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Q5.31:
What will be the correct order for the wavelengths of absorption in the visible region for the following: \([Ni(NO_{2})_{6}]^{4-}\), \([Ni(NH_{3})_{6}]^{2+}\), \([Ni(H_{2}O)_{6}]^{2+}\)?

Solution :

Step 1: Identifying the Central Metal Ion and Oxidation State

In all three complexes, the central metal ion is Nickel ($Ni$). Let us determine the oxidation state for each:

  • For $[Ni(NO_2)_6]^{4-}$: $x + 6(-1) = -4 \Rightarrow x = +2$. Thus, $Ni^{2+}$ ($d^8$ configuration).
  • For $[Ni(NH_3)_6]^{2+}$: $x + 6(0) = +2 \Rightarrow x = +2$. Thus, $Ni^{2+}$ ($d^8$ configuration).
  • For $[Ni(H_2O)_6]^{2+}$: $x + 6(0) = +2 \Rightarrow x = +2$. Thus, $Ni^{2+}$ ($d^8$ configuration).

[Per the principle of oxidation state calculation in coordination chemistry, all complexes contain $Ni^{2+}$.]

Step 2: Relationship Between Crystal Field Splitting ($\Delta_o$) and Wavelength ($\lambda$)

The energy of the absorbed photon ($\Delta_o$) is inversely proportional to the wavelength ($\lambda$) of the absorbed light. This is governed by the relation:

$\Delta_o = E = \frac{hc}{\lambda}$

[Per the Planck-Einstein relation, where $h$ is Planck's constant and $c$ is the speed of light.]

Therefore, a larger crystal field splitting energy ($\Delta_o$) results in the absorption of light at a shorter wavelength ($\lambda$).

Step 3: Applying the Spectrochemical Series

The magnitude of $\Delta_o$ depends on the strength of the ligand. According to the spectrochemical series, the order of increasing field strength for the given ligands is:

$H_2O < NH_3 < NO_2^-$

[Per the Spectrochemical Series: ligands are arranged by their ability to cause crystal field splitting based on their donor atoms and $\pi$-bonding capabilities.]

Step 4: Determining the Order of Crystal Field Splitting ($\Delta_o$)

Based on the ligand field strength identified in Step 3, the order of the crystal field splitting energy for the complexes is:

$[Ni(H_2O)_6]^{2+} < [Ni(NH_3)_6]^{2+} < [Ni(NO_2)_6]^{4-}$

Step 5: Determining the Order of Absorption Wavelengths ($\lambda$)

Since $\Delta_o \propto \frac{1}{\lambda}$, we invert the order derived in Step 4 to obtain the order of wavelengths of absorption:

$\lambda([Ni(H_2O)_6]^{2+}) > \lambda([Ni(NH_3)_6]^{2+}) > \lambda([Ni(NO_2)_6]^{4-})$

Visual Representation of Splitting

H2O NH3 NO2- Increasing Crystal Field Splitting (Energy)

Final Solution: The correct order of wavelengths of absorption is: $[Ni(H_2O)_6]^{2+} > [Ni(NH_3)_6]^{2+} > [Ni(NO_2)_6]^{4-}$.


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