Question

Which of the following complexes are diamagnetic? (a) \(\left[\mathrm{Ni}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2}\) (b) \(\left[\mathrm{Co}(\mathrm{CN})_{6}\right]^{3}\) (c) \(\left[\mathrm{HgI}_{4}\right]^{2}\) (d) \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\)

Short answer

Complexes (b) and (c) are diamagnetic.

Step-by-step solution

Understanding Diamagnetism

Diamagnetic substances have all paired electrons, meaning there are no unpaired electrons in their electron configuration. We need to determine the electron configuration of each complex to check for unpaired electrons.

Analyze Complex (a)

For \([\mathrm{Ni}(\mathrm{H}_{2}\mathrm{O})_{6}]^{2+}\), nickel is in a +2 oxidation state. The electron configuration for \(\mathrm{Ni}^{2+}\) is \([\mathrm{Ar}]\ 3d^8\). In an octahedral field with water as a ligand (weak field), it does not cause pairing of electrons. Thus, there are 2 unpaired electrons, making this complex paramagnetic.

Analyze Complex (b)

For \([\mathrm{Co}(\mathrm{CN})_{6}]^{3-}\), cobalt is in a +3 oxidation state. The electron configuration for \(\mathrm{Co}^{3+}\) is \([\mathrm{Ar}]\ 3d^6\). \(\mathrm{CN}^-\) is a strong field ligand, causing electron pairing in the \(3d\) orbitals. This results in 0 unpaired electrons, making the complex diamagnetic.

Analyze Complex (c)

For \([\mathrm{HgI}_{4}]^{2-}\), mercury is in a +2 oxidation state. The electron configuration for \(\mathrm{Hg}^{2+}\) is \([\mathrm{Xe}]\ 4f^{14}\ 5d^{10}\). All electrons are paired in \(5d\) sublevel, making this complex diamagnetic.

Analyze Complex (d)

For \([\mathrm{Cu}(\mathrm{NH}_{3})_{4}]^{2+}\), copper is in a +2 oxidation state. The electron configuration for \(\mathrm{Cu}^{2+}\) is \([\mathrm{Ar}]\ 3d^9\). \(\mathrm{NH}_{3}\) is a medium strength field ligand and does not cause pairing of the 9th electron, leading to 1 unpaired electron in \(3d\). Thus, this complex is paramagnetic.

Key concepts

Electron Configuration

Electron configuration is the arrangement of electrons around the nucleus of an atom in its atomic orbitals. Understanding electron configurations helps us predict an atom's chemical behavior and its interactions in forming compounds. Core electrons are tightly bound to the atom, whereas valence electrons are involved in interactions and reactions. For transition metals, the d-orbital plays a significant role. For example, Nickel in a +2 oxidation state has the electron configuration \[ [\text{Ar}]\ 3d^8 \] This indicates that two electrons are removed from the 4s orbital. Correctly assigning electron configurations helps determine whether substances are diamagnetic or paramagnetic by revealing paired or unpaired electrons.

Paramagnetic

Paramagnetism occurs in substances that have one or more unpaired electrons. The presence of unpaired electrons in a material allows it to be attracted to a magnetic field. For instance, the complex \( \left[\text{Ni}(\text{H}_2\text{O})_6\right]^{2+} \) has nickel in a +2 oxidation state, leading to an electron configuration of \[ [\text{Ar}]\ 3d^8 \] In Ni, the electrons do not completely pair in the presence of water, a weak-field ligand, resulting in paramagnetism. Other examples include compounds where medium or weak ligands prevent complete pairing, leading to a magnetic moment due to unpaired electrons.

Oxidation State

The oxidation state is a concept used to describe the electrons transfer in the formation of a chemical compound. It is defined as the hypothetical charge that an atom would have if all bonds were ionic. Understanding the oxidation state of a metal within a complex is crucial for determining electron configuration and magnetic properties. For example, in \( \left[\text{Co}(\text{CN})_6\right]^{3-} \), the cobalt is in a +3 oxidation state. With the electron configuration \[ [\text{Ar}]\ 3d^6 \] paired due to the strong field ligand CN⁻, it leads to a diamagnetic compound because all electrons are paired, indicating no net magnetic moment.

Ligands in Coordination Complexes

Ligands are ions or molecules that donate a pair of electrons to the central metal atom, forming coordinate bonds and creating a coordination complex. The nature of the ligand affects the electron configuration of the metal.

• Strong field ligands, such as CN⁻, can cause electron pairing in the d orbitals.
• Weak field ligands, like H₂O, often do not cause such pairing, leaving some electrons unpaired.

For example, in \( \left[\text{Co}(\text{CN})_6\right]^{3-} \), CN⁻ is a strong field ligand, resulting in all electrons being paired in the 3d orbitals, making the complex diamagnetic. Understanding the role of ligands is essential in predicting the magnetic properties and stability of the complex.