How is 1-propoxypropane synthesised from...

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

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The following two methods can be used:
a. Williamson's synthesis
i. `overset (3CH_(3)CH_(2)CH_(2)OH+PBr_(3)) underset (Propan-1-ol)` `rarr` `overset (3CH_(3)CH_(2)CH_(2)Br+H_(3)PO_(3) underset (1-Bromopropane)`
ii. `overset (2CH_(3)CH_(2)CH_(2)OH+2Na) underset (Propan-1-ol)` `rarr` `overset (2CH_(3)CH_(2)CH_(2)O^(-)NA^(o+)+H_(2) underset (Sod. propoxide)`

b. By the dehydration of 1-propanol with conc. `H_(2)SO_(4)` at 431 K.

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