coordination compounds often show various types of isomerism. The isomerism can be categorized in two main types
(a) structural isomerism
(b) stereo or space isomerism Structural isomerism arises due to the difference in structures of coordination-sempounds while stereo or space isomerism arises on account of the different positions and arrangements of ligands (atoms or groups) in space around the metal lonStructural isomerism can be classified in following types (i) tonization isomers- which give different ions in solution, e.g. `[CoBr(NH_(3))_(5)]]SO_(4)` and `[Co(SO_(4))_(5)(NH_(3))_(5)]Br`
Hydrate isomers which differ in `H_(2)O` as ligand or as hydration, e.g. `[Cr(H_(2)O)_(5)]CI_(2)(H_(2)O)]Cl_(2).H_(2)O[CrCl_(2)(H_(2)O)]CI.2H_(2)O`
(iii) Linkage isomers, which differ in atom linked to 'metal atom, e.g. `[CO(NO_(2))(NH_(3))_(5)]^(2+)`and`CO(ONO)(NH_(3))_(6)]^(2+)`
Coordination isomers- which involve interchange of ligands, e.g. `[Co(NH_(3))_(6)] [Cr(CN)_(6)]` and`[Cr(NH_(3))_(6)] [Co(CN)_(6)]`
(v) Coordination position isomerism-which arises in the bridged complexes due to the difference in the attachment of ligands with the metal atoms
Qcoordinate isomerism 33. How many hydrate isomers are possible with the formulae `CrCl_(3).6H_(2)O`

Options

A. Six
B. Four
C. Three
D. Two

Answer

To determine how many hydrate isomers are possible for the compound \( \text{CrCl}_3 \cdot 6\text{H}_2\text{O} \), we will analyze the coordination complex and the arrangement of water molecules as ligands and as hydration.

### Step-by-Step Solution:

1. **Identify the Coordination Number**:
The coordination number of chromium (Cr) in \( \text{CrCl}_3 \cdot 6\text{H}_2\text{O} \) is 6, which means it can coordinate with six ligands.

2. **Understand Hydrate Isomers**:
Hydrate isomers are those that differ in the arrangement of water molecules, either as ligands (inside the coordination sphere) or as hydration (outside the coordination sphere).

3. **Possible Arrangements**:
- **All Water as Ligands**: The first isomer can have all six water molecules coordinated to the chromium:
\[ [\text{Cr}(\text{H}_2\text{O})_6]^{3+} + 3\text{Cl}^- \]

- **Five Water as Ligands and One Chloride Ion**: The second isomer can have five water molecules as ligands and one chloride ion:
\[ [\text{Cr}(\text{H}_2\text{O})_5\text{Cl}]^{2+} + 2\text{Cl}^- + \text{H}_2\text{O} \]

- **Four Water as Ligands and Two Chloride Ions**: The third isomer can have four water molecules as ligands and two chloride ions:
\[ [\text{Cr}(\text{H}_2\text{O})_4\text{Cl}_2]^{+} + \text{Cl}^- + 2\text{H}_2\text{O} \]

4. **Check for Validity of Isomers**:
- The first isomer is valid as it contains only water as ligands.
- The second isomer is valid as it has one chloride ion and five water molecules.
- The third isomer is valid as it has two chloride ions and four water molecules.
- Any configuration with three or more water molecules outside the coordination sphere is not possible because water is a neutral species and cannot satisfy the charge balance required for the coordination complex.

5. **Conclusion**:
Therefore, the total number of hydrate isomers possible for \( \text{CrCl}_3 \cdot 6\text{H}_2\text{O} \) is **three**.

### Final Answer:
The number of hydrate isomers possible with the formula \( \text{CrCl}_3 \cdot 6\text{H}_2\text{O} \) is **3**.

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