Question

The magnetic moment (spin only) of \(\left[\mathrm{NiCl}_{4}\right]^{2-}\) is: \(\quad[\mathbf{2 0 1 1}]\) (a) \(1.41 \mathrm{BM}\) (b) \(5.64 \mathrm{BM}\) (c) \(1.28 \mathrm{BM}\) (d) \(2.82 \mathrm{BM}\)

Short answer

The magnetic moment of \(\left[\mathrm{NiCl}_{4}\right]^{2-}\) is \(2.82 \mathrm{BM}\).

Step-by-step solution

Identify the oxidation state of Ni

In the complex \(\left[ \text{NiCl}_4 \right]^{2-}\), chlorine (Cl) is a monodentate ligand and typically carries a charge of -1. Let the oxidation state of Ni be \(x\). Then, setting up the equation: \[ x + 4(-1) = -2 \]. Solving for \(x\), we find the oxidation state of Ni is +2.

Determine the electron configuration of Ni

The atomic number of nickel (Ni) is 28, and its neutral atom electron configuration is \([\text{Ar}] 3d^{8} 4s^{2}\). In the +2 oxidation state, two electrons are lost, usually from the 4s and the 3d orbitals, resulting in \([\text{Ar}] 3d^{8}\).

Identify the geometry and type of ligand

\(\left[\text{NiCl}_4\right]^{2-}\) is a tetrahedral complex, as it is coordinated with four chloride ions (weak field ligands). In a tetrahedral field, there is less splitting of d-orbitals, and no pairing of electrons occurs as it is typically high spin.

Count the unpaired electrons in Ni

In the \([\text{Ar}] 3d^{8}\) configuration for a tetrahedral complex, we find that the distribution of electrons in the \(3d\) orbitals will not fill completely due to the weak field, resulting in two unpaired electrons.

Calculate the magnetic moment

The magnetic moment \((\mu)\) of a complex can be calculated using the formula \(\mu = \sqrt{n(n+2)} \text{ BM}\), where \(n\) is the number of unpaired electrons. Here, \(n=2\), so: \[\mu = \sqrt{2(2+2)} = \sqrt{8} = 2.82 \text{ BM}\].

Key concepts

Nickel Complexes

Nickel complexes are fascinating and pivotal in the field of coordination chemistry. Nickel, being a transition metal, forms a variety of complexes with different ligands. When nickel ions combine with ligands such as chloride (iCl_{4}]^{2-}), they create what we know as nickel complexes.
One of the primary tasks when analyzing nickel complexes is determining the oxidation state of nickel. As seen in iCl_{4}]^{2-}, chloride ions are monodentate ligands. Each carries a -1 charge, leading us to deduce that the nickel ion must counterbalance this with a +2 charge to achieve the overall -2 charge of the complex.
Nickel complexes are particularly intriguing due to their magnetic properties. Their ability to exhibit a magnetic moment greatly depends on their structure and the nature of the ligands involved. Understanding these interactions helps in exploring their wide array of applications, from catalysis to material science.

Tetrahedral Geometry

In coordination chemistry, geometry plays a crucial role in determining the properties of complexes. For the iCl_{4}]^{2-} complex, the geometry is tetrahedral. This means that the nickel ion is surrounded by four chloride ions arranged at the corners of a tetrahedron.
The consideration of tetrahedral geometry is key because it influences the energy levels and the distribution of electrons within the complex. In a tetrahedral field, the d-orbitals split into two sets of orbitals with different energy levels. However, the energy splitting is less than that observed in octahedral complexes, and thus, they generally exhibit high-spin configurations.
Understanding the geometry is essential for predicting several chemical and physical properties like color, reactivity, and particularly, magnetic properties. In this case, the tetrahedral geometry, combined with weak field ligands such as chloride ions, results in unpaired electrons and a noticeable magnetic moment.

Electron Configuration

Electron configuration is integral to deciphering the behavior of transition metal complexes like iCl_{4}]^{2-}. Nickel, with an atomic number of 28, normally possesses the electron configuration r] 3d^{8} 4s^{2}. However, in the +2 oxidation state, two electrons are removed, generally from the 4s orbital and one from the 3d orbital, resulting in r] 3d^{8}.
This configuration is especially telling when assessing the magnetic and spectroscopic properties of the complex. For the tetrahedral iCl_{4}]^{2-}, the ^{8}] configuration means that electrons fill the lower-energy d-orbitals first, but sufficient orbital splitting still results in unpaired electrons.
Such nuances in electron configuration emphasize the function of electronic structure analysis in predicting properties such as magnetic moments. Each electron not only contributes to chemical bonding but also largely affects how these complexes interact with external magnetic fields.

Unpaired Electrons

Unpaired electrons serve as the primary reason behind the magnetic properties of transition metal complexes. In the iCl_{4}]^{2-} configuration, the electron configuration of r] 3d^{8}] results in two unpaired electrons.
Unpaired electrons in the d-orbitals create magnetic moments through their spins. The presence of unpaired electrons indicates a high-spin state, especially in tetrahedral geometries with weak field ligands like chloride. This is because there is less splitting energy, which leads to a situation where the electrons avoid pairing.
Calculating the number of unpaired electrons allows us to estimate the magnetic moment using the formula u = sqrt{n(n+2)} BM], where n is the number of unpaired electrons. This leads us to the calculation observed in the exercise, determining that the magnetic moment for iCl_{4}]^{2-} is 2.82 BM. Understanding unpaired electrons gives insight into how external magnetic influences might alter or interact with the complex.