Question

Estimate the wavelength of maximum absorption for the octahedral ion hexa-aquanickel(II) from the fact that its solutions are colored green by transmitted light. Estimate the crystal field splitting energy${\mathbf{∆}}_{\mathbf{\circ }}\mathbf{(}\mathit{i}\mathit{n}\mathbf{}\mathit{k}\mathit{J}\mathbf{}\mathit{m}\mathit{o}{\mathit{l}}^{\mathbf{-}\mathbf{1}}\mathbf{)}$

Short answer

The crystal filed splitting energy for the complex hexa aqua nickel (II) is 186 kJ/mol.

Step-by-step solution

Molecular orbital theory

Molecular orbitals are formed as linear combinations of atomic orbitals of the different atoms of the complex. In this, the valence d, s, and p orbitals of the central metal, as well as the s and p orbitals of the ligands form a set.

Explanation

From the transmitted color of the light, we can predict the color absorbed by the compound. As per the color wheel, the color absorb for green light is red color and its wavelength is 640 nm-700 nm.

Color wheel

Step 3:

Thus, the wavelength of maximum absorption for octahedral ion Hexa aqua nickel (II) ion is 640 nm. From this, we can calculate the crystal field splitting energy for ${∆}_{\circ }$as:

$E_{photon}=\frac{hc}{\lambda }$

Here,

*h is Planck’s constant, i.e., $6.626\times {10}^{-34}Js$.

*c is the speed of the light, i.e.,$3\times {10}^{8}m/s$.

*$\lambda$is the wavelength of the light, i.e.,$640\times {10}^{-9}m$.

On substituting the given values, we get

$$\begin{gathered} E_{photon}=\frac{hc}{\lambda } \\ =\frac{6.626\times {10}^{-34}Js\times 3\times {10}^{8}m/s}{640\times {10}^{-9}m} \\ =0.031\times {10}^{-17} \\ =3.1\times {10}^{-19}J/molecule \end{gathered}$$

This value of J/molecule is converted to kJ/mol as:

The standard relationship between kJ and J is 1 kJ= 1000 J, and$1mol=6.022\times {10}^{23}mol$.

The conversion is done as:

$$\begin{gathered} E_{photon}=3.1\times {10}^{-19}J/molecule\times \frac{1kJ}{1000J}\times \frac{6.022\times {10}^{23}mol}{1mol} \\ =18.6\times {10}^{4-3} \\ =18.6\times 10 \\ =186kJmo{l}^{-1} \end{gathered}$$

Thus, the crystal filed splitting energy for the complex hexa aqua nickel (II) is 186 kJ/mol.