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 three unique geometrical isomers: Trans-1, Trans-2, and Cis-1. Both Trans-1 and Trans-2 have planes of symmetry, so they do not have optical isomers. However, Cis-1 does not have a plane of symmetry and exists in two non-superimposable mirror-image forms, making it the only isomer with optical isomers.

Step-by-step solution

Calculate Coordination Number

The coordination number of the given complex is 6 since there are 6 ligands attached to the central metal atom, Platinum. The possible geometrical shapes it can adopt are octahedral, which is the most common for coordination number 6.

Draw All Possible Arrangements with Different Ligands

There are three different types of ligands in the given complex - CN, Br, and H2O. We need to place these ligands in a way that generates the maximum number of unique geometrical arrangements. In the octahedral geometry, we have several possible unique arrangements, as listed below: 1. Having Br and CN ligands as trans: (a) Trans-1: One Br and one CN ligand on a trans position, while H2O and the other CN are in cis positions. (b) Trans-2: Both Br ligands in trans positions and both CN ligands in cis positions. 2. Having Br and CN ligands as cis: (c) Cis-1: Both CN ligands in cis positions, and one Br and one H2O in the remaining positions. So, we have three unique geometrical isomers: Trans-1, Trans-2, and Cis-1.

Identify Isomers with Optical Isomers

Optical isomers are non-superimposable mirror images of each other and have no plane of symmetry. We will check each geometrical isomer for that condition. Trans-1 has a plane of symmetry, and therefore it doesn't have any optical isomers. Trans-2 also has a plane of symmetry, and thus, it doesn't have any optical isomers either. However, Cis-1 is found to not have a plane of symmetry and can exist in two non-superimposable mirror-image forms. Thus, Cis-1 has optical isomers.

Draw the Optical Isomers of Cis-1

Cis-1 has two optical isomers that are mirror images of each other. To represent these isomers, we will use the wedges and dashes notation: Wedges indicate that the ligand is coming out of the plane towards us, while dashes imply it is going away from us. In the first optical isomer, we can place one Br with a wedge and H2O with a dash on the adjacent position. In the second optical isomer, we can place the Br with a dash and H2O with a wedge in the adjacent position. In summary, we have identified three unique geometrical isomers of \(\mathrm{Pt}(\mathrm{CN})_{2}\mathrm{Br}_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\) and found that one of them (Cis-1) has optical isomers.

Key concepts

Understanding Coordination Chemistry

At the heart of coordination chemistry is the study of compounds formed when central metal atoms or ions bond with a cohort of molecules or ions known as ligands. These fascinating complexes are held together by coordinate covalent bonds, where both electrons in the bond originate from the ligands, which act as Lewis bases (electron pair donors), and the metal ions act as Lewis acids (electron pair acceptors).
A crucial concept to master here is that of coordination number – the total number of points of attachment to the central atom. In our exercise, Pt(CN)_{2}Br_{2}(H_{2}O)_{2}, it's evident from the formula that Platinum’s coordination number is 6, signifying an array of potential geometric configurations.

• An in-depth understanding of how ligands arrange themselves around a central atom can unveil the distinct properties of coordination compounds.
• The arrangement is not simply a matter of aesthetic interest; it affects reactivity, magnetism, color, and more.

Coordination chemistry does not just grace the pages of academic textbooks; it pervades areas such as catalysis, biological systems (like hemoglobin), and materials science. As such, learning and visualizing these metal-ligand assemblies can provide a profound insight into both nature's designs and human innovation.

Deciphering Octahedral Complexes

Octahedral complexes are coordination compounds where six ligands symmetrically surround a central metal atom, forming an octahedral geometry. This shape can be envisaged as a square bipyramid – a square base with pyramidal structures capping either side.
When you encounter a coordination compound in your studies, like Pt(CN)_{2}Br_{2}(H_{2}O)_{2}, the visualization of its structure profoundly impacts your understanding:

Recognizing Geometrical Isomers in Octahedral Complexes

In the example from the exercise, the challenge lies in placing the CN, Br, and H₂O ligands to uncover all unique geometrical isomers. Key points to remember include:

• The 'trans' arrangement indicates opposite positions across the center, while 'cis' indicates adjacent positions.
• Understanding the spatial distribution of ligands allows predicting the properties and reactivity of the compound.

Visualizing these structures involves developing a mental 3D map of the complex, where mastery can lead to a deeper appreciation of coordination's spatial dance.

Exploring Optical Isomerism

Diving into the realm of optical isomerism unveils a type of stereoisomerism (3D arrangement of atoms) that is critical in numerous fields, ranging from pharmacology to materials science. Optical isomers, or enantiomers, are non-superimposable mirror images of each other and a key property is that they rotate plane-polarized light in different directions.
In our exercise, among the geometric isomers identified, only Cis-1 exhibits this characteristic, as it doesn't have a plane of symmetry. Therefore, this isomer exists as a pair of optical isomers.

Why is Optical Isomerism Important?

• Understanding optical isomerism can mean understanding why two seemingly identical substances can have drastically different effects in biological systems.
• This concept has real-world implications in drug design, as one enantiomer of a drug may be beneficial, while its mirror image could be inert or even harmful.

For students and scientists alike, the ability to identify and create specific optical isomers is a powerful tool in developing new substances with desired properties and behaviors.