Suggest the possible pathways of coverting `(R)-n-C_(3)H_(7)CH(OH)CH_(3)(A)` into its ethyl ether `n-C_(3)H_(7)CH(OC_(2)H_(5))CH_(3)` using Fischer projections and give their R, S designations.

Explanation

There are two pathways. In path 1, (A) reacts first with K and then with ethyl tosylate `(C_(2)H_(5)Ots)` to form (R) ethyl ether. [Tosyl(Ts) is p-`MeC_(6)H_(4)SO_(2)^(-)`]. In path 2, (A) reacts with tosyl chloride (TsCl) and then with `C_(2)H_(5)bar(O)K^(+)` to form (S) enantiomer. ltbegt
In path 1, the chiral centre is in the nucleophile and none of its bonds are broken, resulting in retention of the configuration in the ether. Path 2 differs in that ethoxide attacks the chiral carbon back side in an `S_(N^(2))` reaction with inversion of configuration.