Which of the following statement is/are incorrect for the complex `[Cr(H_(2)O)_(6)]Cl_(3)`?

Options

A. It has a magnetic moment of 3.83 BM.
B. The distribution of 3d electrons in `3dxy^(1),3dyz^(1),3dzx^(1)`
C. The ligand has satisfied both primary and secondary valencies of chromium.
D. It shows ionization as well as hydrate isomerism.

Explanation

To determine which statements are incorrect for the complex \([Cr(H_2O)_6]Cl_3\), we will analyze each statement step by step.

### Step 1: Determine the oxidation state of chromium
The complex is \([Cr(H_2O)_6]Cl_3\). The oxidation state of chromium (Cr) can be calculated as follows:

Let the oxidation state of Cr be \(X\). The ligands \(H_2O\) are neutral, contributing 0 to the overall charge. The three chloride ions (Cl) have a charge of -1 each, contributing a total of -3.

Setting up the equation:
\[ X + 0 - 3 = 0 \quad \Rightarrow \quad X = +3 \]

**Hint:** Remember that neutral ligands do not affect the oxidation state, while anionic ligands contribute negatively.

### Step 2: Determine the electronic configuration of chromium in the +3 oxidation state
The atomic number of chromium is 24. The ground state electronic configuration is:
\[ [Ar] 3d^5 4s^1 \]
In the +3 oxidation state, chromium loses 3 electrons (2 from 4s and 1 from 3d):
\[ 3d^3 \]

**Hint:** The electronic configuration changes with the loss of electrons, particularly from the 4s orbital before the 3d.

### Step 3: Determine the number of unpaired electrons
Since \(H_2O\) is a weak field ligand, it does not cause pairing of electrons. For \(3d^3\), the distribution of electrons in the d-orbitals is:
- \(d_{xy}^1\)
- \(d_{yz}^1\)
- \(d_{zx}^1\)

Thus, there are 3 unpaired electrons.

**Hint:** Weak field ligands lead to high spin configurations, meaning electrons will occupy different orbitals before pairing.

### Step 4: Calculate the magnetic moment
The magnetic moment (\(\mu\)) can be calculated using the formula:
\[ \mu = \sqrt{n(n + 2)} \]
where \(n\) is the number of unpaired electrons. Here, \(n = 3\):
\[ \mu = \sqrt{3(3 + 2)} = \sqrt{15} \approx 3.87 \text{ Bohr magneton} \]

**Hint:** The magnetic moment indicates the presence of unpaired electrons; more unpaired electrons lead to a higher magnetic moment.

### Step 5: Analyze the statements
1. **Statement 1:** "It has a magnetic moment of 3.83 Bohr magneton."
- This is **correct** as our calculation shows it is approximately 3.87 Bohr magneton.

2. **Statement 2:** "The distribution of 3d electrons in \(d_{xy}^1, d_{yz}^1, d_{zx}^1\)."
- This is **correct** as we have established the distribution of the 3 unpaired electrons.

3. **Statement 3:** "The ligand has satisfied both primary and secondary valencies."
- This is **incorrect**. The primary valency (oxidation state) is not satisfied by \(H_2O\) since it is a neutral ligand.

4. **Statement 4:** "It shows ionization as well as hydrate isomerism."
- This is **incorrect**. The complex can show hydrate isomerism but not ionization isomerism because \(H_2O\) is neutral and does not allow for ion exchange.

### Conclusion
The incorrect statements are 3 and 4.