Rank the following in order of decreasing \(\Delta\) and energy of light absorbed: \(\left[\mathrm{Cr}(\mathrm{en})_{3}\right]^{3+},\left[\mathrm{Cr}(\mathrm{CN})_{6}\right]^{3-},\left[\mathrm{CrCl}_{6}\right]^{3-}\)

Ligand field strength is a core concept in Ligand Field Theory. It refers to the ability of a ligand to split the d-orbitals of a transition metal ion when forming a complex. Different ligands cause different levels of splitting. The strength of the ligand field directly depends on the ligand itself.

A strong field ligand, such as cyanide \([\text{CN}^{-}]\), causes a large splitting of the d-orbitals. In contrast, a weak field ligand like chloride \([\text{Cl}^{-}]\) causes minimal splitting. Ligands like ethylenediamine \([\text{en}]\) fall somewhere in the middle, providing a moderate field strength.

Understanding ligand field strength helps predict properties of metal complexes, like color and magnetic behavior. Complexes with strong field ligands often absorb light of higher energy compared to those with weak field ligands.

Crystal field splitting, represented by \(\Delta_{o}\), is the energy difference between different sets of d-orbitals in a transition metal complex. When transition metal ions form bonds with ligands, interactions between the ligands and the d-orbitals of the metal cause the orbitals to split into different energy levels.

In an octahedral complex, such as the compounds mentioned in the exercise, the splitting separates the d-orbitals into two sets: \({e_g}\) (higher energy) and \({t_{2g}}\) (lower energy). The magnitude of this splitting, \(\Delta_{o}\), largely depends on the field strength of the ligands involved.

Notably, strong field ligands like cyanide \([\text{CN}^{-}]\) produce a large \(\Delta_{o}\), whereas weak field ligands like chloride \([\text{Cl}^{-}]\) result in a smaller splitting. The overall size of \(\Delta_{o}\) affects how much energy is absorbed when electrons transition between these split orbitals, impacting the color of the complex.

Transition metal complexes are compounds consisting of a transition metal ion bonded to one or more ligands. These complexes often exhibit unique chemical and physical properties, including vibrant colors and varied magnetic properties, which result from the interactions between metal d-orbitals and the ligands.

The nature of the ligands and their arrangement around the metal ion can significantly alter these properties. For example, in the given exercise, we have three complexes:

• \([\text{Cr(CN)}_{6}]^{3-}\)
• \([\text{Cr(en)}_{3}]^{3+}\)
• \([\text{CrCl}_{6}]^{3-}\)

In these complexes, cyanide is a strong field ligand, ethylenediamine a moderate field ligand, and chloride a weak field ligand.

As the field strength of the ligands increases, the energy difference between split d-orbitals also increases, and so does the energy of light absorbed. Thus, \([\text{Cr(CN)}_{6}]^{3-}\) absorbs higher energy light compared to \([\text{CrCl}_{6}]^{3-}\). Understanding these principles is crucial for predicting and explaining the behavior of transition metal complexes in various chemical environments.