Draw a structural formula of the polymer resulting from base-catalyzed polymerization of each compound. Would you expect the polymers to be optically active? \((S)-(+)\)-lactide is the dilactone formed from two molecules of \((S)\) - \((+)\)-lactic acid.

\((S)-(+)\)-lactide is a dilactone formed from two molecules of \((S)\)-\((+)\)-lactic acid, which is the chiral form of lactic acid with a specific rotation. The structure of \((S)\)-\((+)\)-lactic acid is as follows: ``` H \ C -- OH / \ HO C \ O ``` Since \((S)-(+)\)-lactide is formed from two molecules of \((S)\)-\((+)\)-lactic acid, it would have the following cyclic structure: ``` O || C -- O / \ O C \ / \ C -- O / \ O C \ OH ```

In the base-catalyzed polymerization of \((S)-(+)\)-lactide, the ester linkage between the two lactic acid molecules in the lactide is broken and reactive sites are generated. These reactive sites on the lactide molecules combine with each other, leading to the formation of the polymer. The resulting polymer, polylactic acid (PLA), has the following repeating structural unit: ``` -[C(O)C]**n** Where: n is the number of repeating units in the polymer. ``` To better visualize the polymer structure, let's draw it: ``` O || C -- O -- C -- O -- C -- O -- C -- O -- ... -- C -- O -- C / \ ^ / \ ^ / \ ^ / \ ... / \ ^ O C O C O C O O C \ / \ / \ / \ C -- O -- C -- O -- C -- O -- ... -- C -- O / \ O C \ OH ```

Optical activity refers to the ability of a compound to rotate the plane of plane-polarized light. Chiral compounds exhibit optical activity. In the case of \((S)-(+)\)-lactide, the starting material is optically active as it has a chiral center (the carbon atom bonded to the hydroxyl group). When this lactide undergoes base-catalyzed polymerization, the resulting polymer (PLA) also has the chiral carbon atoms in its repeating units. Meanwhile, the stereochemistry of the chiral centers is preserved throughout the polymerization process. Thus, the resulting polylactic acid (PLA) polymer would also be optically active.