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Magazine Chapter 23: Problem 91
Draw orbital-energy splitting diagrams and use the spectrochemical series to show the orbital occupancy for each of the following (assuming that \(\mathrm{H}_{2} \mathrm{O}\) is a weak-field ligand): (a) \(\left[\mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{3-}\left(\mathrm{C}_{2} \mathrm{O}_{4}^{2-}\right.\) creates a weaker field than \(\mathrm{H}_{2} \mathrm{O}\) does. \()\) (b) \(\left[\mathrm{Co}(\mathrm{CN})_{6}\right]^{4-}\) (c) \(\left[\mathrm{MnCl}_{6}\right]^{4-}\)
Short Answer
Expert verified
[Fe(C_2O_4)_3]^{3-}: t_{2g}^3e_g^2, [Co(CN)_6]^{4-}: t_{2g}^6e_g^1, [MnCl_6]^{4-}: t_{2g}^3e_g^2.
Step by step solution
01
- Determine the oxidation state of the metal ion
To solve the problem, first identify the oxidation state of the central metal ion for each complex. (a) For \(\bigg[\text{Fe}\big(\text{C}_2\text{O}_4\big)_3\bigg]^{3-}\), oxalate \(\big(\text{C}_2\text{O}_4^{2-}\big)\) has a -2 charge and there are three such ligands giving a total charge of -6. The overall charge on the complex is -3, so the oxidation state of \(\text{Fe}\) must be \(+3\). (b) For \(\bigg[\text{Co}\big(\text{CN}\big)_6\bigg]^{4-}\), cyanide \(\big(\text{CN}^-\big)\) has a -1 charge and there are six such ligands giving a total charge of -6. The overall charge on the complex is -4, so the oxidation state of \(\text{Co}\) must be \(+2\). (c) For \(\bigg[\text{MnCl}_6\bigg]^{4-}\), chloride \(\big(\text{Cl}^-\big)\) has a -1 charge and there are six such ligands giving a total charge of -6. The overall charge on the complex is -4, so the oxidation state of \(\text{Mn}\) must be \(+2\).
02
- Identify the electronic configuration of the metal ions
Determine the electronic configuration of the metal ions in their respective oxidation states: (a) \(\text{Fe}^{3+}: [\text{Ar}] 3d^5\) (b) \(\text{Co}^{2+}: [\text{Ar}] 3d^7\) (c) \(\text{Mn}^{2+}: [\text{Ar}] 3d^5\)
03
- Determine the field strength of the ligands
Using the spectrochemical series, arrange the given ligands in terms of their field strengths: \(\text{CN}^- > \text{H}_2\text{O} > \text{Cl}^- > \text{C}_2\text{O}_4^{2-}\). This indicates that \(\text{CN}^-\) is a strong-field ligand, while \(\text{C}_2\text{O}_4^{2-}\) and \(\text{Cl}^-\) are weak-field ligands. \(\text{H}_2\text{O}\) is intermediate.
04
- Draw orbital-energy splitting diagrams
Draw the octahedral crystal field splitting diagrams for each ion and place the electrons according to the field strength:(a) For \(\bigg[\text{Fe}\big(\text{C}_2\text{O}_4\big)_3\bigg]^{3-}\), \(\text{C}_2\text{O}_4^{2-}\) is weaker than \(\text{H}_2\text{O}\), so assume weak-field. The \(\text{d}\)-orbitals are split into \(\text{t}_{2g}\) and \(\text{e}_g\) with a small energy gap, and all five electrons are placed in \(\text{t}_{2g}\) and \(\text{e}_g\) orbits \((3 \text{t}_{2g} + 2 \text{e}_g})\) following Hund's rule.(b) For \(\bigg[\text{Co}\big(\text{CN}\big)_6\bigg]^{4-}\), \(\text{CN}^-\) is a strong-field ligand, the \(\text{d}\)-orbitals split with a larger energy gap, filling \(\text{t}_{2g}\) first in a low-spin configuration with electrons paired, showing \(\text{t}_{2g}^6 \text{e}_g^1 \) configuration.(c) For \(\bigg[\text{MnCl}_6\bigg]^{4-}\), \(\text{Cl}^-\) is a weak-field ligand, similar to \(\big[\text{Fe}\big(\text{C}_2\text{O}_4\big)_3\bigg]^{3-}\)), with weak-field, an octahedral field splits the \(\text{d}\)-orbitals into \(\text{t}_{2g}\) and \(\text{e}_g\) sets, and the \(\text{d}\)-electrons fill with weak splitting.
