Question

Experiments show that \(\mathrm{K}_{4}\left[\mathrm{Cr}(\mathrm{CN})_{6}\right]\) is paramagnetic and has two unpaired electrons. The related complex \(\mathrm{K}_{4}\left[\mathrm{Cr}(\mathrm{SCN})_{6}\right]\) is paramagnetic and has four unpaired electrons. Account for the magnetism of each compound using the ligand field model. Predict where the SCN - ion occurs in the spectrochemical series relative to CN \(^{-}\).

Short answer

SCN\(^{-}\) is a weaker field ligand than CN\(^{-}\) and is lower in the spectrochemical series.

Step-by-step solution

Understand the Ligand Field Theory

Ligand Field Theory explains the splitting of the d-orbitals in transition metal complexes due to the presence of ligands. The extent of this splitting affects the distribution of electrons among the d-orbitals, thereby influencing the magnetic properties of the compound.

Analyze \\([\mathrm{Cr}([\mathrm{CN})_{6}]^{4-}\\) Complex

In \([\mathrm{Cr}([\mathrm{CN})_{6}]^{4-}\), CN\(^{-}\) is a strong field ligand that causes large splitting of the d-orbitals (large \(\Delta\) value). As a result, electrons pair up in the lower energy orbitals. Since the resulting complex is paramagnetic with two unpaired electrons, they occupy the higher t\(_{2g}\) orbitals (3 orbitals) with minimal unpaired electrons.

Analyze \\([\mathrm{Cr}([\mathrm{SCN})_{6}]^{4-}\) Complex

In \([\mathrm{Cr}([\mathrm{SCN})_{6}]^{4-}\), SCN\(^{-}\) is a weaker field ligand compared to CN\(^{-}\), resulting in a smaller d-orbital splitting (small \(\Delta\) value). This allows more unpaired electrons due to less electron pairing in the lower energy orbitals. The complex is paramagnetic with four unpaired electrons, indicating occupancy in both e\(_g\) and t\(_{2g}\) orbitals.

Predicting the Spectrochemical Series Position for SCN\(^-\)

Given that SCN\(^-\) results in a complex with more unpaired electrons than CN\(^{-}\), SCN\(^-\) must be a weaker field ligand than CN\(^-\). Thus, SCN\(^-\) is positioned lower than CN\(^-\) in the spectrochemical series.

Key concepts

Paramagnetism

Paramagnetism refers to a property of certain materials that are attracted to an external magnetic field. This occurs when there are unpaired electrons present in the material. In the context of transition metal complexes, paramagnetic behavior is an important feature to consider, as it can provide insight into the electronic configuration and nature of the d-orbitals.
In the case of \([\mathrm{Cr(CN)_{6}}]^{4-}\) and \([\mathrm{Cr(SCN)_{6}}]^{4-}\) complexes, these compounds both exhibit paramagnetism but with different numbers of unpaired electrons. **Why is this important?**

• It helps predict how the material will interact with a magnetic field.
  
• The number of unpaired electrons can indicate the strength and nature of the ligands surrounding the metal center.
  

Analyzing the electron configuration based on ligand field theory, helps us understand the extent of paramagnetism in these complexes.

Spectrochemical Series

The spectrochemical series is a list that ranks ligands based on their ability to split the d-orbitals of a central metal ion. Ligands at the top of the series, like CN\(-\), cause a larger d-orbital splitting. This results in fewer unpaired electrons and potentially low-spin configurations.
**Where does SCN\(^{-}\) fit?**

• Since SCN\(^{-}\) leads to more unpaired electrons compared to CN\(-\), it is a weaker field ligand.
  
• Thus, SCN\(^{-}\) appears lower in the spectrochemical series than CN\(-\).
  

This ordering helps chemists predict properties such as color, magnetism, and reactivity of metal complexes.

d-Orbital Splitting

d-Orbital Splitting is the outcome of interactions between the central metal ion's d-orbitals and surrounding ligands in a complex. When ligands approach a transition metal ion, they cause the degenerate d-orbitals to split into groups of differing energies. The amount of this energy difference is called the crystal field splitting energy, denoted as \( \Delta \).
Here's how it applies to our complexes:- **For \(\mathrm{Cr(CN)_{6}}^{4-}\):** - CN\(-\) is a strong field ligand, causing significant splitting. - Electrons tend to pair up in the lower energy orbitals.
- There's a minimal number of unpaired electrons resulting in t\(_{2g}\) \(3\) orbitals with paired electrons.
- **For \(\mathrm{Cr(SCN)_{6}}^{4-}\):** - SCN\(-\) is a weaker ligand, leading to smaller splitting. - This allows for more unpaired electrons since there's less pairing demand.
This difference in splitting is crucial for understanding the magnetic and optical properties of complexes.

Transition Metal Complexes

Transition Metal Complexes are coordination entities formed from transition metal ions bonded to ligands. These complexes exhibit a wide range of chemical behaviors, largely due to the electronic configuration of the metal center and its interaction with the ligands.
**Why are they special?**

• They can display a variety of colors because of electronic transitions between d-orbitals.
  
• Their magnetic properties, such as paramagnetism, vary depending on ligand field effects and electron pairing.
  
• Understanding these complexes is crucial in fields such as catalysis, materials science, and bioinorganic chemistry.
  

Learning how ligands like CN\(-\) and SCN\(-\) influence these complexes enhances our understanding of their electronic structures and potential applications.