Isomerism shown by the complex pair $[Cr(H_2O)_6]Cl_3$ and $[Cr(H_2O)_5Cl]Cl_2.H_2O$ is

Hydrate isomerism

The correct answer is Option (1) → Hydrate isomerism

In coordination chemistry, hydrate isomerism (also called solvate isomerism) occurs when water molecules can either act as ligands inside the coordination sphere or remain outside as water of crystallization.

In such cases, the total number of atoms remains the same, but the position of water molecules changes between the coordination sphere and the crystal lattice.

Consider the given complexes:

1. $([Cr(H_2O)_6]Cl_3$)

Here:

• Chromium is coordinated with six water molecules.
• All water molecules are inside the coordination sphere.
• Three chloride ions are present outside the coordination sphere as counter ions.

Coordination sphere:

$([Cr(H_2O)_6]^{3+})$

2. $([Cr(H_2O)_5Cl]Cl_2 . H_2O)$

Here:

• Chromium is coordinated with five water molecules and one chloride ligand.
• Two chloride ions are present outside the coordination sphere.
• One water molecule exists as water of crystallization outside the coordination sphere.

Coordination sphere:

$([Cr(H_2O)_5Cl]^{2+}$

Thus, the difference between the two complexes lies in the position of water molecules:

• In the first complex, all six water molecules are coordinated.
• In the second complex, five water molecules are coordinated, and one water molecule is outside the coordination sphere.

This interchange of water molecules between coordination sphere and crystal lattice results in hydrate isomerism.

Option-wise Explanation

Option 1: Hydrate isomerism

Hydrate isomerism occurs when water molecules may either coordinate with the metal ion or exist outside the coordination sphere as water of crystallization. Since the given complexes differ in the position of one water molecule and one chloride ligand, this type of isomerism is present. Therefore, this option is correct.

Option 2: Coordination isomerism

Coordination isomerism occurs when both cationic and anionic species are complex ions and ligands exchange between them. In the given complexes, only one coordination entity is present, and chloride ions act merely as counter ions. Hence this option is incorrect.

Option 3: Linkage isomerism

Linkage isomerism arises when an ambidentate ligand can attach to the metal through two different donor atoms, such as ($NO_2^-$) attaching through nitrogen or oxygen. Since neither water nor chloride is an ambidentate ligand here, this option is incorrect.

Option 4: Geometrical isomerism

Geometrical isomerism occurs due to different spatial arrangements of ligands (cis–trans or fac-mer). The given complexes differ in composition rather than spatial arrangement, so geometrical isomerism does not occur. Hence this option is incorrect.