Question

Figure 21.17 shows that the cis isomer of \(\mathrm{Co}(\mathrm{en})_{2} \mathrm{Cl}_{2}^{+}\) is optically active while the trans isomer is not optically active. Is the same true for \(\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}+?\) Explain.

Short answer

The same is true for Co(NH\(_{3}\))\(_{4}\mathrm{Cl}_{2}^{+}\), as the cis isomer is optically active due to its chirality, while the trans isomer is not optically active due to its symmetry. This is similar to the optical activity observed for the Co(en)\(_{2}\mathrm{Cl}_{2}^{+}\) isomers.

Step-by-step solution

Understanding optical activity

Optical activity is the ability of a substance to rotate the plane of polarized light. A molecule is considered to be optically active if it exists in a chiral form, meaning it cannot be superimposed with its mirror image. A molecule is considered chiral if it has at least one chiral center, which is usually a carbon atom with four different groups or substituents attached to it. In these given coordination compounds, the chiral center would be the central metal ion (Co) with different adjacent ligands.

Determine the structure of cis and trans isomers of Co(NH\(_{3}\))\(_{4}\mathrm{Cl}_{2}^{+}\)

Both isomers have the same chemical formula, but they differ in the positions of the ligands around the coordination sphere of the Co atom. In the cis isomer, the two Cl ligands are adjacent to each other, while in the trans isomer, they are opposite to each other. To better visualize these structures, consider the following representations: cis-Co(NH\(_{3}\))\(_{4}\mathrm{Cl}_{2}^{+}\): ``` NH3 | Cl-Co-Cl | NH3 ``` trans-Co(NH\(_{3}\))\(_{4}\mathrm{Cl}_{2}^{+}\): ``` NH3 | Cl-Co-NH3 | Cl ```

Examine the cis isomer of Co(NH\(_{3}\))\(_{4}\mathrm{Cl}_{2}^{+}\) for chirality

With the cis-isomer, the Co atom is connected to: 1. Two Cl atoms next to each other 2. Four NH3 groups around it Because the Co atom has two Cl and four NH\(_{3}\) groups in a specific arrangement around it, we can conclude that there is chirality in the cis isomer, resulting in optical activity.

Examine the trans isomer of Co(NH\(_{3}\))\(_{4}\mathrm{Cl}_{2}^{+}\) for chirality

With the trans-isomer, the Co atom is connected to: 1. Two Cl atoms opposite to each other 2. Four NH3 groups around it In this case, the trans isomer has a plane of symmetry that divides the molecule into two mirror images that can be superimposed onto each other. Due to this symmetry, the trans isomer does not display chirality, and therefore, it is not optically active. In conclusion, the cis isomer of Co(NH\(_{3}\))\(_{4}\mathrm{Cl}_{2}^{+}\) is optically active while the trans isomer is not, which is the same as observed for the Co(en)\(_{2}\mathrm{Cl}_{2}^{+}\) isomers.

Key concepts

Optical Activity

Optical activity is an important concept in stereochemistry, especially when discussing molecules that can exist in chiral forms. The term describes a molecule's ability to rotate the plane of polarized light. If a molecule is optically active, it will change the direction of this light as it passes through.

This property arises from the presence of chirality within the molecule, meaning it has an asymmetric structure that cannot be superimposed onto its mirror image, much like how your left hand doesn't fit into a right glove. In the case of coordination compounds, optical activity hinges on the configuration of ligands around a central metal atom, like cobalt (Co). If the arrangement of these ligands creates a chiral structure, the molecule will be optically active.

Cis-trans Isomers

Cis-trans isomers are a fascinating type of stereoisomerism where the same chemical composition can have different geometric configurations. This is particularly common in coordination compounds.

For coordination compounds, like those containing cobalt, the cis isomer is when two identical ligands are adjacent to each other. On the other hand, in the trans isomer, these identical ligands are located on opposite sides of the central metal. These spatial arrangements result in the completely different chemical properties such as optical activity. In the example given, the cis-isomer of Co(NH eft{3});_4 eft{Cl};_2^+ is optically active because it forms a chiral structure. By contrast, the trans isomer does not, due to its symmetry that allows its mirror image to be superimposed.

Coordination Compounds

Coordination compounds are complex structures made up of a central metal atom or ion surrounded by molecules or ions called ligands. These ligands are bonded to the central metal, forming coordination bonds and unique complex structures.

The interesting part about coordination compounds is how these structures can vary greatly due to the different possible arrangements of ligands around the metal center. These complex shapes and arrangements often lead to isomerism, including geometric isomerism like the cis-trans isomerism discussed earlier. The geometric arrangement affects the properties of the compound significantly, such as optical activity and even color.

Chiral Center

A chiral center is a specific type of carbon or, more broadly, an atom within a molecule that is bonded to four different groups or substituents. In the context of coordination compounds, the chiral center can also involve a metal ion surrounded by a distinct set of ligands contributing to the overall chirality of the compound.

For coordination complexes, if the central metal has ligands arranged in a way that creates a non-superimposable mirror image, that metal acts as a chiral center. This is pivotal in determining the optical activity of the compound. In the example of Co(NH eft{3});_4 eft{Cl};_2^+, whether the compound possesses a chiral center depends heavily on the arrangement of NH eft{3} and Cl ligands around the cobalt ion, affecting its optical properties.