(* *)(O)-Hunderset(-H_(2)O)overset(("Slow"))rarrCH_(3)-underset(1^(@)"Carbocation")(CH_(2))-overset(o+)CH_(2)`
The primary carbocation attacks another moleculs of propan -1-ol by `S_(N^(1))` mechanism.
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