Step 1: Understanding the complex
The given complex is \( [ \text{Pt(NH}_3\text{)}_4\text{Cl}_2 ]\text{Br}_2 \), where:
- Pt is the central metal ion, Platinum (Pt).
- \( NH_3 \) is a neutral ligand, ammonia.
- \( Cl^- \) and \( Br^- \) are negatively charged ligands, chloride and bromide, respectively.
- There are 4 ammonia molecules, 2 chloride ions, and 2 bromide ions coordinated to the platinum ion.
The complex has the general formula \( [ \text{Pt(NH}_3\text{)}_4\text{Cl}_2 ]\text{Br}_2 \), which means it contains a coordination sphere where platinum is surrounded by 4 ammonia molecules, 2 chloride ions, and the 2 bromide ions are outside the coordination sphere (as counter-ions). Step 2: Types of isomers
There are two main types of isomers that can arise in this type of complex:
1. Geometrical isomers: These arise due to different spatial arrangements of the ligands around the central metal ion.
2. Optical isomers: These arise due to the chiral nature of the complex, where the complex is non-superimposable on its mirror image. Step 3: Geometrical isomerism
In this complex, the two chloride ions (\( \text{Cl}^- \)) can either be placed adjacent to each other (cis-isomer) or opposite to each other (trans-isomer) in the coordination sphere.
- Cis-isomer: The two chloride ions are adjacent to each other.
- Trans-isomer: The two chloride ions are opposite to each other.
Thus, there are 2 possible geometrical isomers based on the relative position of the chloride ions. Step 4: Optical isomerism
The complex \( [ \text{Pt(NH}_3\text{)}_4\text{Cl}_2 ]\text{Br}_2 \) can also exhibit optical isomerism. This is because in the cis configuration, the arrangement of ligands around the platinum ion can create a chiral center. The cis-isomer will have two mirror-image forms (optical isomers).
Thus, there are 2 optical isomers for the cis-isomer. Step 5: Counting the total number of isomers
We have:
- 2 geometrical isomers (cis and trans).
- 2 optical isomers for the cis-isomer.
Therefore, the total number of isomers is:
\[
2 \, (\text{cis and trans}) \times 3 \, (\text{2 for cis and 1 for trans}) = 6
\]
Step 6: Conclusion
Thus, the total number of possible isomers for the complex \( [ \text{Pt(NH}_3\text{)}_4\text{Cl}_2 ]\text{Br}_2 \) is 6.
In simple words, multiple compounds having the same molecular formulae but different structural formulae are referred to as isomers and this entire phenomenon is described as ‘Isomerism’. ‘Isos’ and ‘meros’ are Greek words that translate to ‘equal parts’.
Types of Isomerism:
Isomerism can be differentiated by primary types and their subtypes.
Structural Isomerism
Ring Chain Isomerism, Chain Isomerism, Tautomerism, Functional Isomerism, Metamerism, and Positional Isomerism are the subtypes of Structural Isomerism.
Stereoisomerism
Optical Isomerism & Geometric Isomerism are the two subtypes of Stereoisomerism.
The phenomenon when the compounds start showing isomerism because of their different structure is termed Structural Isomerism. Example - Isobutane and n-butane
Structural Isomerism can further be classified into various types such as chain isomerism, positional isomerism, functional isomerism, metamerism, ring-chain isomerism, and tautomerism.
Ring Chain isomerism
In the ring chain isomerism, there will be an open-chain structure in any one of the isomers and the remaining will have a closed chain or a ring structure. These kinds of compounds are known as ring chain isomers and this phenomenon is termed ring chain isomerism. The number of pi bonds in ring chain isomers will be different. Example - Cyclopropane and Propene. Their molecular formula is C3H6
Chain isomerism
In chain isomerism, there will be different branches of carbon atoms in multiple isomers compounds but still, their molecular formula remains the same. Skeleton isomerism is the other term used to refer to chain isomerism. Example- 2 methyl butane, 2-2 dimethyl propane, and n-pentane. Their molecular formula is C5H12
Tautomerism
In tautomerism, there will be a difference in isomer compounds only in the position of electrons, protons, and atoms. Tautomers take place in an equilibrium state as they can easily interchange. Example - Keto-enol tautomerism
Functional Isomerism
In functional isomerism, the isomer compounds with different functional groups have the same molecular formula. Example - dimethyl ether and ethanol. They both have the same molecular formula C2H6 O. The functional group of Ethanol is ‘OH’ while the Functional group of dimethyl ether is ‘R-O-R’.
Metamerism
In metamerism, each side of the functional group has the presence of different alkyl chains. Compared with other types of isomerism, metamerism is rarely found and is constrained to molecules with atoms. Example - Methoxy-propane (CH3OC3H7) & ethoxyethane (C2H5OC2H5)
Positional Isomerism
In Positional isomerism, the functional groups and substituents of a structural isomer will have different positions. Example - 1-Chloropropane and 2-Chloropropane
Stereoisomerism
The phenomenon when compounds start showing different spatial arrangements of atoms even when their molecular formula is the same is termed Stereoisomerism. Example - 1,2 - dichloroethene (C2H2CI2)
Optical isomerism
In optical isomerism, the isomer Compounds differ in terms of optical activity but are mirror images of each other. In this subtype of Stereoisomerism, carbon atoms are connected to four different groups and this is known as the chiral center. Enantiomers is the term mostly used to refer to optical isomers.
In Dextro optical isomers plane of polarized light is rotated to the right. In Laevo optical Isomers, the plane of polarized light is rotated to the left.
Geometric isomerism
In geometric isomerism, the spatial positions of molecules are locked because of the presence of a double bond or ring structure. It is often referred to as Cis-Trans isomerism. Groups connected to ring structure carbon atom must be different in geometric isomerism.
are isomeric compounds. 
are functional group isomers.
