The \(E^{\circ}\) values for two low-spin iron complexes in acidic solution are as follows: $$ \begin{aligned} \left[\mathrm{Fe}(o-\mathrm{phen})_{3}\right]^{3+}(a q)+\mathrm{e}^{-} \rightleftharpoons \\ \left[\mathrm{Fe}(o-\mathrm{phen})_{3}\right]^{2+}(a q) & E^{\circ}=1.12 \mathrm{~V} \end{aligned} $$ $$ \begin{aligned} \left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}(a q)+\mathrm{e}^{-} \rightleftharpoons & \\ &\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}(a q) \quad E^{\circ}=0.36 \mathrm{~V} \end{aligned} $$ (a) Is it thermodynamically favorable to reduce both Fe(III) complexes to their Fe(II) analogs? Explain. (b) Which complex, \(\left[\mathrm{Fe}(o \text { -phen })_{3}\right]^{3+}\) or \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-},\) is more difficult to reduce? (c) Suggest an explanation for your answer to (b).

Short Answer

Expert verified
(a) Yes, it is thermodynamically favorable to reduce both Fe(III) complexes to their Fe(II) analogs since their E° values are positive: \(E^{\circ} \left[\mathrm{Fe}(o-\mathrm{phen})_{3}\right]^{3+}/[\mathrm{Fe}(o-\mathrm{phen})_{3}\right]^{2+} = 1.12\mathrm{~V}\); \(E^{\circ} \left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}/[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-} = 0.36\mathrm{~V}\). (b) The complex \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}\) is more difficult to reduce since it has a lower E° value compared to \(\left[\mathrm{Fe}(o-\mathrm{phen})_{3}\right]^{3+}\). (c) The structural differences in ligands cause the reduction difficulty: \(o-\mathrm{phen}\) ligands in \(\left[\mathrm{Fe}(o-\mathrm{phen})_{3}\right]^{3+}\) have a stronger overlap with the metal ion, making it easier to reduce, while the cyanide ions in \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}\) do not have the same strong stabilizing effect.

Step by step solution

01

(a) Determine the Thermodynamic Favorability

To determine the thermodynamic favorability of reducing the two iron complexes, we will look at the E° values provided in the exercise: \(\left[\mathrm{Fe}(o-\mathrm{phen})_{3}\right]^{3+}(a q)+\mathrm{e}^{-} \rightleftharpoons \left[\mathrm{Fe}(o-\mathrm{phen})_{3}\right]^{2+}(a q)\); \(E^{\circ}=1.12\mathrm{~V}\) \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}(a q)+\mathrm{e}^{-} \rightleftharpoons \left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}(a q) \quad E^{\circ}=0.36\mathrm{~V}\) Both E° values are positive, which implies that the reduction of both Fe(III) complexes to their Fe(II) counterparts is thermodynamically favorable.
02

(b) Compare Reduction Potentials

To see which complex is more difficult to reduce, we will compare their E° values: \(E°\left[\mathrm{Fe}(o-\mathrm{phen})_{3}\right]^{3+}/[\mathrm{Fe}(o-\mathrm{phen})_{3}\right]^{2+} = 1.12\mathrm{~V}\) \(E°\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}/[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-} = 0.36\mathrm{~V}\) Since the E° value for the reduction of the \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}\) complex is lower, it is more difficult to reduce.
03

(c) Suggest an Explanation for Reduction Difficulty

An explanation for the difference in reduction difficulty can be found in the ligands coordinating the central iron atom. The \(o- phen\) ligands in the \(\left[\mathrm{Fe}(o- \mathrm{phen})_{3}\right]^{3+}\) complex are large, planar, and aromatic ligands, which results in a stronger overlap between the metal ion and the ligand orbitals, stabilizing the reduced Fe(II) state and making it easier to reduce. On the other hand, the ligands in the \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}\) complex are cyanide ions. While cyanide ions have strong σ-donor and π-acceptor properties, their overall stabilizing effect on the Fe(II) state is not as strong as that of the larger and more conjugated \(o - phen\) ligands. Consequently, the \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}\) complex is more difficult to reduce than the \(\left[\mathrm{Fe}(o-\mathrm{phen})_{3}\right]^{3+}\) complex.

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Most popular questions from this chapter

When Alfred Werner was developing the field of coordination chemistry, it was argued by some that the optical activity he observed in the chiral complexes he had prepared was due to the presence of carbon atoms in the molecule. To disprove this argument, Werner synthesized a chiral complex of cobalt that had no carbon atoms in it, and he was able to resolve it into its enantiomers. Design a cobalt(III) complex that would be chiral if it could be synthesized and that contains no carbon atoms. (It may not be possible to synthesize the complex you design, but we will not worry about that for now.)

Carbon monoxide is toxic because it binds more strongly to the iron in hemoglobin (Hb) than does \(\mathrm{O}_{2}\), as indicated by these approximate standard free-energy changes in blood: $$ \begin{aligned} \mathrm{Hb}+\mathrm{O}_{2} & \longrightarrow \mathrm{HbO}_{2} & \Delta G^{\circ}=-70 \mathrm{~kJ} \\ \mathrm{Hb}+\mathrm{CO} & \longrightarrow \mathrm{HbCO} & \Delta G^{\circ}=-80 \mathrm{~kJ} \end{aligned} $$ Using these data, estimate the equilibrium constant at 298 K for the equilibrium $$ \mathrm{HbO}_{2}+\mathrm{CO} \rightleftharpoons \mathrm{HbCO}+\mathrm{O}_{2} $$

For each of the following metals, write the electronic configuration of the atom and its \(2+\) ion: $(\mathbf{a}) \mathrm{Mn},(\mathbf{b}) \mathrm{Ru},(\mathbf{c}) \mathrm{Rh} .$ Draw the crystal-field energy-level diagram for the \(d\) orbitals of an octahedral complex, and show the placement of the \(d\) electrons for each \(2+\) ion, assuming a strong-field complex. How many unpaired electrons are there in each case?

Which periodic trend is partially responsible for the observation that the maximum oxidation state of the transition-metal elements peaks near groups 7 and \(8 ?(\mathbf{a})\) The number of valence electrons reaches a maximum at group 8. (b) The effective nuclear charge increases on moving left across each period. (c) The radii of the transition-metal elements reach a minimum for group \(8,\) and as the size of the atoms decreases it becomes easier to remove electrons.

For a given metal ion and set of ligands, is the crystal-field splitting energy larger for a tetrahedral or an octahedral geometry?

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