Question

Figure \(20-17\) shows that the \(c i s\) isomer of \(\mathrm{Co}(\mathrm{en})_{2} \mathrm{Cl}_{2}^{+}\) is optically active while the \(t r a n s\) isomer is not optically active. Is the same true for \(\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}^{+} ?\) Explain.

Short answer

Both the cis and trans isomers of Co(NH3)4Cl2+ are not chiral as they have planes of symmetry. Thus, neither the cis nor the trans isomer of Co(NH3)4Cl2+ is optically active, which is different from the example of Co(en)2Cl2+ where the cis-isomer was optically active, and the trans-isomer was optically inactive.

Step-by-step solution

Analyze cis-isomer of Co(NH3)4Cl2+

The cis-isomer of Co(NH3)4Cl2+ has the two chloride ligands placed adjacent to each other. To determine if this molecule is chiral, we need to look for any planes of symmetry. It has one plane of symmetry along the plane through the metal center and the two chloride ligands. If we reflect all other atoms over this plane, the molecule is superimposable upon itself. Since the cis-isomer of Co(NH3)4Cl2+ has a plane of symmetry, it is not chiral and therefore optically inactive.

Analyze trans-isomer of Co(NH3)4Cl2+

The trans-isomer of Co(NH3)4Cl2+ has the two chloride ligands placed opposite to each other. To determine if this molecule is chiral, we need to look for any planes of symmetry. It has one plane of symmetry along the plane through the metal center and the two chloride ligands. If we reflect all other atoms over this plane, the molecule is superimposable upon itself. Since the trans-isomer of Co(NH3)4Cl2+ has a plane of symmetry, it is not chiral and therefore optically inactive.

Conclusion

Both the cis and trans isomers of Co(NH3)4Cl2+ have planes of symmetry and are not chiral. Therefore, neither the cis nor the trans isomer of Co(NH3)4Cl2+ is optically active. This is different from the given example of Co(en)2Cl2+, where the cis-isomer was optically active and the trans-isomer was optically inactive.

Key concepts

Chirality

Chirality is a geometric property of some molecules and ions; a chiral molecule/ion is non-superimposable on its mirror image. This is analogous to having a left hand and a right hand; they are mirror images but cannot be perfectly aligned on top of one another. Chirality often plays a key role in the optical activity of compounds.

In coordination compounds, like those involving cobalt (Co), chirality arises when arrangements of ligands are such that they create a non-superimposable mirror image. The classic example of chiral molecules are those with a stereocenter, such as a carbon atom with four different substituents. However, coordination compounds may exhibit chirality without a stereocenter, due to their three-dimensional shape and arrangement of ligands.

Cis-trans Isomerism

Cis-trans isomerism is a type of stereoisomerism where isomers have the same chemical formula but differ in the spatial orientation of groups within the molecule. In coordination compounds, cis isomers have two identical or similar ligands adjacent to each other, while trans isomers have these ligands opposite to each other.

Cis-trans isomerism can affect the chemical and physical properties of a compound, including solubility, boiling point, and reactivity. From an optical perspective, cis isomers sometimes display optical activity if they lack an internal plane of symmetry, while trans isomers often do not, due to the symmetry plane dividing the molecule into two mirrored halves.

Co(NH3)4Cl2+ Isomers

In the case of the coordination compound Co(NH3)4Cl2+, we investigate the potential for optical activity in its cis and trans isomers. The presence of an internal plane of symmetry can be an indication that the molecule is optically inactive. For the cis-isomer of Co(NH3)4Cl2+, the two chloride ligands are next to each other, creating a plane of symmetry through the metal center and the chloride ligands.

Similarly, the trans-isomer, with chloride ligands opposite each other, also has a plane of symmetry. Because both isomers have these symmetry elements, neither form of Co(NH3)4Cl2+ is chiral, hence they are optically inactive. This contrasts with certain other coordination compounds where different spatial arrangements of ligands can lead to chirality and optical activity.

Symmetry in Molecules

Symmetry in molecules refers to the balanced arrangement of atoms or groups of atoms in a molecule. Molecules can have various symmetry elements, including planes of symmetry (mirror planes), axes of symmetry (where a molecule can be rotated by a certain degree and still appear the same), and centers of symmetry.

Understanding symmetry is crucial in chemistry as it helps predict the physical and chemical properties of molecules. Symmetrical molecules tend to be less reactive and in the context of optical activity, molecules with a plane of symmetry are typically optically inactive because they cannot interact with plane-polarized light in a way that results in its rotation. The presence or absence of symmetry elements is fundamental to determining chirality and, as a consequence, the optical behavior of a compound in coordination chemistry.