Question

The complex ion \(\mathrm{NiCl}_{4}^{2-}\) has two unpaired electrons, whereas \(\mathrm{Ni}(\mathrm{CN})_{4}{ }^{2-}\) is diamagnetic. Propose structures for these two complex ions.

Short answer

The proposed structures for the two complex ions are: 1. \(NiCl_{4}^{2-}\): Tetrahedral structure with two unpaired electrons due to weak field ligands (chloride ions). 2. \(Ni(CN)_{4}^{2-}\): Square planar structure with no unpaired electrons due to strong field ligands (cyanide ions).

Step-by-step solution

Determine the oxidation state

First, we need to determine the oxidation state of the nickel (Ni) in both complex ions. For \(NiCl_{4}^{2-}\): 4 chloride ions, each with a -1 charge, results in a total charge of -4. So the nickel must have an oxidation state of +2 to compensate and give an overall charge of -2 for the ion. For \(Ni(CN)_{4}^{2-}\): 4 cyanide ions, each with a -1 charge, also results in a total charge of -4. In this case, the nickel must also have an oxidation state of +2 to compensate and give an overall charge of -2 for the ion. In both complex ions, the nickel ion has an oxidation state of +2.

Determine the electron configuration

Next, we need to find out the electron configuration of the nickel ion in the +2 oxidation state. The atom Ni has an atomic number of 28, which means it has 28 electrons in its ground state. The electron configuration for the ground state Ni is [Ar]3d^8 4s^2, where [Ar] represents the electron configuration of the argon atom (1s^2 2s^2 2p^6 3s^2 3p^6). When we remove 2 electrons from Ni to obtain the Ni^2+ ion, we get the following electron configuration: \[Ni^{2+}: [Ar]3d^8\]

Apply Crystal Field Theory

Now we will apply Crystal Field Theory (CFT) to each complex ion. CFT is used to describe the interaction between the central metal ion and the ligands in a complex ion. In the case of \(NiCl_{4}^{2-}\), the chlorine ligands are considered weak field ligands. This means that they will not cause a significant splitting of the 3d orbital energy levels. Thus, Ni^2+ with the electron configuration [Ar]3d^8 will have the electrons distributed as such: two sets of paired electrons and two unpaired electrons, satisfying the given condition that \(NiCl_{4}^{2-}\) has two unpaired electrons. The structure proposed for \(NiCl_{4}^{2-}\) is a tetrahedral one (4 ligands). In the case of \(Ni(CN)_{4}^{2-}\), the cyanide ligands are considered strong field ligands. This means that they will cause a significant splitting of the 3d orbital energy levels. The electron configuration of Ni^2+ in a strong field will cause the electrons to pair up in the lower energy d orbitals, resulting in a diamagnetic complex as mentioned in the problem statement. The structure proposed for \(Ni(CN)_{4}^{2-}\) is a square planar one (4 ligands).

Conclusion

The proposed structures for the two complex ions are: 1. \(NiCl_{4}^{2-}\): Tetrahedral structure with two unpaired electrons due to weak field ligands (chloride ions). 2. \(Ni(CN)_{4}^{2-}\): Square planar structure with no unpaired electrons due to strong field ligands (cyanide ions).

Key concepts

Crystal Field Theory

Crystal Field Theory (CFT) is a model that describes the breaking up of degenerate (same energy) d-orbitals in transition metal ions when they form coordination compounds. When ligands approach the central metal ion, the spatial distribution of the ligands around the central ion affects the energy levels of the d-orbitals. Depending on the geometry of the complex, certain orbitals will experience more repulsion and have higher energy than others.

This change in energy levels leads to what we call 'crystal field splitting'. Strong field ligands, like cyanide (CN⁻), cause a significant separation in the d-orbitals' energy, leading to a low-spin configuration where electrons are more likely to pair up in the lower energy orbitals. Weak field ligands, like chloride (Cl⁻), result in a smaller splitting and typically cause a high-spin configuration where electrons will occupy higher energy orbitals to minimize electron pairing.

Electron Configuration

Electron configuration describes the arrangement of electrons around an atomic nucleus according to specific rules. For transition metals, the electron configuration significantly influences their chemistry, including the formation of complex ions. When transition metals like nickel (Ni) form ions, they generally lose their outer s-orbital electrons first before losing d-orbital electrons.

The electron configuration of a free Ni atom is [Ar]3d⁸4s², but once it loses two electrons to become Ni²⁺, the configuration is [Ar]3d⁸. Understanding this is key to predicting magnetic properties and the geometry of the transition metal complexes.

Ligands

Ligands are ions or molecules that bind to a central metal atom to form a coordination complex. They can have different effects on the metal ion's d-orbitals depending on their field strength. Ligands like water, ammonia, and chloride are typical examples of weak field ligands, and they tend to produce high-spin complexes. Conversely, ligands such as cyanide, carbon monoxide, and phosphines are strong field ligands, often creating low-spin complexes.

The number and spatial arrangement of ligands around the metal ion, known as the coordination number and geometry, respectively, determine the shape and properties of the complex. The nature of ligands and their arrangement are crucial in applications such as catalysis, material science, and medicine.

Oxidation State

The oxidation state, also known as the oxidation number, is a concept that allows chemists to keep track of electron transfer in chemical reactions, especially redox reactions. It is essentially a bookkeeping tool that assigns a hypothetical charge to atoms in a molecule or ion if the electrons were assigned to the more electronegative atom. In coordination chemistry, the oxidation state of the metal center is paramount in determining the overall properties of the complex ion.

The oxidation state helps predict how many electrons are in the d-orbitals of the metal, which influences the magnetism and geometry of the complex. For instance, a nickel ion (Ni) in a +2 oxidation state, as in the complex ions NiCl₄²⁻ and Ni(CN)₄²⁻, will have different physical and chemical properties based on the ligands attached and their respective field strengths.