Question

Arrange the following ligands in order of increasing field strength: \(\mathrm{Br}^{-}, \mathrm{F}^{-},[\mathrm{CN}]^{-}, \mathrm{NH}_{3},[\mathrm{OH}]^{-}, \mathrm{H}_{2} \mathrm{O}\).

Short answer

The ligands in increasing order of field strength are: \( \mathrm{Br}^{-}, \mathrm{F}^{-}, [\mathrm{OH}]^{-}, \mathrm{H}_{2}\mathrm{O}, \mathrm{NH}_{3}, [\mathrm{CN}]^{-} \).

Step-by-step solution

Understanding Ligand Field Theory

Ligand field strength is a consideration in crystal field theory, which determines the strength by which a ligand can split the d-orbital energy levels of a metal ion. Ligands causing large splitting are called strong-field, while those causing small splitting are weak-field.

Categorizing Ligands

We categorize ligands into strong-field and weak-field according to the spectrochemical series, which is an experimentally determined order of ligands based on their field strength.

Referencing the Spectrochemical Series

The spectrochemical series ranks ligands like this from weak to strong field: \( \mathrm{I}^{-} < \mathrm{Br}^{-} < \mathrm{S}^{2-} < \mathrm{SCN}^{-} < \mathrm{Cl}^{-} < \mathrm{F}^{-} < \mathrm{OH}^{-} < \mathrm{H}_{2}\mathrm{O} < \mathrm{NH}_{3} < \mathrm{en} < \mathrm{CN}^{-} \). We will use this to rank our given ligands.

Arranging the Given Ligands

According to the spectrochemical series, the given ligands are arranged in increasing order of field strength as follows: \( \mathrm{Br}^{-}, \mathrm{F}^{-}, [\mathrm{OH}]^{-}, \mathrm{H}_{2}\mathrm{O}, \mathrm{NH}_{3}, [\mathrm{CN}]^{-} \).

Key concepts

Spectrochemical Series

In the world of coordination chemistry, the spectrochemical series is a vital concept. It's essentially a list of ligands ranked by the strength of the field they produce when binding to a central metal ion. This has direct implications on how these ligands affect the energy levels of the metal's d orbitals. The order is determined experimentally and helps chemists predict the behavior of complexes.

Here's how it works:

• Ligands at the beginning of the series, like \( \mathrm{I}^{-} \), are considered weak-field ligands. They cause small splitting of the d orbitals.
• Strong-field ligands, like \( [\mathrm{CN}]^{-} \), appear later in the series and result in large splitting.

This series helps us predict various properties of complexes, including their color and magnetic behavior. For example, weak-field ligands often lead to complexes that are paramagnetic due to unpaired electrons, while strong-field ligands might result in diamagnetic complexes by pairing up the d electrons.

Crystal Field Theory

Crystal field theory (CFT) provides a model to understand and predict the splitting of the metal ion's d orbitals when approached by ligands. This theory treats the ligands as point charges and offers a simplistic yet powerful way to examine complex electronic structures.

Important aspects of CFT:

• When ligands approach a metal ion, the d orbitals, which are originally degenerate (meaning they have the same energy), experience repulsion due to the negative charges of the ligands.
• This repulsion causes the d orbitals to split into different energy levels. The pattern of this splitting depends not only on the type of ligand but also on the geometric arrangement of ligands around the metal ion.

Through CFT, we gain a fundamental understanding of how the nature of the ligands affects the electronic arrangements of the central metal ion, influencing the entire complex's properties.

D-orbital Splitting

D-orbital splitting is central in determining how ligands affect a metal's electronic structure. When ligands bind, the d orbital degeneracy is broken, leading to different energy levels among the five d orbitals.

Key points to understand d-orbital splitting include:

• The specific pattern of splitting is called the "crystal field splitting." This can be measured and varies substantially between different geometries like octahedral, tetrahedral, or square planar configurations.
• In an octahedral field, the d orbitals split into two sets: the lower energy \( t_{2g} \) orbitals and the higher energy \( e_{g} \) orbitals. The difference in energy between these two sets is termed \( \Delta_{o} \).

How these levels are filled with electrons depends on the ligands and their placement in the spectrochemical series. Strong-field ligands may cause electrons to fill lower energy levels first, even resulting in pairing, while weak-field ligands allow more electrons to remain unpaired.