In which of the following octahedral complexes of Co (at. no. 27), will the magnitude of `Delta_o` be the highest?

Options

A. `[Co(CN)_6]^(3-)`
B. `[Co(C_2O_4)_3]^(3-)`
C. `[Co(H_2O)_6]^(3+)`
D. `[Co(NH_3)_6]^(3+)`

Answer

To determine which octahedral complex of cobalt (Co) has the highest magnitude of crystal field splitting energy (Δo), we can follow these steps:

### Step 1: Understand Crystal Field Splitting
In octahedral complexes, the five d-orbitals of the transition metal ion split into two sets due to the presence of ligands. The two sets are:
- Higher energy orbitals: \(d_{x^2-y^2}\) and \(d_{z^2}\) (collectively referred to as \(e_g\))
- Lower energy orbitals: \(d_{xy}\), \(d_{yz}\), and \(d_{zx}\) (collectively referred to as \(t_{2g}\))

The energy difference between these two sets is known as the crystal field splitting energy (Δo).

### Step 2: Identify the Nature of Ligands
The magnitude of Δo depends on the nature of the ligands surrounding the metal ion. Ligands can be classified as either weak field ligands or strong field ligands:
- Weak field ligands (e.g., I⁻, Br⁻, F⁻) cause small splitting.
- Strong field ligands (e.g., CN⁻, CO, NH₃) cause larger splitting.

### Step 3: Refer to the Spectrochemical Series
The strength of ligands can be arranged in the spectrochemical series, which helps us determine the relative splitting caused by different ligands. The order from weak field to strong field is:
I⁻ < Br⁻ < SCN⁻ < F⁻ < OH⁻ < H₂O < NH₃ < en < CN⁻ < CO

### Step 4: Analyze the Given Options
Assuming we have a list of ligands in the octahedral complexes of cobalt, we need to identify which ligand is the strongest based on the spectrochemical series.

For example, if the options include:
1. [Co(CN)₆]³⁻
2. [Co(H₂O)₆]²⁺
3. [Co(NH₃)₆]³⁺
4. [Co(Cl)₆]³⁻

We can analyze them as follows:
- CN⁻ is a strong field ligand.
- H₂O is a moderate field ligand.
- NH₃ is a stronger field ligand than H₂O but weaker than CN⁻.
- Cl⁻ is a weak field ligand.

### Step 5: Conclusion
From the analysis, the complex with CN⁻ will have the highest Δo because it is the strongest ligand among the options. Therefore, the answer is:

**The octahedral complex with the highest magnitude of Δo is [Co(CN)₆]³⁻.**