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Chapter 21: Problem 53

Draw the \(d\) -orbital splitting diagrams for the octahedral complex ions of each of the following. a. \(\mathrm{Fe}^{2+}\) (high and low spin) b. \(\mathrm{Fe}^{3+}(\text { high spin })\) c. \(\mathrm{Ni}^{2+}\)

Short Answer

Expert verified
The d-orbital splitting diagrams for the given octahedral complex ions are as follows: a. \(\mathrm{Fe}^{2+}(3d^6)\): High spin: \(t_{2g}\): ↑(1, ↓1), ↑(2, ↓2), ↑(3, ↓3); \(e_g\): ↑(4), ↑(5), ↑(6) Low spin: \(t_{2g}\): ↑(1, ↓1), ↑(2, ↓2), ↑(3, ↓3); \(e_g\): ↑(1) b. \(\mathrm{Fe}^{3+}(3d^5)\): (High spin) \(t_{2g}\): ↑(1, ↓1), ↑(2, ↓2), ↑(3, ↓3); \(e_g\): ↑(1), ↑(2) c. \(\mathrm{Ni}^{2+}(3d^8)\): (High spin) \(t_{2g}\): ↑(1, ↓1), ↑(2, ↓2), ↑(3, ↓3); \(e_g\): ↑(1, ↓1), ↑(2, ↓2), ↑(3)

Step by step solution

01

Identify the Electron Configuration of the Metal Ions

The electron configurations for the given metal ions are: a. \(\mathrm{Fe}^{2+}\): [Ar] \(3d^6\) b. \(\mathrm{Fe}^{3+}\): [Ar] \(3d^5\) c. \(\mathrm{Ni}^{2+}\): [Ar] \(3d^8\)
02

Understand the Energy Levels of d-Orbitals in Octahedral Complexes

In an octahedral complex, the five \(d\) orbitals split into two different energy levels: three degenerate orbitals with lower energy, usually written as \(t_{2g}\), and two degenerate orbitals with higher energy, written as \(e_g\).
03

Draw the Diagrams for \(\mathrm{Fe}^{2+}\) in High and Low Spin Cases

For high spin complexes, we fill up the \(d\) orbitals according to the Hund's rule. For low spin complexes, we try to pair electrons in the \(t_{2g}\) orbitals before we fill the \(e_g\) orbitals. a. \(\mathrm{Fe}^{2+}(3d^6)\): High spin: 1. Fill the \(t_{2g}\) orbitals with 3 electrons: ↑(1, ↓1), ↑(2, ↓2), ↑(3, ↓3) 2. Fill the \(e_g\) orbitals with 3 remaining electrons: ↑(4), ↑(5), ↑(6) Low spin: 1. Fill the \(t_{2g}\) orbitals with 5 electrons: ↑(1, ↓1), ↑(2, ↓2), ↑(3, ↓3) 2. Fill the \(e_g\) orbitals with 1 remaining electron: ↑(1)
04

Draw the Diagram for \(\mathrm{Fe}^{3+}\) in a High Spin Complex

b. \(\mathrm{Fe}^{3+}(3d^5)\): High spin: 1. Fill the \(t_{2g}\) orbitals with 3 electrons: ↑(1, ↓1), ↑(2, ↓2), ↑(3, ↓3) 2. Fill the \(e_g\) orbitals with 2 remaining electrons: ↑(1), ↑(2)
05

Draw the Diagram for \(\mathrm{Ni}^{2+}\)

c. \(\mathrm{Ni}^{2+}(3d^8)\): Since it's not specified if it's high or low spin, we will consider the \(\mathrm{Ni}^{2+}\) case in high spin. 1. Fill the \(t_{2g}\) orbitals with 3 electrons: ↑(1, ↓1), ↑(2, ↓2), ↑(3, ↓3) 2. Fill the \(e_g\) orbitals with 5 remaining electrons: ↑(1, ↓1), ↑(2, ↓2), ↑(3) Here, you have filled up the \(d\)-orbitals following basic principles of crystal field theory. These diagrams illustrate the splitting of the \(d\)-orbitals in octahedral complex ions for the given transition metal ions in high and low spin cases.

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Most popular questions from this chapter

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