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Chapter 20: Problem 14

Tetrahedral complexes of \(\mathrm{Co}^{2+}\) are quite common. Use a \(d\) -orbital splitting diagram to rationalize the stability of \(\mathrm{Co}^{2+}\) tetrahedral complex ions.

Short Answer

Expert verified
The stability of Co^2+ tetrahedral complex can be rationalized using the d-orbital splitting diagram. In a tetrahedral complex, the d-orbitals split into two energy levels: the lower energy level t_2 set (triply degenerate) and the higher energy level e set (doubly degenerate). Co^2+ has an electron configuration of [Ar] 3d^7, which, when filled according to Hund's rule and Aufbau principle, results in a high-spin configuration that minimizes the overall energy. The stability of the complex is due to the fully filled t_2 orbitals, which have lower energy, and partially filled e orbitals with higher energy lone pairs.

Step by step solution

01

Identify the Electronic Configuration of Co^2+

Co (cobalt) has an atomic number of 27, which gives it an electron configuration of Co: [Ar] 3d^7 4s^2. When Co becomes Co^2+, it loses two electrons, resulting in the electron configuration of Co^2+: [Ar] 3d^7.
02

Examine the d-orbital Splitting in Tetrahedral Complex

In a tetrahedral complex, the d-orbital splitting is different than that of an octahedral complex. The d-orbitals split into two energy levels, with three orbitals at a lower energy level (known as the triply degenerate set t_2) and two orbitals at a higher energy level (known as the doubly degenerate set e). The energy gap between these two sets of orbitals is known as the crystal field splitting energy, denoted as Δ_t.
03

Fill the Electron Configuration in the d-orbital Splitting Diagram

Given that Co^2+ has an electron configuration of [Ar] 3d^7, we can now distribute these 7 electrons among the available d-orbitals in the tetrahedral complex according to Hund's rule and Aufbau principle. 1. Fill the lower energy level orbitals (t_2 set) with 3 electrons. 2. Fill the higher energy level orbitals (e set) with the remaining 4 electrons. The d-orbital splitting diagram will show the t_2 set with 3 electrons (fully filled) and the e set with 4 electrons (spread across two orbitals with two lone pairs).
04

Rationalize the Stability of Co^2+ Tetrahedral Complex

Due to the crystal field splitting energy caused by the ligands, tetrahedral complexes lead to lower energy gap (Δ_t) than octahedral complexes. In the case of Co^2+ tetrahedral complex, the high-spin configuration (where no d-orbitals are fully filled) minimizes the overall energy, contributing to the stability of the complex. The t_2 orbitals are fully filled which results in lower energy, while the e orbitals are partially filled with higher energy lone pairs. Hence, the distribution of electrons in the d-orbital splitting diagram rationalizes the stability of the Co^2+ tetrahedral complex.

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Most popular questions from this chapter

The complex ion \(\mathrm{Cu}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}\) has an absorption maximum at around \(800 \mathrm{nm} .\) When four ammonias replace water, \(\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}^{2+},\) the absorption maximum shifts to around \(600 \mathrm{nm} .\) What do these results signify in terms of the relative field splittings of \(\mathrm{NH}_{3}\) and \(\mathrm{H}_{2} \mathrm{O}\) ? Explain.

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