Problem 54
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 \(\mathrm{CN}^{-}.\)
Step-by-Step Solution
Verified Answer
SCN^- is weaker and occurs below CN^- in the spectrochemical series.
1Step 1: Identify the Characteristics of Ligands
In the ligand field model, ligands can cause different splitting in the d-orbitals of metal ions. The magnitude of the splitting depends on the ligand's position in the spectrochemical series. The ligands \(\text{CN}^-\) and \(\text{SCN}^-\) are known for their distinct positions in this series; \(\text{CN}^-\) is a strong field ligand, while the position of \(\text{SCN}^-\) needs to be determined based on given unpaired electron observations.
2Step 2: Analyze the Cr(CN)_6 Complex
For \(\text{K}_4\left[\text{Cr}(\text{CN})_6\right]\), it is given that the complex is paramagnetic with two unpaired electrons. Chromium has a typical electron configuration of \(\text{d}^5\) when it is in a 2+ oxidation state, but in this case, it is assumed to be in a 3+ state (i.e., \(\text{d}^3\) due to the charge on the complex). The \(\text{CN}^-\) ligand causes a strong field to bring about a significant splitting and thus forces pairing of electrons into t₂g orbitals, leaving two unpaired electrons.
3Step 3: Analyze the Cr(SCN)_6 Complex
For \(\text{K}_4\left[\text{Cr}(\text{SCN})_6\right]\), the complex is said to have four unpaired electrons. This requires the d-orbitals not to be significantly split to allow more number of unpaired electrons, which is typically the behavior of weak field ligands. As a result of weaker field splitting, \(\text{SCN}^-\) maintains more electrons in the unpaired state, aligning with an electron configuration in a high spin state.
4Step 4: Compare Ligand Field Strength and Spectrochical Series
Given that \(\text{CN}^-\) is a strong field ligand that results in a lower number of unpaired electrons, it concludes that \(\text{SCN}^-\) is a weaker field relative to \(\text{CN}^-\) since it results in a higher number of unpaired electrons. As such, in the spectrochemical series, \(\text{SCN}^-\) would be placed lower than \(\text{CN}^-\).
Key Concepts
ParamagnetismSpectrochemical Seriesd-orbital Splitting
Paramagnetism
Paramagnetism is a fascinating property of certain materials that makes them attracted to a magnetic field. This happens because these materials have unpaired electrons. Inside an atom or molecule, electrons can either be paired or unpaired. Paired electrons spin in opposite directions, effectively canceling out each other's magnetic field. However, unpaired electrons spin in the same direction, which creates a net magnetic moment.
When a material like \(\text{K}_4[\text{Cr}(\text{CN})_6]\) is paramagnetic, it means there are unpaired electrons present. In this case, experiments show that there are two unpaired electrons. This results due to the arrangement of electrons in the d-orbitals of chromium influenced by the strong field ligand, \(\text{CN}^-\). Contrast this with \(\text{K}_4[\text{Cr}(\text{SCN})_6]\), where there are four unpaired electrons. The lesser splitting of d-orbitals by the weaker field ligand \(\text{SCN}^-\) allows more electrons to remain unpaired, enhancing its paramagnetic properties.
Understanding paramagnetism helps explain why certain substances are drawn to magnetic fields, which is an essential concept in chemistry, particularly when discussing transition metal complexes and their electronic configurations.
When a material like \(\text{K}_4[\text{Cr}(\text{CN})_6]\) is paramagnetic, it means there are unpaired electrons present. In this case, experiments show that there are two unpaired electrons. This results due to the arrangement of electrons in the d-orbitals of chromium influenced by the strong field ligand, \(\text{CN}^-\). Contrast this with \(\text{K}_4[\text{Cr}(\text{SCN})_6]\), where there are four unpaired electrons. The lesser splitting of d-orbitals by the weaker field ligand \(\text{SCN}^-\) allows more electrons to remain unpaired, enhancing its paramagnetic properties.
