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) \(\left[\mathrm{MnCl}_{6}\right]^{4-}\)

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 \(+2\).

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) \(\text{Mn}^{2+}: [\text{Ar}] 3d^5\)

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.

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.

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.