Question

The \(\Delta_o\) of [Cr(H\(_2\)O)\(_6\)]\(^3+\), [CrF\(_6\)]\(^3-\), and [Cr(CN)\(_6\)]\(^3-\) follows the order:

• A. [Cr(H\(_2\)O)\(_6\)]\(^3+\) > [CrF\(_6\)]\(^3-\) > [Cr(CN)\(_6\)]\(^3-\)
• B. [CrF\(_6\)]\(^3-\) > [Cr(H\(_2\)O)\(_6\)]\(^3+\) > [Cr(CN)\(_6\)]\(^3-\)
• C. [Cr(CN)\(_6\)]\(^3-\) > [Cr(H\(_2\)O)\(_6\)]\(^3+\) > [CrF\(_6\)]\(^3-\)
• D. [CrF\(_6\)]\(^3-\) > [Cr(CN)\(_6\)]\(^3-\) > [Cr(H\(_2\)O)\(_6\)]\(^3+\)

Hint:

In ligand field theory, the strength of the ligand determines the splitting energy (\(\Delta_o\)). Strong field ligands like CN\(^-\) cause greater splitting than weak field ligands like H\(_2\)O or F\(^-\).

Answer 1

The Correct Option is C

The question asks for the order of the crystal field splitting energy (\(\Delta_o\)) for three chromium complexes: \([Cr(H_2O)_6]^{3+}\), \([CrF_6]^{3-}\), and \([Cr(CN)_6]^{3-}\). The value of \(\Delta_o\) is influenced by the nature of the ligands surrounding the metal ion. Ligands that create a stronger ligand field cause a larger splitting energy.

Step 1: Analyzing the ligands.
In ligand field theory, ligands can be classified as strong field or weak field ligands. Strong field ligands cause larger splitting in the d-orbitals, while weak field ligands cause smaller splitting. - Cyanide (CN\(^-\)) is a strong field ligand, meaning it will cause a large crystal field splitting and therefore a high \(\Delta_o\). - Water (H\(_2\)O) is a weak field ligand, and as a result, the crystal field splitting will be smaller. - Fluoride (F\(^-\)) is also a weak field ligand, but slightly stronger than water, so the crystal field splitting will be between cyanide and water.

Step 2: Determining the order of \(\Delta_o\).
- Since cyanide (CN\(^-\)) is a strong field ligand, the complex \([Cr(CN)_6]^{3-}\) will have the highest \(\Delta_o\). - Water (H\(_2\)O) is weaker than cyanide, so \([Cr(H_2O)_6]^{3+}\) will have a smaller \(\Delta_o\). - Fluoride (F\(^-\)) is weaker than both cyanide and water, so \([CrF_6]^{3-}\) will have the lowest \(\Delta_o\). Thus, the correct order of \(\Delta_o\) is: \[ \text{[Cr(CN)\(_6\)]}^3- > \text{[Cr(H\(_2\)O)\(_6\)]}^3+ > \text{[CrF\(_6\)]}^3-. \] The correct answer is (C).