You prepare sec-butyl tosylate from alcohol of \([\alpha]+6.9^{\circ}\). On hydrolysis with aqueous base, this ester gives sec-buty1 alcohol of \([\alpha]-6.9^{\circ}\). Without knowing the configuration or optical purity of the starting alcohol, what (if anything) can you say about the stereochemistry of the hydrolysis step?

Hydrolysis with an aqueous base usually involves breaking of a certain bond and replacing it with a -OH group (hydroxide ion). In this case, we can deduce that the hydrolysis step involves the cleavage of the bond between the butyl group and the tosylate ion, which is then substituted by a hydroxide ion adding a -OH group to the butyl group (forming the sec-butyl alcohol).

Since the tosylate ion is a good leaving group, the hydrolysis step most probably involves a nucleophilic substitution reaction. In this case, aqueous base (hydroxide ion) is the nucleophile, and sec-butyl tosylate is the substrate. For a stereochemistry comparison, we can consider the two main types of nucleophilic substitutions: 1. SN1: Involving a two-step mechanism, the intermediate carbocation can lead to a stereochemistry mix of products as its recombination with the nucleophile can happen with equal probability from either side. This results in racemization, where both R and S enantiomers are formed with equal probability, giving a racemic mixture. 2. SN2: Involving a single-step mechanism, the nucleophile attacks the chiral center directly from the opposite side of the leaving group. This results in complete inversion of stereochemistry since all atoms attached to the chiral center switch places.

The starting alcohol has an optical rotation of \([\alpha]+6.9^{\circ}\), which means it has either an excess of R-enantiomer or an excess of S-enantiomers. When hydrolyzed, the rotation changes to \([\alpha]-6.9^{\circ}\), meaning the rotation went from positive to negative or vice versa. The hydrolysis stereochemistry depends on the difference between the resulting alcohol's enantiomeric concentrations. Since the changes in optical rotation are equal in magnitude but opposite in direction, it suggests that there could be a complete inversion of the stereochemistry in the hydrolysis, pointing towards an SN2 mechanism.

Based on the equal change in optical rotation in opposite directions before and after hydrolysis, it is reasonable to conclude that the stereochemistry of the hydrolysis step involves an SN2 nucleophilic substitution mechanism with complete inversion of the stereochemistry. This means that R-enantiomers in the starting material become S-enantiomers and vice versa.