Problem 14 - Chemistry An Atoms First Approach

Question

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.

Step-by-Step Solution

Answer

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 1: 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.

Step 2: 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.

Step 3: 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).

Step 4: 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.