The correct order of the wavelength maxima of the absorption band in the ultraviolet-visible region for the given complexes is

[Co(NH_3)_5(Cl)]^2+ < [Co(NH_3)_5(H_2O)]^3+ < [Co(NH_3)_6]^3+ < [Co(CN)_6]^3-

[Co(CN)_6]^3- < [Co(NH_3)_5(Cl)]^2+ < [Co(NH_3)_5(H_2O)]^3+ < [Co(NH_3)_6]^3+

[Co(NH_3)_6]^3+ < [Co(CN)_6]^3- < [Co(NH_3)_5(Cl)]^2+ < [Co(NH_3)_5(H_2O)]^3+

Coordination Compounds PYQ — JEE Advanced 2025 · Shift 1 · Q2 with Solution

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Correct answer: A

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Relating Wavelength of Absorption to Crystal Field Splitting Energy

The color of coordination compounds is due to the absorption of light, which causes d-d electron transitions. The energy absorbed corresponds to the crystal field splitting energy ( $\\\Delta_o$$$ for octahedral complexes). The relationship between the absorbed energy (E), the wavelength of maximum absorption ($ \\lambda_{max}$$$), and the crystal field splitting energy is given by:

u = \frac{hc}{\lambda_{max}}$$ where h is Planck's constant and c is the speed of light. From this relationship, we can see that the crystal field splitting energy ($\\\\Delta_o$$$) is inversely proportional to the wavelength of maximum absorption ($\\\\lambda_{max}$$$): $$\Delta_o \propto \frac{1}{\lambda_{max}}$$ This means that a complex with a larger $\\\\Delta_o$$$ will absorb light of a shorter wavelength. 2. **Identifying the Central Metal Ion and Ligands** Let's analyze the given complexes: * $[Co(CN)_6]^{3-}$: Oxidation state of Co is +3. Ligands are six $CN^-$. Central ion is $Co^{3+}$. * $[Co(NH_3)_6]^{3+}$: Oxidation state of Co is +3. Ligands are six $NH_3$. Central ion is $Co^{3+}$. * $[Co(NH_3)_5(H_2O)]^{3+}$: Oxidation state of Co is +3. Ligands are five $NH_3$ and one $H_2O$. Central ion is $Co^{3+}$. * $[Co(NH_3)_5(Cl)]^{2+}$: Oxidation state of Co is +3. Ligands are five $NH_3$ and one $Cl^-$. Central ion is $Co^{3+}$. In all four complexes, the central metal ion is $Co^{3+}$. Therefore, the difference in the crystal field splitting energy ($\\\\Delta_o$$$) will primarily depend on the nature of the ligands attached to it. 3. **Applying the Spectrochemical Series** The magnitude of $\\\\Delta_o$$$ is determined by the strength of the ligands. The spectrochemical series arranges ligands in order of their increasing field strength (their ability to cause d-orbital splitting). The ligands involved in the given complexes are $CN^-$, $NH_3$, $H_2O$, and $Cl^-$. Their order in the spectrochemical series is: $$Cl^- < H_2O < NH_3 < CN^-$$ This is the order of increasing ligand field strength. A stronger ligand causes a larger $\\\\Delta_o$$$. 4. **Determining the Order of $\\\\Delta_o$$$ for the Complexes** Based on the ligand field strengths, we can now arrange the complexes in order of increasing $\\\\Delta_o$$$: * $[Co(CN)_6]^{3-}$ has six $CN^-$ ligands, the strongest in the series. It will have the largest $\\\\Delta_o$$$. * $[Co(NH_3)_6]^{3+}$ has six $NH_3$ ligands. Since $NH_3$ is weaker than $CN^-$, its $\\\\Delta_o$$$ will be smaller than that of the cyanide complex. * For mixed ligand complexes, the overall field strength can be considered as an average of the constituent ligands. * In $[Co(NH_3)_5(H_2O)]^{3+}$, one strong $NH_3$ ligand is replaced by a weaker $H_2O$ ligand. Thus, the average ligand field strength is less than that of $[Co(NH_3)_6]^{3+}$. * In $[Co(NH_3)_5(Cl)]^{2+}$, one strong $NH_3$ ligand is replaced by an even weaker $Cl^-$ ligand. Thus, the average ligand field strength is less than that of $[Co(NH_3)_5(H_2O)]^{3+}$. So, the order of the crystal field splitting energy ($\\\\Delta_o$$$) is: $$\Delta_o([Co(NH_3)_5(Cl)]^{2+}) < \Delta_o([Co(NH_3)_5(H_2O)]^{3+}) < \Delta_o([Co(NH_3)_6]^{3+}) < \Delta_o([Co(CN)_6]^{3-})$$ 5. **Determining the Order of Wavelength Maxima ($\\\\lambda_{max}$$$)** Since $\\\\lambda_{max}$$$ is inversely proportional to $\\\\Delta_o$$$, the order of the wavelength maxima will be the reverse of the order of $\\\\Delta_o$$$. Therefore, the correct order of $\\\\lambda_{max}$$$ is: $$[Co(CN)_6]^{3-} < [Co(NH_3)_6]^{3+} < [Co(NH_3)_5(H_2O)]^{3+} < [Co(NH_3)_5(Cl)]^{2+}$$ Comparing this with the options provided: * A: $[Co(CN)_6]^{3-}$ < $[Co(NH_3)_6]^{3+}$ < $[Co(NH_3)_5(H_2O)]^{3+}$ < $[Co(NH_3)_5(Cl)]^{2+}$ - This matches our derived order. * B: This is the order of $\\\\Delta_o$$$, not $\\\\lambda_{max}$$$ . * C: Incorrect order. * D: Incorrect order. Thus, the correct option is A.

