The enantiopure alcohol shown is converted to the tosylate (TsCl, pyridine), which is then treated with $NaBr$ in DMF. Separately, the alcohol is treated with $PBr X_{3}$ . Select all correct statements.

AThe tosylate has the same spatial arrangement at the stereocentre as the alcohol
BThe $NaBr$ step gives (S)-2-bromobutane
C $PBr X_{3}$ gives (S)-2-bromobutane (with inversion)
DConcentrated HBr converts the alcohol to (R)-2-bromobutane with more than 95 percent retention

Answer: A, B, C

The compound is (R)-butan-2-ol. Tosylation leaves the C-O bond intact, so the tosylate keeps the arrangement.

S X_{N} 2

by bromide inverts it, giving (S)-2-bromobutane (S).

PBr X_{3}

also converts a secondary alcohol by

S X_{N} 2

displacement of the activated oxygen, giving the same (S)-bromide. Concentrated HBr proceeds largely by

S X_{N} 1

/mixed pathways with substantial racemisation, not clean retention. Correct: first three.