Question

Consider the following complexes:
\([CoCl(NH_3)_5]^{2+}\) (A)
\([Co(CN)_6]^{3-}\) (B)
\([Co(NH_3)_5(H_2O)]^{3+}\) (C)
\([Cu(H_2O)_4]^{2+}\) (D)
The correct order of A, B, C, and D in terms of wavenumber of light absorbed is:

• A. C < D < A < B
• B. D < A < C < B
• C. A < C < B < D
• D. B < C < A < D

Answer 1

The Correct Option is B

To determine the correct order of complexes \([CoCl(NH_3)_5]^{2+}\), \([Co(CN)_6]^{3-}\), \([Co(NH_3)_5(H_2O)]^{3+}\), and \([Cu(H_2O)_4]^{2+}\) in terms of the wavenumber of light absorbed, we need to understand the concept of ligand field strength and the spectrochemical series.

• The wavenumber of light absorbed by a complex is directly related to the ligand field splitting energy \(\Delta\) of the metal-ligand interaction. A stronger field ligand results in a larger splitting and a higher wavenumber of absorbed light.
• The spectrochemical series ranks ligands from weak to strong field, approximately as follows: \(H_2O < Cl^- < NH_3 < CN^-\). Thus, CN^- is a stronger field ligand compared to NH₃, which is stronger than Cl^- and H₂O.

Let's analyze the complexes one by one:

1. \([CoCl(NH_3)_5]^{2+}\) (A): In this complex, the ligands are NH₃ and Cl^-. NH₃ (a stronger ligand than Cl^-) will primarily determine the field strength.
2. \([Co(CN)_6]^{3-}\) (B): This complex has CN^- ligands, which are very strong field ligands, resulting in a high wavenumber.
3. \([Co(NH_3)_5(H_2O)]^{3+}\) (C): With NH₃ as the primary ligands and one H₂O (weaker than NH₃), this complex is intermediate in field strength.
4. \([Cu(H_2O)_4]^{2+}\) (D): This complex only has H₂O ligands, which are weak field ligands, resulting in a low wavenumber.

Based on the above analysis, the order of the complexes in terms of increasing wavenumber is:

1. (D) \([Cu(H_2O)_4]^{2+}\): Weakest field, lowest wavenumber.
2. (A) \([CoCl(NH_3)_5]^{2+}\): Weaker compared to (C) due to the presence of Cl^-.
3. (C) \([Co(NH_3)_5(H_2O)]^{3+}\): Medium field strength.
4. (B) \([Co(CN)_6]^{3-}\): Strongest field, highest wavenumber.

Therefore, the correct order in terms of increasing wavenumber is: \(D < A < C < B\), which matches the given correct answer.

Answer 2

As the ligand field strength increases, the energy of light absorbed by the complex also increases. Since wavenumber $\bar{\nu} \propto$ energy of absorbed light, the order of wavenumber depends on the ligand strength.
For [Co(CN)$_6$]$^{3-}$ (B), CN$^-$ is a strong field ligand (highest $\bar{\nu}$).
For [Co(NH$_3$)$_5$(H$_2$O)]$^{3+}$ (C), NH$_3$ and H$_2$O have moderate ligand field strength.
For [Cu(H$_2$O)$_4$]$^{2+}$ (D), H$_2$O is a weaker field ligand.
For [CoCl(NH$_3$)$_5$]$^{2+}$ (A), Cl$^-$ is the weakest field ligand (lowest $\bar{\nu}$).
Thus, the order is:
\[D < A < C < B.\]