05
- Determine the electron occupancy
Using the spectrochemical series and the diagrams from Step 4, distribute the electrons according to the ligand field strength: (a) \(\big[\text{Fe}\big(\text{C}_2\text{O}_4\big)_3\bigg]^{3-}\) results in \(\text{t}_{2g}^3 \text{e}_g^2\) configuration. (b) \(\big[\text{Co}\big(\text{CN}\big)_6\bigg]^{4-}\) results in \(\text{t}_{2g}^6 \text{e}_g^1\) configuration. (c) \(\big[\text{MnCl}_6\bigg]^{4-}\) results in \(\text{t}_{2g}^3 \text{e}_g^2\) configuration.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Crystal Field Theory
Crystal Field Theory (CFT) helps us understand the electronic structures of metal complexes. It explains how metal ions interact with ligands to split their d-orbitals into different energy levels. This splitting occurs because the ligands鈥� electrons repel the electrons in the d-orbital of the metal ion. The magnitude of this splitting depends on the arrangement of the ligands around the metal ion. In an octahedral arrangement, the d-orbitals split into two sets: the lower-energy \(t_{2g}\) and the higher-energy \(e_g\). The energy difference between these sets is called the crystal field splitting energy, denoted as \(\triangle_o\). Understanding CFT is essential for predicting the electronic configuration, magnetic properties, and colors of metal complexes.
Spectrochemical Series
The spectrochemical series is a list of common ligands arranged in order of their ability to split the d-orbitals of a central metal ion. This series helps predict whether a complex will be high-spin or low-spin based on the strength of the ligand field. Strong-field ligands, like \(\text{CN}^-\), cause a large splitting of the d-orbitals, leading to low-spin complexes where electrons pair up in the lower-energy orbitals. Weak-field ligands, such as \(\text{Cl}^-\) and \(\text{H}_2\text{O}\), cause smaller splitting, resulting in high-spin complexes where electrons occupy all available orbitals before pairing. The spectrochemical series is crucial for determining the electronic configuration of metal complexes and is used extensively in crystal field theory.
Oxidation State Determination
Determining the oxidation state of a central metal ion in a complex is the first step in predicting its electronic configuration and properties. This involves knowing the charges on the ligands and the overall charge of the complex. For instance, in \(\bigg[\text{Fe}\big(\text{C}_2\text{O}_4\big)_3\bigg]^{3-}\), each \(\text{C}_2\text{O}_4^{2-}\) ligand has a -2 charge, and there are three of them, giving a total ligand charge of -6. Since the complex overall has a -3 charge, the oxidation state of iron must be +3 to balance it out. Correctly identifying the oxidation state is necessary to determine the metal's electronic configuration and predict the behavior of the complex.
Electronic Configuration
The electronic configuration of the metal ion in a complex defines how its electrons are distributed among the available orbitals. For example, an \(\text{Fe}^{3+}\) ion has the configuration \([\text{Ar}] 3d^5\). When placed in a crystal field, the d-electrons will occupy the \(t_{2g}\) and \(e_g\) orbitals according to the splitting pattern dictated by the ligands' field strength. Weak-field ligands will lead to a larger number of unpaired electrons (high-spin), whereas strong-field ligands result in fewer unpaired electrons (low-spin). Correctly distributing the electrons among the orbitals allows us to predict magnetic properties and reactivities of metal complexes.
Ligand Field Strength
Ligand field strength describes the ability of ligands to split the d-orbitals of a metal ion. It essentially measures how strongly the ligand's electric field interacts with the metal ion's electrons. Strong-field ligands, like \(\text{CN}^-\), create a large splitting energy and often result in low-spin configurations. In contrast, weak-field ligands such as \(\text{H}_2\text{O}\) and \(\text{Cl}^-\) produce smaller splittings, resulting in high-spin configurations. Ligand field strength influences many properties of metal complexes, including their color, magnetic behavior, and stability. By understanding ligand field strength, chemists can predict and manipulate the behaviors of complex molecules.
