Problem 59 - Chemistry: The Central Science in SI Units, Global Edition

Question

A classmate says, “A weak-field ligand usually means the complex is high spin." Is your classmate correct? Explain.

Step-by-Step Solution

Answer

Yes, your classmate is correct. Weak-field ligands cause a small splitting of the d-orbital energy levels in a transition-metal complex, making it energetically favorable for electrons to occupy higher energy orbitals rather than pairing up in the same orbital. This leads to the formation of high-spin complexes, which follow Hund's rule and have a greater number of unpaired electrons.

Step 1: Understanding Weak-field Ligands and High-spin Complexes

Weak-field ligands are those that cause a small splitting of the d-orbital energy levels in a transition-metal complex. In such a complex, the difference in energy between the d-orbitals is small, and it becomes easy for electrons to be promoted to higher energy orbitals. High-spin complexes are those in which the electrons of a transition-metal complex occupy all available energy levels (orbitals) before going into a double-occupancy state (i.e., two electrons with opposite spins in the same orbital). This behavior follows Hund's rule, which states that for a given electron configuration, the term with maximum multiplicity (greatest number of unpaired electrons) has the lowest energy.

Step 2: Connecting Weak-field Ligands and High-spin Complexes

Weak-field ligands lead to a smaller splitting of d-orbitals, meaning that the energy difference between the orbitals is less significant. Consequently, it becomes energetically favorable for electrons to move up to the higher energy orbital rather than pairing with another electron in the same orbital. This results in the formation of high-spin complexes, with more unpaired electrons occupying the available orbitals.

Step 3: Assessing the Classmate's Statement

The classmate's statement is indeed correct. Generally, weak-field ligands are associated with high-spin complexes, which means that they cause a small splitting of the d-orbital energy levels. As a result, electrons can easily be promoted to higher energy orbitals, giving rise to high-spin complexes with more unpaired electrons occupying the available orbitals according to Hund's rule.

Key Concepts

Weak-field Ligands

In coordination chemistry, ligands are molecules or ions that bind to a central metal atom to form a coordination complex. Understanding weak-field ligands is key to discussing electron configurations and properties of these complexes. Weak-field ligands are characterized by their inability to cause a large energy difference, known as "d-orbital splitting," in the energy levels of metal d-orbitals. When these ligands bind to a metal, they only cause a slight separation in the metal's d-orbitals' energy. This minimal splitting implies that electrons don't need much energy to occupy the higher energy d-orbitals.

• Small separation of d-orbital energies
• Electrons easily fill higher energy orbitals
• Promotes formation of high-spin complexes

Therefore, weak-field ligands are typically linked to high-spin configurations, as electrons are inclined to spread out across all available orbitals, rather than pair up in lower energy orbitals.

High-spin Complexes

High-spin complexes are fascinating in coordination chemistry, primarily involving transition metal ions where the arrangement of electrons is crucial. In these complexes, electrons tend to fill all the available orbitals singly before any one orbital gets a second electron. This is in contrast to low-spin complexes, where electrons prefer to pair up in lower energy orbitals first. Such behavior is because the energy required to pair up two electrons is more than the energy needed to place an electron in a higher orbital, especially when using weak-field ligands.

• Maximizes the number of unpaired electrons
• Occurs when energy cost of splitting is low
• Strongly influenced by weak-field ligands

This results in complexes with maximum spin multiplicity, which corresponds to having more unpaired electrons because energy costs are minimized. High-spin configurations have distinct magnetic properties due to these unpaired electrons.

d-orbital Splitting

The concept of d-orbital splitting is central to understanding why certain transition metal complexes have specific properties. When ligands approach the transition metal, their electrons interact with the d-orbitals of the metal ion, resulting in the division of the five degenerate d-orbitals into sets of different energy levels. This phenomenon is governed by the nature of the ligands and their ability to influence metal electrons. Strong-field ligands cause a large d-orbital splitting, leading to low-spin configurations, while weak-field ligands cause a small splitting, leading to high-spin complexes.

• Five d-orbitals split into different energy levels
• Influenced by the strength of ligands
• Critical in determining spin state

The energy difference created during splitting determines whether electrons will pair up in the lower energy orbitals or occupy the higher ones unpaired. This is essential in assessing magnetic properties and reactivity.

Hund's Rule

Hund's Rule is pivotal in determining how electrons occupy degenerate orbitals (orbitals with the same energy). It states that electrons will fill an empty orbital before pairing up in an occupied one. This rule ensures that electron repulsion is minimized and the stability of the atom or molecule is maximized. In the context of coordination chemistry and high-spin complexes, Hund's Rule helps explain why electrons singly occupy all orbitals before any pairing occurs. It's particularly applicable to complexes where weak-field ligands and minimal d-orbital splitting are involved.

• Maximizes number of unpaired electrons
• Minimizes electron-electron repulsions
• Results in high stability

This principle helps predict and rationalize the magnetic and electron distribution properties of coordination complexes, reinforcing why weak-field ligands often lead to high-spin situations.