Draw the crystal-field energy-level diagrams and show the placement of electrons for each of the following complexes:
d. [NiCl₄]²⁺ (tetrahedral),

Verified step by step guidance

1. Step 1: Identify the metal ion and its oxidation state. In this case, it's Ni2+. The electron configuration of Ni is [Ar] 3d8 4s2. Since it's in the +2 oxidation state, it loses the 4s electrons, leaving it with [Ar] 3d8.
2. Step 2: Identify the geometry of the complex. In this case, it's tetrahedral. In a tetrahedral complex, the d orbitals split into two energy levels: the higher energy level (e) consists of the dxy, dxz, and dyz orbitals, and the lower energy level (t2) consists of the dz2 and dx2-y2 orbitals.
3. Step 3: Fill in the electrons according to Hund's rule, which states that electrons fill each orbital singly before any orbital gets a second electron. Since Ni2+ has 8 d electrons, fill in the 5 lower energy orbitals first, then the 3 higher energy orbitals.
4. Step 4: Draw the crystal-field energy-level diagram. The lower energy level (t2) should be filled with 5 electrons and the higher energy level (e) should be filled with 3 electrons.
5. Step 5: Remember that the energy difference between the two levels in a tetrahedral complex is smaller than in an octahedral complex, due to the different orientations of the ligands in relation to the d orbitals.

Key Concepts

Crystal Field Theory

Crystal Field Theory (CFT) explains the electronic structure of transition metal complexes by considering the interaction between the metal ion's d-orbitals and the electric fields produced by surrounding ligands. In this theory, the degeneracy of d-orbitals is lifted, leading to different energy levels based on the geometry of the complex, such as octahedral or tetrahedral arrangements.

Tetrahedral Complexes

In tetrahedral complexes, the arrangement of ligands around the central metal ion creates a specific geometry where the d-orbitals split into two sets: the lower-energy e set (dxy, dyz, dzx) and the higher-energy t2 set (dx2-y2, dz2). This splitting is less pronounced than in octahedral complexes, resulting in a smaller energy difference between the orbitals, which influences electron placement and the overall stability of the complex.

Electron Configuration and Placement

The electron configuration of a transition metal ion determines how electrons are distributed among the available d-orbitals. For [NiCl4]2+, nickel is in the +2 oxidation state, leading to a d8 configuration. In a tetrahedral field, the electrons will fill the lower-energy e orbitals first, followed by the higher-energy t2 orbitals, which is crucial for accurately drawing the crystal-field energy-level diagram.