Question

The \(\operatorname{Co}\left(\mathrm{NH}_{3}\right)_{6}^{3+}\) ion is diamagnetic, but \(\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}\) is para-magnetic. Explain.

Short answer

The \(\operatorname{Co}\left(\mathrm{NH}_{3}\right)_{6}^{3+}\) ion is diamagnetic because Co(III) has no unpaired electrons in its d orbitals with an electronic configuration of \([Ar]~3d^6\). On the other hand, the \(\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}\) ion is para-magnetic because Fe(II) has one unpaired electron in its d orbitals with an electronic configuration of \([Ar]~3d^4\).

Step-by-step solution

Determine the oxidation states of the central metal ions

Our first step is to determine the oxidation states of the cobalt (Co) and iron (Fe) in the given complexes. 1. \(\operatorname{Co}\left(\mathrm{NH}_{3}\right)_{6}^{3+}\) has a charge of \(+3\). Since \(\mathrm{NH}_{3}\) is a neutral ligand, the oxidation state of Co in this complex is +3. 2. \(\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}\) has a charge of +2. Since \(\mathrm{H}_{2}\mathrm{O}\) is a neutral ligand, the oxidation state of Fe in this complex is +2.

Determine the electronic configurations of Co(III) and Fe(II)

Now, let's find the electronic configurations for Co(III) and Fe(II). 1. Co: The atomic number of Co is 27, so the ground state electronic configuration is \([Ar]~4s^2~3d^7\). When Co loses three electrons to reach an oxidation state of +3, its electronic configuration becomes \([Ar]~3d^6\). 2. Fe: The atomic number of Fe is 26, so the ground state electronic configuration is \([Ar]~4s^2~3d^6\). When Fe loses two electrons to reach an oxidation state of +2, its electronic configuration becomes \([Ar]~3d^4\).

Determine the presence or absence of unpaired electrons in the given complexes

Now, let's fill the d orbitals with the electrons in Co(III) and Fe(II) and determine if there are any unpaired electrons. 1. Co(III): Since cobalt is in the +3 oxidation state, it has six d electrons (\(3d^6\)). According to the Aufbau principle and Hund's rule, the d electrons will occupy the five 3d orbitals in the following configuration: \[↓↓~↓↓~↓↓~0~0\] As we can see, there are no unpaired electrons in Co(III). 2. Fe(II): Since iron is in the +2 oxidation state, it has four d electrons (\(3d^4\)). Again, according to the Aufbau principle and Hund's rule, the d electrons will occupy the five 3d orbitals in the following configuration: \[↓↓~↓↓~↑~0~0\] As we can see, there is one unpaired electron in Fe(II).

Explain the magnetic properties of the given complexes

We will now explain the magnetic properties of the complexes based on the presence or absence of unpaired electrons. 1. \(\operatorname{Co}\left(\mathrm{NH}_{3}\right)_{6}^{3+}\): Since there are no unpaired electrons in Co(III), the complex will be diamagnetic, meaning it will not be attracted to an external magnetic field. 2. \(\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}\): Since there is one unpaired electron in Fe(II), the complex will be para-magnetic, meaning it will be attracted to an external magnetic field. In conclusion, the \(\operatorname{Co}\left(\mathrm{NH}_{3}\right)_{6}^{3+}\) ion is diamagnetic because Co(III) has no unpaired electrons in its d orbitals, while the \(\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}\) ion is para-magnetic because Fe(II) has one unpaired electron in its d orbitals.

Key concepts

Diamagnetism and Paramagnetism

The magnetic properties of coordination compounds, such as diamagnetism and paramagnetism, are primarily determined by the presence of unpaired electrons in their d orbitals.

Diamagnetic substances have all their electrons paired and, as a result, they develop a magnetic moment of zero. In a magnetic field, diamagnetic compounds are weakly repelled since they induce a magnetization opposite to the applied field.

Conversely, paramagnetic substances contain one or more unpaired electrons, which give rise to a magnetic moment. These unpaired electrons generate individual magnetic fields, and when an external magnetic field is applied, the substance is attracted towards it. The strength of paramagnetism is directly proportional to the number of unpaired electrons.

For example, iron(II) in \( \text{Fe}\left(\text{H}_2 \text{O}\right)_6^{2+}\) displays one unpaired electron and shows paramagnetic behavior, while cobalt(III) in \( \text{Co}\left(\text{NH}_3\right)_6^{3+}\) contains no unpaired electrons and is diamagnetic.

Oxidation States of Transition Metals

Understanding the oxidation states of transition metals is crucial in determining their electronic configurations, which in turn affects their magnetic and chemical properties. The oxidation state, also known as oxidation number, reflects the degree of oxidation of an atom in a compound.

• Neutral ligands, such as water (\(\text{H}_2\text{O}\)) and ammonia (\(\text{NH}_3\)), do not affect the oxidation state of the central metal.
• Anionic ligands increase the negative charge of the complex, raising the oxidation state of the metal.
• Cationic ligands decrease the oxidation state by contributing positive charge to the complex.

The overall charge of a coordination compound is the sum of the oxidation state of the central metal and the charge carried by the ligands. The oxidation states are integral in predicting the reactivity and bonding in metal complexes.

Electronic Configuration of Metal Ions

The electronic configuration of metal ions is determined by the number of electrons that reside in the outer shells, particularly the d orbitals, after the metal has lost a certain number of electrons to achieve its oxidation state.

For instance, cobalt (Co) has an atomic number of 27. In its neutral state, Co has 27 electrons, with 7 of them in the 3d orbitals. As \( \text{Co}^{3+}\), it loses three electrons, resulting in a \( 3d^6 \) electronic configuration. This configuration has all electrons paired and thus, the ion is diamagnetic.

On the other hand, iron (Fe) has an atomic number of 26. As \( \text{Fe}^{2+}\), it loses two electrons, leading to a \( 3d^4 \) configuration. With one unpaired electron remaining, this accounts for the Fe(II) ion's paramagnetic nature. This treatment of electronic configuration forms the basis for predicting the magnetic properties of transition metal complexes.

Ligand Field Theory

Ligand Field Theory provides a deeper understanding of how ligands affect the distribution of electrons in the d orbitals of transition metal ions, impacting their color, magnetism, and reactivity.

According to this theory, ligands surrounding a metal ion create an electric field that splits the d orbitals into different energy levels. Non-degenerate orbitals (those at different energy levels) experience crystal field splitting. For example, in an octahedral complex, the d orbitals split into two sets: the lower-energy \( t_{2g} \) orbitals and the higher-energy \( e_g \) orbitals.

The arrangement of electrons within these orbitals after the crystal field splitting determines the strength of the complex's magnetic fields and its magnetic properties. Field strength of ligands and their ability to cause splitting can drastically change the magnetic moments of coordination compounds, which explains why seemingly similar compounds can exhibit such varying magnetic behaviors.