Question

Arrange the following in increasing order of their crystal field splitting energy: 

• A. \( I < II < III < IV \)
• B. \( IV < I < II < III \)
• C. \( I < III < II < IV \)
• D. \( IV < II < I < III \) \

Hint:

Crystal field splitting energy depends on ligand strength. Strong field ligands like \( CN^- \) cause large splitting, while weak field ligands like \( F^- \) lead to small splitting.

Answer 1

The Correct Option is B

Step 1: Understanding Crystal Field Splitting Energy 
Crystal field splitting energy (\( \Delta \)) depends on:
- The ligand field strength in the spectrochemical series.
- The oxidation state and nature of the metal ion.
The spectrochemical series ranks ligands in increasing order of field strength: \[ F^-<H_2O<NH_3<CN^- \] Step 2: Analyzing the Given Complexes 
1. [CoF\(_6\)]\(^{3-}\): Fluoride (\( F^- \)) is a weak field ligand, leading to the smallest splitting energy.
2. [Co(H\(_2\)O)\(_6\)]\(^{2+}\): Water (\( H_2O \)) is a weak field ligand, but stronger than fluoride.
3. [Co(NH\(_3\))\(_6\)]\(^{2+}\): Ammonia (\( NH_3 \)) is a moderate field ligand, leading to greater splitting than \( H_2O \).
4. [Co(CN\(_6\))]\(^{3-}\): Cyanide (\( CN^- \)) is a strong field ligand, causing the highest splitting energy.
Step 3: Arranging in Increasing Order 
Since crystal field splitting energy increases with ligand field strength: \[ [CoF_6]^{3-}<[Co(H_2O)_6]^{2+}<[Co(NH_3)_6]^{2+}<[Co(CN)_6]^{3-} \] Step 4: Evaluating the Given Options 
- Option (1): Incorrect, as \( IV \) should have the lowest splitting.
- Option (2): Correct, as \( IV<I<II<III \) follows the correct increasing order.
- Option (3): Incorrect, as it places \( III \) before \( II \).
- Option (4): Incorrect, as it misplaces the order.
Thus, the correct answer is 

Option (2).