using CFT,calculate the magnetic CFSE and indicate the spin of [NiCl4]-2

To calculate the magnetic Crystal Field Stabilization Energy (CFSE) for the complex ion [NiCl4]²⁻ using Crystal Field Theory (CFT), we first need to understand the electronic configuration of nickel and how it interacts with the ligands in this tetrahedral complex.

Understanding Nickel's Electron Configuration

Nickel (Ni) has an atomic number of 28, which gives it an electron configuration of [Ar] 3d⁸ 4s². In the case of [NiCl4]²⁻, nickel is in the +2 oxidation state, meaning it loses two electrons. Therefore, the electron configuration for Ni²⁺ becomes [Ar] 3d⁸.

Tetrahedral Complexes and Crystal Field Splitting

In a tetrahedral complex, the arrangement of ligands causes the d-orbitals to split into two sets: the lower energy set (e) and the higher energy set (t₂). The energy difference between these sets is smaller than in octahedral complexes, leading to a different CFSE calculation.

Determining the CFSE

For tetrahedral complexes, the CFSE can be calculated using the formula:

• CFSE = (number of electrons in e_g orbitals) × (0.4 Δ) - (number of electrons in t_2g orbitals) × (0.6 Δ)

In the case of [NiCl4]²⁻, the 3d⁸ configuration will fill the orbitals as follows:

• t₂ orbitals: 6 electrons (3 pairs)
• e orbitals: 2 electrons (1 pair)

Now, we can calculate the CFSE:

• CFSE = (2 × 0.4 Δ) + (6 × 0.6 Δ) = 0.8 Δ + 3.6 Δ = 4.4 Δ

Magnetic Properties and Spin State

Next, we need to determine the spin state of the complex. Since [NiCl4]²⁻ has a d⁸ configuration, we can analyze the electron arrangement:

• In a tetrahedral field, the electrons tend to remain unpaired due to the weaker field strength of the chloride ligands (which are weak field ligands).
• This results in a high-spin configuration, where the electrons occupy the higher energy orbitals before pairing occurs.

For [NiCl4]²⁻, we have 2 unpaired electrons in the t₂ orbitals, leading to a high-spin state. This means that the complex will exhibit paramagnetism due to the presence of unpaired electrons.

Final Summary

In summary, the magnetic CFSE for [NiCl4]²⁻ is calculated to be 4.4 Δ, and the complex has a high-spin state with 2 unpaired electrons, making it paramagnetic. Understanding these concepts helps in predicting the behavior of transition metal complexes in various chemical environments.