Problem 21 - General Chemistry: Principles and Modern Applications

Question

Predict: (a) which of the complex ions, \(\left[\mathrm{MoCl}_{6}\right]^{3-}\) and \(\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+},\) is diamagnetic and which is paramagnetic; (b) the number of unpaired electrons expected for the tetrahedral complex ion \(\left[\mathrm{CoCl}_{4}\right]^{2-}\).

Step-by-Step Solution

Answer

\(\left[\mathrm{MoCl}_{6}\right]^{3-}\) and \(\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+}\) are both diamagnetic. \(\left[\mathrm{CoCl}_{4}\right]^{2-}\) has 3 unpaired electrons.

Step 1: Define magnetic property

First, remember the definitions for paramagnetic and diamagnetic substances. A diamagnetic substance is one that does not have any unpaired electrons and is not attracted to a magnetic field. On the other hand, paramagnetic substances do have unpaired electrons and are attracted to a magnetic field.

Step 2: Find the Electron Configuration for each Complex

Find the electron configuration for the central atom in each complex. For \(\left[\mathrm{MoCl}_{6}\right]^{3-}\), Mo (molybdenum) has 42 electrons but the oxidation state here is +3, thus it has 36 valence electrons, which are all paired. For \(\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+}\), Co (cobalt) has 27 electrons and oxidation state of +3, thus left 24 electrons which are all paired as well.

Step 3: Determine the Type of Magnetic Properties

Since both molybdenum and cobalt have all paired electrons, both \(\left[\mathrm{MoCl}_{6}\right]^{3-}\) and \(\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+}\) are diamagnetic.

Step 4: Electron Configuration for the Second Part

For the tetrahedral complex ion \(\left[\mathrm{CoCl}_{4}\right]^{2-}\), cobalt has 27 electrons with oxidation state of +2, which leaves us with 25 electrons. In the tetrahedral complex, cobalt doesn't pair its electrons.

Step 5: Determining the Number of Unpaired Electrons

Since cobalt doesn't pair its electrons in the tetrahedral complex, it has 3 unpaired electrons after we fill up the electron orbitals.

Key Concepts

Paramagnetic vs Diamagnetic

Understanding the difference between paramagnetic and diamagnetic substances is vital in coordination chemistry. - **Paramagnetic substances** are those that are attracted to magnetic fields due to the presence of unpaired electrons. - **Diamagnetic substances** have all their electrons paired up and are not attracted to magnetic fields. Electrons are like tiny magnets, and their magnetic effects cancel each other out when paired. However, when electrons are unpaired, their magnetic fields add up, making materials paramagnetic. Identifying whether a compound is paramagnetic or diamagnetic provides insights into the electron arrangement within the compound.

Unpaired Electrons

Unpaired electrons play a crucial role in determining the magnetic properties of complexes. When examining a complex ion, assess the number of unpaired electrons:- If the complex has unpaired electrons, it is likely paramagnetic.- If all electrons are paired, the complex is diamagnetic.Let's consider the tetrahedral complex ion \( [\text{CoCl}_4]^{2-} \). Cobalt in this complex has an oxidation state of +2, so you deal with 25 electrons. In a tetrahedral arrangement, fewer ligands mean a weaker crystal field, allowing for unpaired electrons to exist.This specific arrangement often leads to several unpaired electrons in metal complexes, influencing both magnetic properties and reactivity.

Coordination Chemistry

Coordination chemistry explores how transition metals form complexes with various ligands. - Central metal ions are surrounded by molecules or ions, called ligands. - Ligands can affect a complex's electron configuration, magnetic properties, and color.Consider the complex \( [\text{Co(en)}_3]^{3+} \). Cobalt is at the center with ethylenediamine (en) as a ligand. This type of ligand offers stronger crystal fields, which means it is likely to pair up the electrons in cobalt's d-orbitals, leading to diamagnetism.Coordination chemistry provides insight into the versatility and adaptability of chemical bonding around transition metals.

Electron Configuration in Complexes

The electron configuration of central atoms within complexes dictates the magnetic properties and stability. Let's break it down:- Each transition metal has a unique electron configuration contributing to its characteristics.- Oxidation state adjustments lead to changes in electron counts, dictating magnetic nature. - Crystal field theory suggests that ligands influence the electron arrangement in available orbitals, affecting magnetic properties.For instance, molybdenum in \( [\text{MoCl}_6]^{3-} \) has a configuration that results in all paired electrons in its d-orbitals because it has been oxidized to +3, leaving behind 36 electrons. These pair easily, leading to diamagnetism. Understanding electron fill patterns such as these is fundamental in coordination chemistry.