Which of the following is incorrectly matched?

Options

A. `{:("Complex","Number of unpaired electrons"),({FeF_(6)]^(3-),5):}`
B. `{:("Complex","Number of unpaired electrons"),([Cr(en)_(3)]^(2+),2):}`
C. `{:("Complex","Number of unpaired electrons"),([Co(NH_(3))_(6)]^(3+),4):}`
D. `{:("Complex","Number of unpaired electrons"),({Mn(H_(2)O)_(6)]^(2+),5):}`

Answer

To determine which of the following coordination compounds is incorrectly matched with the number of unpaired electrons, we will analyze each compound step by step.

### Step 1: Analyze the first compound - \( \text{FeF}_6^{3-} \)

1. **Determine the oxidation state of Iron (Fe)**:
- Let \( x \) be the oxidation state of Fe.
- The charge of the complex is -3.
- Fluoride (F) is a -1 charge ligand and there are 6 of them.
- Therefore, the equation is:
\[ x + 6(-1) = -3 \implies x - 6 = -3 \implies x = +3 \]

2. **Electronic configuration of \( \text{Fe}^{3+} \)**:
- The atomic number of Fe is 26, so the ground state configuration is \( [Ar] 4s^2 3d^6 \).
- For \( \text{Fe}^{3+} \), we remove 3 electrons (2 from 4s and 1 from 3d):
\[ [Ar] 4s^0 3d^5 \]

3. **Determine the number of unpaired electrons**:
- In \( 3d^5 \), all five electrons are unpaired.
- Therefore, \( \text{FeF}_6^{3-} \) has **5 unpaired electrons**.

### Step 2: Analyze the second compound - \( \text{Cr}(\text{en})_3^{2+} \)

1. **Determine the oxidation state of Chromium (Cr)**:
- Let \( x \) be the oxidation state of Cr.
- Ethylenediamine (en) is a neutral ligand.
- The charge of the complex is +2.
- Therefore, the equation is:
\[ x + 3(0) = +2 \implies x = +2 \]

2. **Electronic configuration of \( \text{Cr}^{2+} \)**:
- The atomic number of Cr is 24, so the ground state configuration is \( [Ar] 4s^2 3d^4 \).
- For \( \text{Cr}^{2+} \), we remove 2 electrons (both from 4s):
\[ [Ar] 4s^0 3d^4 \]

3. **Determine the number of unpaired electrons**:
- In \( 3d^4 \) with a strong field ligand (en), the electrons will pair up.
- The configuration will be \( 3d^4 \) resulting in **4 unpaired electrons**.

### Step 3: Analyze the third compound - \( \text{Co}(\text{NH}_3)_6^{3+} \)

1. **Determine the oxidation state of Cobalt (Co)**:
- Let \( x \) be the oxidation state of Co.
- Ammonia (NH3) is a neutral ligand.
- The charge of the complex is +3.
- Therefore, the equation is:
\[ x + 6(0) = +3 \implies x = +3 \]

2. **Electronic configuration of \( \text{Co}^{3+} \)**:
- The atomic number of Co is 27, so the ground state configuration is \( [Ar] 4s^2 3d^7 \).
- For \( \text{Co}^{3+} \), we remove 3 electrons (2 from 4s and 1 from 3d):
\[ [Ar] 4s^0 3d^6 \]

3. **Determine the number of unpaired electrons**:
- In \( 3d^6 \) with a strong field ligand (NH3), the electrons will pair up:
- The configuration will be \( 3d^6 \) resulting in **4 unpaired electrons**.

### Step 4: Analyze the fourth compound - \( \text{Mn}(\text{H}_2\text{O})_6^{2+} \)

1. **Determine the oxidation state of Manganese (Mn)**:
- Let \( x \) be the oxidation state of Mn.
- Water (H2O) is a neutral ligand.
- The charge of the complex is +2.
- Therefore, the equation is:
\[ x + 6(0) = +2 \implies x = +2 \]

2. **Electronic configuration of \( \text{Mn}^{2+} \)**:
- The atomic number of Mn is 25, so the ground state configuration is \( [Ar] 4s^2 3d^5 \).
- For \( \text{Mn}^{2+} \), we remove 2 electrons (both from 4s):
\[ [Ar] 4s^0 3d^5 \]

3. **Determine the number of unpaired electrons**:
- In \( 3d^5 \), all five electrons are unpaired.
- Therefore, \( \text{Mn}(\text{H}_2\text{O})_6^{2+} \) has **5 unpaired electrons**.

### Conclusion

Now, let's summarize the findings:

1. \( \text{FeF}_6^{3-} \) - 5 unpaired electrons
2. \( \text{Cr}(\text{en})_3^{2+} \) - 4 unpaired electrons
3. \( \text{Co}(\text{NH}_3)_6^{3+} \) - 4 unpaired electrons
4. \( \text{Mn}(\text{H}_2\text{O})_6^{2+} \) - 5 unpaired electrons

The incorrectly matched compound is \( \text{Cr}(\text{en})_3^{2+} \) which should have **4 unpaired electrons** instead of the stated 2.