Acetylacetone, abbreviated acacH, is a bidentate ligand. It loses a proton and coordinates as acac \(^{-}\), as shown below, where \(\mathrm{M}\) is a transition metal: Which of the following complexes are optically active: cis\(\mathrm{Cr}(\mathrm{acac})_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\), trans \(-\mathrm{Cr}(\mathrm{acac})_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\), and \(\mathrm{Cr}(\mathrm{acac})_{3} ?\)

In the cis configuration, the two acac ligands and the two H2O molecules are located in adjacent positions (90° apart) around the metal center. To determine whether this complex is chiral, we should visualize its mirror image and analyze whether the two structures are superimposable or not. If the mirror images are not superimposable, the complex is chiral and therefore optically active.

In the trans configuration, the two acac ligands and the two H2O molecules are in opposite positions (180° apart) around the metal center. Similar to the cis configuration, we should visualize the mirror image of the trans complex and assess whether the two structures can be superimposed. If not, the complex is chiral and optically active.

For this complex, there are three bidentate acac ligands coordinating to the transition metal. To determine whether this complex is optically active, we need to visualize its mirror image and check if the two structures are superimposable. If they are not, the complex is chiral and optically active.

After examining the three complexes and their mirror images, we can determine which of them are chiral and therefore optically active: 1. cis-Cr(acac)2(H2O)2: The metal center in this complex is a chiral center, as the mirror image is not superimposable onto the original molecule. Hence, this complex is optically active. 2. trans-Cr(acac)2(H2O)2: In contrast to the cis configuration, the mirror image of the trans configuration is superimposable onto the original molecule. Therefore, the metal center in this complex is not a chiral center, and the complex is not optically active. 3. Cr(acac)3: The mirror image of this complex is not superimposable onto the original molecule, indicating that the metal center is a chiral center. As a result, the complex is optically active. To conclude, out of the three given complexes, cis-Cr(acac)2(H2O)2 and Cr(acac)3 are optically active, while trans-Cr(acac)2(H2O)2 is not.