4. Answer the following questions.

ii. Draw qualitatively energy-level diagram showing d-orbital splitting in the octahedral environment. Predict the number of unpaired electrons in the complex [Fe(CN)6]4 . Is the complex diamagnetic or paramagnetic? Is it coloured? Explain.


In an octahedral coordination environment, the d-orbitals of the central metal ion split into two sets: the lower energy set (t2g) and the higher energy set (eg) due to the repulsion between ligands along the x, y, and z axes. This splitting is a result of the electrostatic interactions between the negatively charged electrons on the ligands and the positively charged nucleus of the central metal ion.

The energy-level diagram for d-orbital splitting in an octahedral environment looks like this:

↑ | eg | | High Energy | | --------|----------------------- | t2g | | Low Energy | | ↓

In this diagram, the eg orbitals are higher in energy than the t2g orbitals. Now, let’s consider the complex [Fe(CN)6]^4-.

The electron configuration of a neutral Fe atom is [Ar] 3d^6 4s^2. When Fe forms a coordination complex, it will lose two electrons to achieve a +2 oxidation state (Fe^2+). Therefore, the electron configuration of Fe^2+ is [Ar] 3d^6.

In the [Fe(CN)6]^4- complex, there are six CN^- ligands. Each CN^- ligand is a strong-field ligand, which means it will cause significant splitting of the d-orbitals. In this case, the t2g orbitals will be filled with electrons before any electrons occupy the eg orbitals.

So, in the [Fe(CN)6]^4- complex, the electron configuration in the d-orbitals would be:

t2g^6 eg^0

There are no unpaired electrons in this complex because all the d-orbitals are fully occupied. This means that the complex is diamagnetic because it has no unpaired electrons to create magnetic moments.

As for its color, the [Fe(CN)6]^4- complex is colorless. This is because it has a fully filled d-orbital configuration (t2g^6 eg^0), and there are no transitions of electrons between the d-orbitals when it absorbs visible light. Absorption of visible light is responsible for the color of most coordination complexes, but in this case, there are no available electronic transitions within the d-orbitals, resulting in a colorless complex.