Question

Identify each of the following coordination complexes as either diamagnetic or paramagnetic: (a) \(\left[\operatorname{CoBr}\left(\mathrm{NH}_{3}\right)_{5}\right]^{2+}\) (b) \(\left[\mathrm{W}(\mathrm{CN})_{6}\right]^{3-}\) (c) \(\left[\mathrm{VF}_{6}\right]^{3-}\) (d) \(\left[\mathrm{Rh}(\mathrm{o}-\mathrm{phen})_{3}\right]^{3+}\)

Short answer

(a) \(\left[\operatorname{CoBr}\left(\mathrm{NH}_{3}\right)_{5}\right]^{2+}\): Paramagnetic (b) \(\left[\mathrm{W}(\mathrm{CN})_{6}\right]^{3-}\): Diamagnetic (c) \(\left[\mathrm{VF}_{6}\right]^{3-}\): Paramagnetic (d) \(\left[\mathrm{Rh}(\mathrm{o}-\mathrm{phen})_{3}\right]^{3+}\): Diamagnetic

Step-by-step solution

Determining the Electronic Structure of Each Complex

To determine the electronic structure of the metal ions in each complex, we can use the coordination number and metal ion's oxidation state, as well as the crystal field theory. The crystal field theory helps us predict whether the d orbital electrons will be paired or unpaired. We can then use this information to determine whether the complex is diamagnetic or paramagnetic.

(a) \(\left[\operatorname{CoBr}\left(\mathrm{NH}_{3}\right)_{5}\right]^{2+}\)

For this complex, we see that the metal center is Co (cobalt). The coordination number is 6, with one bromide ligand and five ammonia ligands. In order to determine its oxidation state, we also need to consider the charge of the complex. The overall charge is +2, and the charge of the ligands is -1 (Br-) + 0 (NH3) = -1. Thus, the oxidation state of Co is +3. Cobalt has an atomic number of 27, so its electron configuration is \([Ar] 3d^7 4s^2\). In the +3 oxidation state, its configuration will now be \([Ar] 3d^6\). In a high-spin octahedral complex, the electrons are expected to fill the \(t_{2g}\) and \(e_g\) orbitals as follows: \(\uparrow \downarrow\) in \(t_{2g}\) and then one electron each for the remaining \(e_g\) orbitals, leading to four unpaired electrons. Thus, this complex will be paramagnetic.

(b) \(\left[\mathrm{W}(\mathrm{CN})_{6}\right]^{3-}\)

In this complex, the metal center is W (tungsten), and the coordination number is 6. The overall charge of the complex is -3. Since the ligands all have a charge of -1 (CN-), the sum of the ligand charges is -6, so the oxidation state of W is +3. Tungsten has an atomic number of 74, so its electron configuration is \([Xe] 4f^{14} 5d^4 6s^2\). In the +3 oxidation state, its configuration will now be \([Xe] 4f^{14} 5d^3\). The strong-field ligand (CN-) causes the electrons to pair in the \(t_{2g}\) orbitals, leaving no unpaired electrons. Thus, this complex is diamagnetic.

(c) \(\left[\mathrm{VF}_{6}\right]^{3-}\)

In this complex, the metal center is V (vanadium), and the coordination number is 6. The overall charge of the complex is -3. Since the ligands all have a charge of -1 (F-), the sum of the ligand charges is -6, so the oxidation state of V is +3. Vanadium has an atomic number of 23, so its electron configuration is \([Ar] 3d^3 4s^2\). In the +3 oxidation state, its configuration will now be \([Ar] 3d^2\). The weak-field ligand (F-) allows electrons to fill the \(t_{2g}\) and \(e_g\) orbitals in a high-spin configuration, as follows: two unpaired electrons in the \(t_{2g}\) orbitals. Thus, this complex is paramagnetic.

(d) \(\left[\mathrm{Rh}(\mathrm{o}-\mathrm{phen})_{3}\right]^{3+}\)

In this complex, the metal center is Rh (rhodium), and the coordination number is 6. The overall charge of the complex is +3. Since the ligands are neutral (o-phen), the oxidation state of Rh is also +3. Rhodium has an atomic number of 45, so its electron configuration is \([Kr] 4d^8 5s^1\). In the +3 oxidation state, its configuration will now be \([Kr] 4d^6\). The strong-field ligand (o-phen) causes the electrons to pair in the \(t_{2g}\) orbitals, leaving no unpaired electrons. Thus, this complex is diamagnetic.

Summary

We have determined the following: (a) \(\left[\operatorname{CoBr}\left(\mathrm{NH}_{3}\right)_{5}\right]^{2+}\): Paramagnetic (b) \(\left[\mathrm{W}(\mathrm{CN})_{6}\right]^{3-}\): Diamagnetic (c) \(\left[\mathrm{VF}_{6}\right]^{3-}\): Paramagnetic (d) \(\left[\mathrm{Rh}(\mathrm{o}-\mathrm{phen})_{3}\right]^{3+}\): Diamagnetic

Key concepts

Crystal Field Theory

Crystal Field Theory (CFT) is a model that helps us understand the electronic structure of coordination complexes. It describes how ligands, or molecules that donate electrons to metal ions, affect the energy levels of the metal's d orbitals.

In an octahedral complex, which is common, the metal ion is surrounded by six ligands. This arrangement splits the five d orbitals into two groups: three lower-energy orbitals (\(t_{2g}\)) and two higher-energy orbitals (\(e_g\)). This splitting changes the electron configuration and ultimately influences whether a complex is paramagnetic or diamagnetic.

Ligands can be strong-field or weak-field. Strong-field ligands, like CN⁻, cause a larger splitting and usually lead to paired electrons in the \(t_{2g}\) orbitals, making the complex diamagnetic. Weak-field ligands, like F⁻, cause smaller splitting, allowing unpaired electrons in \(e_g\), leading typically to a paramagnetic complex. Understanding these interactions is key to predicting the magnetic properties of coordination complexes.

Electron Configuration

The electron configuration of a metal in a coordination complex determines its chemical behavior and properties. It describes the distribution of electrons among different orbitals. When a metal forms a complex, its oxidation state changes, affecting its electron configuration.

Take cobalt (Co) as an example, where it starts from its ground state \([Ar] 3d^7 4s^2\). If in a complex with an oxidation state of +3, the electron configuration becomes \([Ar] 3d^6\). This change directly impacts how electrons fill available orbitals, influenced by ligand strength.

• A strong-field ligand in a low-spin complex will often result in electron pairing in the lower-energy \(t_{2g}\) orbitals.
• A weak-field ligand in a high-spin complex often allows electrons to occupy both \(t_{2g}\) and \(e_g\) orbitals without pairing.

This knowledge allows chemists to predict whether the complex will exhibit magnetism and how it might interact with other chemical species.

Magnetism in Chemistry

Magnetism in chemistry mainly arises from the presence or absence of unpaired electrons in the coordination complex. It helps in classifying substances as either diamagnetic or paramagnetic.

Diamagnetic substances have all their electrons paired, which results in no net magnetic moment. They are slightly repelled by a magnetic field. For example, a complex like \([\mathrm{W}(\mathrm{CN})_{6}]^{3-}\) has strong-field ligands causing all electrons to pair, resulting in diamagnetism.

Paramagnetic substances have one or more unpaired electrons, leading to a magnetic moment and attraction to an external magnetic field. An example is \([\operatorname{CoBr}(\mathrm{NH}_{3})_{5}]^{2+}\), where weak-field ligands allow electrons to remain unpaired.

These magnetic properties offer insights into molecular structure and bonding, making them important tools in both theoretical and applied chemistry.