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

To determine the electron configuration for each ion, we first need to know the atomic number of each element. Then, we can use the loss of electrons to find the electron configuration for the ion. a. Zn²⁺: Zinc has 30 electrons in its neutral state. When it loses 2 electrons, the configuration is as follows: \([Ar] 3d^8\) b. Co²⁺: Cobalt has 27 electrons in its neutral state. When it loses 2 electrons, the configuration is as follows: \([Ar] 3d^7\) c. Ti³⁺: Titanium has 22 electrons in its neutral state. When it loses 3 electrons, the configuration is as follows: \([Ar] 3d^1\)

In an octahedral complex, the energy level of the d-orbitals splits into two sets: \(t_{2g}\) orbitals (lower energy) and \(e_g\) orbitals (higher energy). The \(t_{2g}\) orbitals include the \(d_{xy}\), \(d_{yz}\), and \(d_{xz}\) orbitals, while the \(e_g\) orbitals include the \(d_{z^2}\) and \(d_{x^2 - y^2}\) orbitals. We will fill the electrons according to the electron configurations obtained in step 1. a. Zn²⁺: \([Ar] 3d^8\) Place 8 electrons in the d-orbitals, respecting the Hund's rule and the Pauli exclusion principle: \(t_{2g}\): ↑↓, ↑↓, ↑↓ \(e_g\) : ↑↓, ↑ b. Co²⁺: \([Ar] 3d^7\) Place 7 electrons in the d-orbitals: Low-spin: \(t_{2g}\): ↑↓, ↑↓, ↑↓ \(e_g\) : ↑↑, 0 High-spin: \(t_{2g}\): ↑, ↑, ↑ \(e_g\) : ↑, ↑ c. Ti³⁺: \([Ar] 3d^1\) Place 1 electron in the d-orbitals: \(t_{2g}\): ↑, 0, 0 \(e_g\) : 0, 0