69. The number of optically inactive geometrical isomers of [Pt(NH₃)₂(py)₂Cl₂]²⁺ is_______ . (where, ‘py’ is pyridine)

Number of Optically Inactive Geometrical Isomers of [Pt(NH₃)₂(py)₂Cl₂]²⁺

Correct Answer

Answer: 3

Understanding the Coordination Compound

Before solving this problem, it is important to identify the structure of the coordination complex. The compound [Pt(NH₃)₂(py)₂Cl₂]²⁺ contains one platinum ion coordinated with six ligands. The ligands are two ammonia (NH₃), two pyridine (py), and two chloride (Cl⁻) ligands. Since the coordination number is six, the complex adopts an octahedral geometry.

The ligand arrangement can therefore be represented as MA₂B₂C₂, where A = NH₃, B = py, and C = Cl⁻. Such octahedral complexes exhibit several geometrical isomers depending on which pairs of identical ligands occupy cis or trans positions.

How Many Geometrical Isomers Are Possible?

For an octahedral complex having the general formula MA₂B₂C₂, there are exactly six geometrical isomers. However, these six isomers are not all optically inactive.

Among these six geometrical arrangements, three possess a plane or center of symmetry and therefore are optically inactive. The remaining three exist as chiral structures that form pairs of enantiomers and are therefore optically active.

Hence, the number of optically inactive geometrical isomers is:

3

Why Are Only Three Isomers Optically Inactive?

An octahedral complex becomes optically inactive when its structure contains a symmetry element such as a mirror plane or an inversion center. These symmetry elements make the molecule superimposable on its mirror image, eliminating chirality.

In the MA₂B₂C₂ system, three geometrical arrangements possess sufficient symmetry to prevent optical activity. The remaining arrangements lack these symmetry elements and therefore exist as non-superimposable mirror images known as enantiomers.

This is a standard stereochemical result frequently tested in CSIR NET, GATE, IIT JAM, and university entrance examinations.

Concept Behind MA₂B₂C₂ Octahedral Complexes

Step 1: Identify the Geometry

The coordination number of platinum is six, indicating an octahedral complex.

Step 2: Recognize the Ligand Pattern

The complex contains three different pairs of identical ligands, making it an MA₂B₂C₂ type complex.

Step 3: Apply the Standard Stereochemistry Rule

Octahedral MA₂B₂C₂ complexes produce six geometrical arrangements. Out of these, three are achiral (optically inactive), while the remaining three are chiral (optically active).

Why the Answer Is 3

Since the question specifically asks for the number of optically inactive geometrical isomers, only the achiral structures should be counted. The three chiral geometrical arrangements are excluded because they exhibit optical activity.

Therefore, the required answer is:

Number of optically inactive geometrical isomers = 3

Detailed Explanation of the Answer

This problem is based entirely on stereochemistry of coordination compounds. Many students attempt to draw all six structures, but this is unnecessary if the standard results for octahedral complexes are known. The MA₂B₂C₂ configuration is one of the most frequently discussed systems in coordination chemistry because it demonstrates both geometrical and optical isomerism simultaneously.

Understanding why some structures possess symmetry while others do not is much more important than memorizing the final number. Whenever an octahedral complex contains three pairs of identical ligands, always check whether the ligand arrangement introduces chirality. In this case, exactly half of the geometrical arrangements are achiral and the remaining half are chiral.

Final Answer

The number of optically inactive geometrical isomers of [Pt(NH₃)₂(py)₂Cl₂]²⁺ is 3.