Chapter 21: Problem 84
Would the complex \(\left[\mathrm{Cr}(\mathrm{CN})_{6}\right]^{4-}\) more likely be low spin or high spin? Could it be diamagnetic?
Short Answer
Expert verified
The complex \(\left[\mathrm{Cr}(\mathrm{CN})_{6}\right]^{4-}\) is likely to be low spin due to cyanide being a strong field ligand, and could potentially be diamagnetic if all electrons are paired.
Step by step solution
01
Identify the ligand
The first step is to identify the ligand attached to the central metal ion. In \(\left[\mathrm{Cr}(\mathrm{CN})_{6}\right]^{4-}\), the ligand is cyanide (CN).
02
Determine the strength of the ligand
Cyanide is a strong field ligand according to the spectrochemical series. This typically means it can cause a large splitting in the d-orbital energy levels of the central metal ion.
03
Examine the electron configuration
The central metal ion here is chromium (Cr) with an atomic number of 24. In its +2 oxidation state (as implied by the 4- charge on six -1 cyanide ligands), Cr would have an electron configuration of \(3d^4\).
04
Determine the spin state
Because cyanide is a strong field ligand, it promotes pairing of electrons. This increases the likelihood that \(\left[\mathrm{Cr}(\mathrm{CN})_{6}\right]^{4-}\) will be low spin, with paired electrons occupying the lower energy d-orbitals first.
05
Consider the possibility of diamagnetism
For a complex to be diamagnetic, all electrons must be paired. In the case of a d^4 configuration under a strong field, it is possible that all electrons will be paired, resulting in a diamagnetic complex. The actual electronic configuration and diamagnetism can be further confirmed by crystal field theory and magnetic susceptibility measurements.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Ligand Field Theory
Ligand Field Theory is a fundamental concept in coordination chemistry, which explains the bonding, electronic structure, and magnetic properties of coordination complexes. It's an adaptation of molecular orbital theory that focuses on the metal ion and its surrounding ligands.
To visualize this, imagine the central metal ion as the sun with ligands orbiting around it like planets. The theory describes how these 'planets' can influence the energy levels of the 'sun', causing shifts that affect properties like color and magnetism.
In practice, when a ligand like cyanide approaches a transition metal ion, it interacts with the d-orbitals of the metal, generating a field that splits these orbitals into separate energy levels. This splitting decides whether electrons in the complex will pair up in lower energy levels or remain unpaired, which in turn dictates magnetic properties and the spin state of the complex.
To visualize this, imagine the central metal ion as the sun with ligands orbiting around it like planets. The theory describes how these 'planets' can influence the energy levels of the 'sun', causing shifts that affect properties like color and magnetism.
In practice, when a ligand like cyanide approaches a transition metal ion, it interacts with the d-orbitals of the metal, generating a field that splits these orbitals into separate energy levels. This splitting decides whether electrons in the complex will pair up in lower energy levels or remain unpaired, which in turn dictates magnetic properties and the spin state of the complex.
Electron Spin States
Electron spin states are pivotal in determining the magnetic properties of coordination complexes. Every electron possesses a tiny magnetic field due to its spin, which can be aligned in one of two ways: up or down.
The key to understanding spin states lies in two terms—'high spin' and 'low spin'. These refer to how electrons are distributed across the split d-orbitals. If the ligand creates a small gap between the orbitals, electrons can easily jump to the higher orbitals, retaining their unpaired spins—this is high spin. Conversely, a large gap caused by a strong field ligand often forces electrons to pair up in the lower orbitals to minimize energy, leading to a low spin state.
In the context of the \(\left[\mathrm{Cr}(\mathrm{CN})_{6}\right]^{4-}\) complex, cyanide as a strong field ligand suggests a low spin state, meaning electrons are more likely to pair up in the lower energy levels.
The key to understanding spin states lies in two terms—'high spin' and 'low spin'. These refer to how electrons are distributed across the split d-orbitals. If the ligand creates a small gap between the orbitals, electrons can easily jump to the higher orbitals, retaining their unpaired spins—this is high spin. Conversely, a large gap caused by a strong field ligand often forces electrons to pair up in the lower orbitals to minimize energy, leading to a low spin state.
