The number of hydrate isomers of `CrCl_(3)*6H_(2)O` are

Options

A. 1
B. 2
C. 3
D. 4

Explanation

To determine the number of hydrate isomers of the compound \( \text{CrCl}_3 \cdot 6\text{H}_2\text{O} \), we need to analyze how the water molecules can be arranged in relation to the chromium ion and the chloride ions. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Structure of the Compound
The compound \( \text{CrCl}_3 \cdot 6\text{H}_2\text{O} \) consists of chromium ions, chloride ions, and water molecules. The chromium ion can coordinate with the chloride ions and water molecules.

**Hint:** Identify the central metal ion and the ligands involved.

### Step 2: Identify Possible Isomeric Forms
Hydrate isomers are formed when water molecules can be arranged differently in relation to the coordination sphere of the metal ion. The possible arrangements include:
1. All 6 water molecules coordinated to the chromium ion.
2. Some water molecules outside the coordination sphere, with chloride ions inside.

**Hint:** Think about how the water molecules can be distributed between the coordination sphere and outside it.

### Step 3: Count the Isomers
1. **All 6 water molecules coordinated:** This is one isomer where all water molecules are inside the coordination sphere.
2. **5 water molecules coordinated and 1 chloride ion inside:** This is the second isomer where one chloride ion replaces one water molecule.
3. **4 water molecules coordinated and 2 chloride ions inside:** This is the third isomer where two chloride ions replace two water molecules.

**Hint:** Ensure that the total number of ligands (water + chloride) remains consistent with the coordination number of chromium.

### Step 4: Verify the Validity of Each Isomer
- The first isomer is valid as all ligands are water.
- The second isomer is valid as it maintains the coordination number.
- The third isomer is valid as well, with two chlorides and four waters.

**Hint:** Check that each isomer maintains the correct coordination number and charge balance.

### Conclusion
The total number of hydrate isomers for \( \text{CrCl}_3 \cdot 6\text{H}_2\text{O} \) is **3**.

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