Understanding paramagnetism helps explain why certain substances are drawn to magnetic fields, which is an essential concept in chemistry, particularly when discussing transition metal complexes and their electronic configurations.
Spectrochemical Series
The spectrochemical series is a crucial tool for chemists. It ranks ligands based on their ability to split the d-orbitals of central metal ions. This splitting determines whether the complex formed is high spin or low spin, influencing the number of unpaired electrons a complex has.
In the context of the complexes in the problem, the ligand \(\text{CN}^-\) is listed high in the spectrochemical series, indicating that it exerts a strong field effect. This causes large splitting of the d-orbitals and usually results in low spin complexes with fewer unpaired electrons. As experimentally noted, \(\text{K}_4[\text{Cr}(\text{CN})_6]\) has only two unpaired electrons.
On the other hand, \(\text{SCN}^-\) demonstrates a weaker field effect, resulting in lesser splitting of d-orbitals. This weaker field allows for more unpaired electrons, making the complex \(\text{K}_4[\text{Cr}(\text{SCN})_6]\) possess four unpaired electrons. Thus, within the spectrochemical series, \(\text{SCN}^-\) is placed lower than \(\text{CN}^-\). Understanding these rankings is vital for predicting the properties of coordination compounds effectively.
In the context of the complexes in the problem, the ligand \(\text{CN}^-\) is listed high in the spectrochemical series, indicating that it exerts a strong field effect. This causes large splitting of the d-orbitals and usually results in low spin complexes with fewer unpaired electrons. As experimentally noted, \(\text{K}_4[\text{Cr}(\text{CN})_6]\) has only two unpaired electrons.
On the other hand, \(\text{SCN}^-\) demonstrates a weaker field effect, resulting in lesser splitting of d-orbitals. This weaker field allows for more unpaired electrons, making the complex \(\text{K}_4[\text{Cr}(\text{SCN})_6]\) possess four unpaired electrons. Thus, within the spectrochemical series, \(\text{SCN}^-\) is placed lower than \(\text{CN}^-\). Understanding these rankings is vital for predicting the properties of coordination compounds effectively.
d-orbital Splitting
In transition metal complexes, the d-orbitals of the central metal ion split into different energy levels in the presence of ligands. This phenomenon is known as d-orbital splitting, and it is critical in determining the electronic configuration of these complexes.
When ligands approach the central metal ion, they interact with the d-orbitals. Depending on the strength of the ligand, which is indicated by its position in the spectrochemical series, the splitting can be either strong or weak. A strong field ligand like \(\text{CN}^-\) causes a significant separation in energy between the \(t_{2g}\) and \(e_g\) sets of orbitals. This leads to a low spin configuration, forcing more electrons to pair up in the lower energy t₂g orbitals, resulting in fewer unpaired electrons.
In contrast, weaker field ligands like \(\text{SCN}^-\) result in smaller energy differences between the orbitals, promoting a high spin state with more unpaired electrons. For example, in \(\text{K}_4[\text{Cr}(\text{SCN})_6]\), the splitting is insufficient to cause extensive pairing, thus leaving four unpaired electrons. By comprehending d-orbital splitting, we can better understand the geometry, color, and magnetic properties of complex ions.
When ligands approach the central metal ion, they interact with the d-orbitals. Depending on the strength of the ligand, which is indicated by its position in the spectrochemical series, the splitting can be either strong or weak. A strong field ligand like \(\text{CN}^-\) causes a significant separation in energy between the \(t_{2g}\) and \(e_g\) sets of orbitals. This leads to a low spin configuration, forcing more electrons to pair up in the lower energy t₂g orbitals, resulting in fewer unpaired electrons.
In contrast, weaker field ligands like \(\text{SCN}^-\) result in smaller energy differences between the orbitals, promoting a high spin state with more unpaired electrons. For example, in \(\text{K}_4[\text{Cr}(\text{SCN})_6]\), the splitting is insufficient to cause extensive pairing, thus leaving four unpaired electrons. By comprehending d-orbital splitting, we can better understand the geometry, color, and magnetic properties of complex ions.
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