Problem 59 - General Chemistry: Principles and Modern Applications

Question

Acetyl acetone undergoes an isomerization to form a type of alcohol called an enol. The enol, abbreviated acacH, can act as a bidentate ligand as the anion acac^-. Which of the following compounds are optically active: \(\operatorname{Co}(\mathrm{acac})_{3} ;\) trans\(\left[\mathrm{Co}(\mathrm{acac})_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\right] \mathrm{Cl}_{2} ; \operatorname{cis}-\left[\mathrm{Co}(\mathrm{acac})_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\right] \mathrm{Cl}_{2} ?\)

Step-by-Step Solution

Answer

Among the given compounds, only \operatorname{cis}-\left[\mathrm{Co}(\mathrm{acac})_{2}\left(\mathrm{H}_{2}\mathrm{O}\right)_{2}\right] \mathrm{Cl}_{2}$ is optically active due to its lack of any symmetry element.

Step 1: Check symmetry of \(\operatorname{Co}(\mathrm{acac})_{3}\)

Observe that \(\operatorname{Co}(\mathrm{acac})_{3}\) is a fac-tris chelate complex, it is not optically active because this complex has a plane of symmetry – thus, it is not a chiral molecule.

Step 2: Check symmetry of trans$\left[\mathrm{Co}(\mathrm{acac})_{2}\left(\mathrm{H}_{2}\mathrm{O}\right)_{2}\right] \mathrm{Cl}_{2}$

In the case of the trans-complex trans$\left[\mathrm{Co}(\mathrm{acac})_{2}\left(\mathrm{H}_{2}\mathrm{O}\right)_{2}\right] \mathrm{Cl}_{2}$, it has a center of inversion and, hence, it is optically inactive.

Step 3: Check symmetry of \operatorname{cis}-\left[\mathrm{Co}(\mathrm{acac})_{2}\left(\mathrm{H}_{2}\mathrm{O}\right)_{2}\right] \mathrm{Cl}_{2}$

Contrarily, the cis-complex \operatorname{cis}-\left[\mathrm{Co}(\mathrm{acac})_{2}\left(\mathrm{H}_{2}\mathrm{O}\right)_{2}\right] \mathrm{Cl}_{2}$, is chiral and, hence, optically active, as it lacks any symmetry element.

Key Concepts

Chiral Molecules

Chiral molecules are like the left and right hands of chemistry; they are mirror images of each other, but cannot be superimposed on one another. This property is known as chirality. A molecule is chiral if it has an asymmetric carbon atom—meaning it's attached to four different atoms or groups of atoms.

Consider a simple molecule like butane, which is not chiral, versus its cousin, 2-butanol, which may exhibit chirality if the second carbon binds with four distinct groups. Chirality is crucial in fields like drug design, as two enantiomers (mirror-image isomers) of a drug can have vastly different effects on the body.

Bidentate Ligand

A bidentate ligand is like a claw that firmly grips a metal atom in a coordination complex. The term 'bidentate' refers to 'two-toothed,' meaning the ligand can form two bonds with a metal ion. These two 'teeth' are usually donor atoms like nitrogen, oxygen, or sulfur that share a lone pair of electrons with the metal.

For instance, ethylenediamine (en) is a classic example of a bidentate ligand. When it binds to a metal center, it forms a five-membered chelate ring, which tends to be particularly stable due to the chelate effect. This added stability is one reason why bidentate ligands are often important in catalysis and biochemical processes.

Symmetry in Chemistry

Symmetry in chemistry is all about balance and equivalence. A molecule is said to have symmetry if parts of it are arranged in a way that can be mapped onto other parts by operations like rotation, reflection, or inversion. Symmetry elements include planes of symmetry (mirror planes), centers of inversion, and axes of rotation.

Knowing symmetry can help predict a molecule's properties, such as whether it's optically active or inactive. In the example of coordination complexes, a molecule with a plane of symmetry or a center of inversion is not chiral and thus is optically inactive. Conversely, without these symmetry elements, a molecule may be chiral and can be expected to rotate plane-polarized light, making it optically active.