In the context of the \(\left[\mathrm{Cr}(\mathrm{CN})_{6}\right]^{4-}\) complex, cyanide as a strong field ligand suggests a low spin state, meaning electrons are more likely to pair up in the lower energy levels.
Diamagnetism
Diamagnetism is a property of materials that do not have any unpaired electrons and are repelled by an external magnetic field. It's like having a crowd where everyone has found a dance partner, eliminating any magnetism that might arise from a single spinning electron.
Coordination complexes can exhibit diamagnetism if all the electrons in the metal ion's d-orbitals are paired. This creates a stable, non-magnetic complex—essentially the opposite of what you'd find in a bar magnet.
The complex in question, \(\left[\mathrm{Cr}(\mathrm{CN})_{6}\right]^{4-}\), could potentially be diamagnetic if, under the influence of the strong field cyanide ligands, all of its chromium's d-electrons are paired. This would mean that the complex would have no net magnetic field and would be repelled by a magnet.
Coordination complexes can exhibit diamagnetism if all the electrons in the metal ion's d-orbitals are paired. This creates a stable, non-magnetic complex—essentially the opposite of what you'd find in a bar magnet.
The complex in question, \(\left[\mathrm{Cr}(\mathrm{CN})_{6}\right]^{4-}\), could potentially be diamagnetic if, under the influence of the strong field cyanide ligands, all of its chromium's d-electrons are paired. This would mean that the complex would have no net magnetic field and would be repelled by a magnet.
Coordination Complexes
Coordination complexes are molecules formed by ions or molecules bound to a central atom, typically a transition metal. They are like a grand ball with a central dignitary—the metal ion—surrounded by an entourage of guests—the ligands.
These complexes, with their diverse structures and ligands, lead to various applications in colorimetry, catalysis, and even in medicine. The nature of the ligands, their strength, and the geometry of the complex play critical roles in defining the chemical behavior and properties of the complex.
The complex \(\left[\mathrm{Cr}(\mathrm{CN})_{6}\right]^{4-}\) exemplifies the intricate dance of interactions that define coordination chemistry. Here, the cyanide ions are the ligands coordinating with the central chromium ion, and their behavior can dramatically influence the complex's properties, such as its magnetic moment and ability to absorb light.
These complexes, with their diverse structures and ligands, lead to various applications in colorimetry, catalysis, and even in medicine. The nature of the ligands, their strength, and the geometry of the complex play critical roles in defining the chemical behavior and properties of the complex.
The complex \(\left[\mathrm{Cr}(\mathrm{CN})_{6}\right]^{4-}\) exemplifies the intricate dance of interactions that define coordination chemistry. Here, the cyanide ions are the ligands coordinating with the central chromium ion, and their behavior can dramatically influence the complex's properties, such as its magnetic moment and ability to absorb light.
Electronic Configuration of Transition Metals
Transition metals have incompletely filled d-orbitals, which allows them to form various oxidation states and thus, diverse coordination complexes. Understanding a transition metal's electronic configuration is like knowing a person's resume—it can tell you a lot about their potential abilities and behavior.
For example, chromium (Cr), with its atomic number 24, usually presents an electron configuration of \(3d^5 4s^1\). However, when forming a complex, the metal ion's electrons are often shuffled to lower energy levels, leading to a different electronic configuration.
The \(\left[\mathrm{Cr}(\mathrm{CN})_{6}\right]^{4-}\) complex has chromium in a +2 oxidation state, so its new 'resume' would read \(3d^4\), shedding two electrons that were in the higher energy 4s and 3d orbitals. This underpins the importance of electron arrangements in predicting the magnetic and optical behavior of the complex.
For example, chromium (Cr), with its atomic number 24, usually presents an electron configuration of \(3d^5 4s^1\). However, when forming a complex, the metal ion's electrons are often shuffled to lower energy levels, leading to a different electronic configuration.
The \(\left[\mathrm{Cr}(\mathrm{CN})_{6}\right]^{4-}\) complex has chromium in a +2 oxidation state, so its new 'resume' would read \(3d^4\), shedding two electrons that were in the higher energy 4s and 3d orbitals. This underpins the importance of electron arrangements in predicting the magnetic and optical behavior of the complex.