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View written solutionFree

Correct answer: A

Step-by-step Solution:

Relating Wavelength of Absorption to Crystal Field Splitting Energy

u = \frac{hc}{\lambda_{max}}$$ where h is Planck's constant and c is the speed of light. From this relationship, we can see that the crystal field splitting energy ($\\\\Delta_o$$$) is inversely proportional to the wavelength of maximum absorption ($\\\\lambda_{max}$$$): $$\Delta_o \propto \frac{1}{\lambda_{max}}$$ This means that a complex with a larger $\\\\Delta_o$$$ will absorb light of a shorter wavelength. 2. **Identifying the Central Metal Ion and Ligands** Let's analyze the given complexes: * $[Co(CN)_6]^{3-}$: Oxidation state of Co is +3. Ligands are six $CN^-$. Central ion is $Co^{3+}$. * $[Co(NH_3)_6]^{3+}$: Oxidation state of Co is +3. Ligands are six $NH_3$. Central ion is $Co^{3+}$. * $[Co(NH_3)_5(H_2O)]^{3+}$: Oxidation state of Co is +3. Ligands are five $NH_3$ and one $H_2O$. Central ion is $Co^{3+}$. * $[Co(NH_3)_5(Cl)]^{2+}$: Oxidation state of Co is +3. Ligands are five $NH_3$ and one $Cl^-$. Central ion is $Co^{3+}$. In all four complexes, the central metal ion is $Co^{3+}$. Therefore, the difference in the crystal field splitting energy ($\\\\Delta_o$$$) will primarily depend on the nature of the ligands attached to it. 3. **Applying the Spectrochemical Series** The magnitude of $\\\\Delta_o$$$ is determined by the strength of the ligands. The spectrochemical series arranges ligands in order of their increasing field strength (their ability to cause d-orbital splitting). The ligands involved in the given complexes are $CN^-$, $NH_3$, $H_2O$, and $Cl^-$. Their order in the spectrochemical series is: $$Cl^- < H_2O < NH_3 < CN^-$$ This is the order of increasing ligand field strength. A stronger ligand causes a larger $\\\\Delta_o$$$. 4. **Determining the Order of $\\\\Delta_o$$$ for the Complexes** Based on the ligand field strengths, we can now arrange the complexes in order of increasing $\\\\Delta_o$$$: * $[Co(CN)_6]^{3-}$ has six $CN^-$ ligands, the strongest in the series. It will have the largest $\\\\Delta_o$$$. * $[Co(NH_3)_6]^{3+}$ has six $NH_3$ ligands. Since $NH_3$ is weaker than $CN^-$, its $\\\\Delta_o$$$ will be smaller than that of the cyanide complex. * For mixed ligand complexes, the overall field strength can be considered as an average of the constituent ligands. * In $[Co(NH_3)_5(H_2O)]^{3+}$, one strong $NH_3$ ligand is replaced by a weaker $H_2O$ ligand. Thus, the average ligand field strength is less than that of $[Co(NH_3)_6]^{3+}$. * In $[Co(NH_3)_5(Cl)]^{2+}$, one strong $NH_3$ ligand is replaced by an even weaker $Cl^-$ ligand. Thus, the average ligand field strength is less than that of $[Co(NH_3)_5(H_2O)]^{3+}$. So, the order of the crystal field splitting energy ($\\\\Delta_o$$$) is: $$\Delta_o([Co(NH_3)_5(Cl)]^{2+}) < \Delta_o([Co(NH_3)_5(H_2O)]^{3+}) < \Delta_o([Co(NH_3)_6]^{3+}) < \Delta_o([Co(CN)_6]^{3-})$$ 5. **Determining the Order of Wavelength Maxima ($\\\\lambda_{max}$$$)** Since $\\\\lambda_{max}$$$ is inversely proportional to $\\\\Delta_o$$$, the order of the wavelength maxima will be the reverse of the order of $\\\\Delta_o$$$. Therefore, the correct order of $\\\\lambda_{max}$$$ is: $$[Co(CN)_6]^{3-} < [Co(NH_3)_6]^{3+} < [Co(NH_3)_5(H_2O)]^{3+} < [Co(NH_3)_5(Cl)]^{2+}$$ Comparing this with the options provided: * A: $[Co(CN)_6]^{3-}$ < $[Co(NH_3)_6]^{3+}$ < $[Co(NH_3)_5(H_2O)]^{3+}$ < $[Co(NH_3)_5(Cl)]^{2+}$ - This matches our derived order. * B: This is the order of $\\\\Delta_o$$$, not $\\\\lambda_{max}$$$ . * C: Incorrect order. * D: Incorrect order. Thus, the correct option is A.

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