Which of the following statements is INCORRECT ? (1) Complex \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4}\left(\mathrm{H}_{2} \mathrm{O}\right) \mathrm{Cl}\right] \mathrm{Br}_{2}\) can show both hydrate as well as ionization isomerism. (2) Complex \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5}\left(\mathrm{H}_{2} \mathrm{O}\right)\right]\left(\mathrm{NO}_{3}\right)_{3}\) can show hydrate isomerism. (3) Complex \(\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{4}\right]\left[\mathrm{PtCl}_{6}\right]\) cannot show coordination isomerism. (4) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4}\left(\mathrm{NO}_{2}\right) \mathrm{Cl}\right] \mathrm{Cl}\) can show both ionization as well as linkage isomerism.

Isomerism in coordination compounds is an interesting and key topic in chemistry. Isomers are compounds with the same chemical formula but different arrangements of atoms, leading to distinct properties. In the context of coordination compounds, several types of isomerism can occur:

- **Ionization Isomerism:** This happens when there is an exchange of ligands between the complex ion and the counter ion. For example, \[ \text{[Co(NH}_3\text{)}_4(\text{H}_2\text{O}) \text{Cl}] \text{Br}_2 \] can show ionization isomerism by swapping its chloride inside the coordination sphere with a bromide ion in the lattice.

- **Hydrate Isomerism:** Similar to ionization isomerism, hydrate isomerism occurs when water molecules can be inside the coordination sphere or outside as molecules of crystallization. A typical example would be \[ \text{[Cr(H}_2\text{O})}_6\text{]Cl}_3 \] and \[ \text{[Cr(H}_2\text{O})}_5\text{Cl]Cl}_2\text{H}_2\text{O.} \]

- **Linkage Isomerism:** This type of isomerism arises when a ligand can coordinate to the central metal atom/ion through two different atoms. A common ligand exhibiting this isomerism is \(\text{NO}_2\), which can attach via nitrogen or oxygen.

Coordination compounds consist of a central metal atom/ion bonded to surrounding ligands. These compounds play a vital role in various chemical processes and applications, from catalysis to biological systems.

- **Central Metal Atom/Ion:** Usually a transition metal capable of forming multiple bonds due to the availability of D-orbitals.

- **Ligands:** Molecules or ions that donate a pair of electrons to the central metal to form coordination bonds. Ligands can be monodentate (single donor atom) like water (H_2O), or multidentate like ethylenediamine (en), which coordinates through two nitrogen atoms.

- **Coordination Sphere:** This is the set of ligands surrounding the central metal atom/ion. For instance, in the complex \[ \text{[Co(NH}_3\text{)}_5(\text{H}_2\text{O})]\text{]}\text{(NO}_3\text{)_3} \], the coordination sphere is \[ \text{[Co(NH}_3\text{)}_5(\text{H}_2\text{O})] \].

- **Coordination Number:** This describes the number of ligand donor atoms bound to the central metal ion. For example, in the compound \[ \text{[Pt(NH}_3\text{)}_4][\text{PtCl}_6] \], platinum in the cationic complex has a coordination number of 4, while platinum in the anionic complex has a coordination number of 6.

Hydrate isomerism, sometimes known as solvate isomerism, is a type of isomerism particularly found in coordination compounds. It involves the different placement of water molecules within the crystal lattice of a compound.

- **Concept:** In hydrate isomerism, water can be either inside the coordination sphere or outside as part of the crystalline network. This leads to compounds with identical formulas but different structures and properties.

- **Examples:** A classic example is the pair \[ \text{[Cr(H}_2\text{O})}_6\text{]Cl}_3 \] and \[ \text{[Cr(H}_2\text{O})}_5\text{Cl]Cl}_2\text{H}_2\text{O} \]. Here, water molecules either participate directly in coordination or exist as lattice water.

- **Properties:** These isomers can have distinct solubility, reactivity, and stability characteristics due to the different environments around the metal center. This makes hydrate isomerism important in understanding and predicting the behavior of coordination compounds in various conditions.