Question

Draw all geometrical isomers of \(\mathrm{Pt}(\mathrm{CN})_{2} \mathrm{Br}_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2} .\) Which of these isomers has an optical isomer? Draw the various optical isomers.

Short answer

The complex \(\mathrm{Pt}(\mathrm{CN})_{2}\mathrm{Br}_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\) has an octahedral geometry with three different ligands and can form two geometrical isomers: fac-isomer and mer-isomer. The fac-isomer has optical activity, as it has an enantiomeric pair of optical isomers with ligands in clockwise and counterclockwise sequences, whereas the mer-isomer does not possess optical isomers.

Step-by-step solution

Identifying the coordination geometry

As the platinum atom has a coordination number of 6, the coordination geometry is octahedral. In an octahedral geometry, the central atom is located at the center of an octahedron, with the six ligands surrounding it at equal distances and angles.

Arranging the ligands into geometrical isomers

For the given complex, we have three different ligands: CN, Br, and H2O. As there are six potential positions around the platinum atom for these ligands, we can draw different geometrical isomers with this arrangement. We look for fac (facial) and mer (meridian) isomers in the complex: 1. fac-isomer: Three different ligands (CN, Br, H2O) occupy adjacent positions on the same face of the octahedron, while the other face has similar ligands in the same arrangement. 2. mer-isomer: The three different ligands (CN, Br, H2O) occupy three alternate positions, creating a meridian on the octahedron.

Identifying optical isomers

For the given complex, the fac-isomer is the only one that displays optical activity, as it has a non-superimposable mirror image. The mer-isomer does not have a mirror image that is non-superimposable, so it does not possess optical isomers.

Drawing optical isomers of the fac-isomer

The fac-isomer has an enantiomeric pair as its optical isomers. These isomers are non-superimposable mirror images of each other: - In the first enantiomer, we can label the positions of the ligands as [CN]-[Br]-[H2O] in a clockwise arrangement on the front face and in the opposite sense on the back face. - In the second enantiomer (the mirror image of the first), the arrangement of ligands will be in a counterclockwise sequence on the front face and in a clockwise sequence on the back face. The resulting optical isomers are the enantiomeric pair of the fac-isomer, distinguished by their arrangement of ligands in a clockwise or counterclockwise sequence.

Key concepts

coordination geometry

Coordination geometry refers to the spatial arrangement of atoms around a central atom in a molecule or complex ion. In this case, the platinum atom is the central atom in the complex \( \mathrm{Pt} \left( \mathrm{CN} \right)_2 \mathrm{Br}_2 \left( \mathrm{H}_2 \mathrm{O} \right)_2 \). The coordination number, which is the total number of ligands bound to the central atom, is 6. This specific coordination number leads us to an octahedral geometry. In an octahedral arrangement, the ligands occupy the vertices of an octahedron, with the central atom placed at the center. This symmetrical configuration allows each ligand to be situated at equal angles and distances from the central atom. Understanding coordination geometry is crucial when predicting the different possible geometrical isomers of a complex, as the spatial arrangement influences the isomerism that can occur.

optical isomers

Optical isomers, or enantiomers, are a type of stereoisomer that are non-superimposable mirror images of each other. These arise in chiral molecules, which do not have an internal plane of symmetry. In the context of coordination chemistry, certain geometrical arrangements can lead to optical isomerism.For the octahedral complex \( \mathrm{Pt} \left( \mathrm{CN} \right)_2 \mathrm{Br}_2 \left( \mathrm{H}_2 \mathrm{O} \right)_2 \), only the fac-isomer can exhibit optical isomerism. This is because the arrangement of the ligands allows for a non-superimposable mirror image to be formed. The fac-isomer has ligands positioned such that when viewed from a certain angle, its reflection in a mirror cannot overlap perfectly with the original, hence forming an optical isomer. These two enantiomers rotate plane-polarized light in different directions, a property used to distinguish optical isomers in practical applications.

octahedral complexes

Octahedral complexes are a common type of coordination complex where a central atom is surrounded by six ligands at equal intervals around it, forming an octahedron shape. This geometry is prevalent in transition metal complexes, like that of platinum in \( \mathrm{Pt} \left( \mathrm{CN} \right)_2 \mathrm{Br}_2 \left( \mathrm{H}_2 \mathrm{O} \right)_2 \).Such complexes are valuable in chemistry due to their structural versatility and the types of isomerism they can display. They can show geometrical isomerism, such as fac and mer isomer forms:

• Facial (fac) isomer: Three identical ligands occupy adjacent positions, forming a face of the octahedron.
• Meridional (mer) isomer: Here, the identical ligands are distributed along a line or meridian across the octahedron.

In octahedral complexes, the fac-isomer often exhibits optical activity, unlike the mer-isomer which lacks the necessary asymmetry. This distinction is critical in understanding the behavior and properties of such complexes in chemistry.