Question

The correct order for wavelengths of light absorbed in the complex ions
[CoCl(NH₃)₅]²⁺, [Co(NH₃)₆]³⁺, [Co(CN)₆]^3- is

• A. [CoCl(NH₃)₅]²⁺ > [Co(NH₃)₆]³⁺> [Co(CN)₆]^3-
• B. [Co(NH₃)₆]³⁺ > [Co(CN)₆]^3- > [CoCl(NH₃)₅]²⁺
• C. [Co(CN)₆]^3- > [CoCl(NH₃)₅]²⁺ > [Co(CN)₆]^3-
• D. [Co(NH₃)₆]³⁺ > [CoCl(NH₃)₅]²⁺ > [Co(CN)₆]^3-

Answer 1

The Correct Option is A

To solve the problem, we need to determine the correct order of wavelengths of light absorbed by the given complex ions: $ \text{[CoCl(NH}_3\text{)}_5\text{]}^{2+} $, $ \text{[Co(NH}_3\text{)}_6\text{]}^{3+} $, and $ \text{[Co(CN)}_6\text{]}^{3-} $. This involves understanding the relationship between ligand field strength, crystal field splitting energy ($ \Delta $), and the wavelength of light absorbed.

1. Understanding Ligand Field Strength:
The wavelength of light absorbed by a complex ion is inversely proportional to the crystal field splitting energy ($ \Delta $). The stronger the ligand field (i.e., the stronger the ligand), the larger the $ \Delta $, and the shorter the wavelength of light absorbed. Conversely, a weaker ligand field results in a smaller $ \Delta $ and a longer wavelength of light absorbed.
The ligands in the complexes are:
- $ \text{NH}_3 $: Strong field ligand.
- $ \text{CN}^- $: Very strong field ligand.
- $ \text{Cl}^- $: Weak field ligand.

2. Analyzing Each Complex:

(A) $ \text{[CoCl(NH}_3\text{)}_5\text{]}^{2+} $:
- Central metal: $ \text{Co}^{2+} $ (d-electron configuration: $ \text{d}^7 $).
- Ligands: One $ \text{Cl}^- $ and five $ \text{NH}_3 $.
- Overall ligand field strength: Primarily determined by $ \text{NH}_3 $ (strong field), but slightly weakened by the presence of one $ \text{Cl}^- $ (weak field).

(B) $ \text{[Co(NH}_3\text{)}_6\text{]}^{3+} $:
- Central metal: $ \text{Co}^{3+} $ (d-electron configuration: $ \text{d}^6 $).
- Ligands: Six $ \text{NH}_3 $.
- Overall ligand field strength: Very strong due to six $ \text{NH}_3 $ ligands.

(C) $ \text{[Co(CN)}_6\text{]}^{3-} $:
- Central metal: $ \text{Co}^{3+} $ (d-electron configuration: $ \text{d}^6 $).
- Ligands: Six $ \text{CN}^- $.
- Overall ligand field strength: Extremely strong due to six $ \text{CN}^- $ ligands, which are very strong field ligands.

3. Comparing Crystal Field Splitting Energies ($ \Delta $):
- $ \text{[Co(CN)}_6\text{]}^{3-} $: Contains six $ \text{CN}^- $ ligands, which are very strong field ligands. This results in the largest $ \Delta $.
- $ \text{[Co(NH}_3\text{)}_6\text{]}^{3+} $: Contains six $ \text{NH}_3 $ ligands, which are strong field ligands. This results in a large $ \Delta $, but slightly smaller than that of $ \text{[Co(CN)}_6\text{]}^{3-} $.
- $ \text{[CoCl(NH}_3\text{)}_5\text{]}^{2+} $: Contains five $ \text{NH}_3 $ ligands and one $ \text{Cl}^- $ ligand. The presence of $ \text{Cl}^- $ weakens the overall ligand field, resulting in a smaller $ \Delta $ compared to the other two complexes.

4. Order of Wavelengths Absorbed:
Since the wavelength of light absorbed is inversely proportional to $ \Delta $, the order of wavelengths absorbed is:
$$ \text{[CoCl(NH}_3\text{)}_5\text{]}^{2+} > \text{[Co(NH}_3\text{)}_6\text{]}^{3+} > \text{[Co(CN)}_6\text{]}^{3-} $$

Final Answer:
The correct order of wavelengths absorbed is $ \text{(A) [CoCl(NH}_3\text{)}_5\text{]}^{2+} > \text{[Co(NH}_3\text{)}_6\text{]}^{3+} > \text{[Co(CN)}_6\text{]}^{3-} $.

Answer 2

To determine the correct order of wavelengths of light absorbed, we need to consider the ligand field theory and the nature of ligands:

Higher oxidation states of metal ions generally lead to larger ligand field splitting (Δ), which absorbs higher energy light (shorter wavelengths).

Stronger field ligands like \( \text{CN}^- \) cause greater splitting and absorb shorter wavelengths, while weaker field ligands like \( \text{Cl}^- \) cause smaller splitting and absorb longer wavelengths.

Given complex ions:
\( \text{[CoCl}_3\text{]}^{5-} \): Chloride is a weak field ligand, so it absorbs longer wavelengths.
\( \text{[Co(NH}_3)_6]^{3+} \): Ammonia is a medium field ligand, so it absorbs intermediate wavelengths.
\({[Co(CN)_6]}^{3-}\): Cyanide is a very strong field ligand, causing the largest splitting and absorbing the shortest wavelengths.

Therefore, the correct order of wavelengths absorbed is:
\( [\text{CoCl}_3]^{5-} \) > \( [\text{Co}(NH_3)_6]^{3+} \) > \( [\text{Co}(CN)_6]^{3-} \)

The correct answer is (A) : The correct order of wavelengths absorbed is $ \text{(A) [CoCl(NH}_3\text{)}_5\text{]}^{2+} > \text{[Co(NH}_3\text{)}_6\text{]}^{3+} > \text{[Co(CN)}_6\text{]}^{3-} $.