Problem 51 - Chemistry The Science in Context

Question

Refining Cobalt One method for refining cobalt involves the formation of the complex ion \(\mathrm{CoCl}_{4}^{2-} .\) This anion is tetrahedral. Is this complex paramagnetic or diamagnetic?

Step-by-Step Solution

Answer

Answer: The cobalt complex ion CoCl4²⁻ is paramagnetic.

Step 1: Find the oxidation state of Co

We are given that the complex ion is \(\mathrm{CoCl}_{4}^{2-}\). There are four chlorine atoms, each having a charge of -1, with the overall charge of the complex being -2. Therefore, the oxidation state of cobalt (Co) must be +2 in order to have a balanced charge in the complex ion.

Step 2: Determine the electron configuration of Co

The atomic number of cobalt is 27, so its ground-state electron configuration is \(1s^22s^22p^63s^23p^64s^23d^7\). When cobalt loses two electrons to form the \(\mathrm{Co}^{2+}\) ion, it will lose both the electrons from the 4s orbital, making the electron configuration of \(\mathrm{Co}^{2+}\) as \(1s^22s^22p^63s^23p^63d^7\).

Step 3: Analyze the complex ion

The tetrahedral \(\mathrm{CoCl}_{4}^{2-}\) complex ion consists of a cobalt ion (Co) coordinated with four chlorine ions (Cl). This complex is formed by the following reaction: $$\mathrm{Co^{2+}} + 4\mathrm{Cl^-} \rightarrow \mathrm{CoCl}_4^{2-}$$ During the complex formation, the d-orbitals of the transition metal ion (Co) are affected by the ligands (Cl) which can cause splitting of the d-orbitals. However, it is important to note that tetrahedral complexes do not experience strong ligand field splitting similar to octahedral complexes. Therefore, we can treat this as a weak-field ligand.

Step 4: Determine the presence of unpaired electrons

The electron configuration of the \(\mathrm{Co}^{2+}\) ion is \(3d^7\). Since the ligand field is weak, that means the complex still has the d orbitals filled according to Hund's rule, with one electron in each orbital until they start to double up. Consequently, we can arrange these 7 electrons in the 5 d orbitals as follows: ↑↓, ↑↓, ↑↓, ↑, ↑. Thus, there are two unpaired electrons present in the \(\mathrm{Co}^{2+}\) ion within the complex.

Step 5: Determine if the complex is paramagnetic or diamagnetic

Since there are unpaired electrons present in the \(\mathrm{Co}^{2+}\) ion within the \(\mathrm{CoCl}_4^{2-}\) complex, we can conclude that the complex is paramagnetic.

Key Concepts

Oxidation State

Understanding the oxidation state of a metal in a complex is a crucial first step when analyzing its chemical behavior. In the context of refining cobalt, we examine the oxidation state of cobalt in the complex \(\mathrm{CoCl}_{4}^{2-}\). Here, cobalt is surrounded by four chloride ions, each carrying a \(-1\) charge. Since the overall charge of the complex ion is \(-2\), we can deduce that cobalt must have an oxidation state of \(+2\). This is because the sum of the oxidation states must equal the overall charge of the complex ion.
This balance can be seen by:

• Cobalt (Co): \(+2\)
• Chloride ions (4 x Cl): \(-1\) each
• Overall complex: \(-2\) charge

This calculation allows us to determine the specific change in electron configuration cobalt undergoes when forming the complex.

Electron Configuration

The electron configuration of an element tells us about the distribution of electrons in an atom's orbitals. This is particularly important in transition metals like cobalt, as the electron configuration influences their chemical properties. Cobalt (Co) has an atomic number of 27, which provides it with 27 electrons in its neutral state. The electron configuration in the ground state is: \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^7\]However, once cobalt forms a \(\mathrm{Co}^{2+}\) ion by losing two electrons, these electrons are removed from the 4s orbital, resulting in:\[1s^2 2s^2 2p^6 3s^2 3p^6 3d^7\]Since the electrons are removed from the outermost shell, the configuration illustrates how the 3d orbitals become the focus during complex formation. This change plays a key role in the future stability and reactivity of cobalt in the complex.

Tetrahedral Complex

The geometry of a metal complex is essential in predicting its chemical behavior and properties. The \(\mathrm{CoCl}_{4}^{2-}\) complex has a tetrahedral shape, which means cobalt is at the center with four chloride ions positioned at the corners of a tetrahedron. This arrangement influences the electronic structure and subsequent reactivity of the complex.
Tetrahedral complexes are characterized by:

• Weak ligand field strength
• No significant d-orbital splitting as observed in octahedral complexes
• Stronger absorption in the visible spectrum, often resulting in different colors

This geometry is critical because it determines the energy state of the d-electrons and therefore affects the overall magnetic properties of the complex.

Paramagnetic and Diamagnetic

Magnetic properties are determined by the presence of unpaired electrons in a complex. The \(\mathrm{CoCl}_{4}^{2-}\) complex specifically demonstrates how electron configuration dictates whether a complex is paramagnetic or diamagnetic.

In the given complex, cobalt is in the \(\mathrm{Co}^{2+}\) state, with an electron configuration \(3d^7\). In a tetrahedral field, due to weak ligand interactions, electrons fill the d-orbitals following Hund's Rule of maximizing unpaired electrons before pairing occurs. Here, the configuration can be represented as:

• \(d^1\)
• \(d^1\)
• \(d^1\)
• \(d^1\)
• \(d^1\)

Thus, leading to unpaired electrons. Hence, the presence of unpaired electrons in the \(\mathrm{Co}^{2+}\) ion renders the \(\mathrm{CoCl}_{4}^{2-}\) complex paramagnetic. This means that the complex is attracted to a magnetic field, in contrast to diamagnetic substances that have all their electrons paired up and exhibit a very weak repulsion to magnetic fields.