Question

The \(E^{\circ}\) values for two iron complexes in acidic solution are as follows: $$ \begin{aligned} \left[\mathrm{Fe}(o-p h e n)_{3}\right]^{3+}(a q)+\mathrm{e}^{-} & \rightleftharpoons\left[\mathrm{Fe}(o-p h e n)_{3}\right]^{2+}(a q) & E^{\circ}=1.12 \mathrm{~V} \\ \left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}(a q)+\mathrm{e}^{-} & \rightleftharpoons\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}(a q) & E^{\circ}=0.36 \mathrm{~V} \end{aligned} $$ (a) What do the relative \(E^{\circ}\) values tell about the relative stabilities of the \(\mathrm{Fe}(\mathrm{II})\) and \(\mathrm{Fe}(\mathrm{III})\) complexes in each case? (b) Account for the more positive \(E^{\circ}\) value for the (o-phen) complex. Both of the Fe(II) complexes are low spin. (Hint: consider the charges carried by the ligands in the two cases.)

Short answer

(a) The relative $E^\circ$ values indicate that the Fe(II) complex with o-phen ligands is more stable than that with CN ligands, as the higher $E^\circ$ value (1.12 V) indicates a higher tendency for the Fe(III) complex to be reduced to Fe(II). Conversely, the Fe(III) complex is less stable in the o-phen case than in the CN case. (b) The more positive $E^\circ$ value for the o-phen complex can be attributed to a lack of charged ligands in the o-phen case, leading to a relative destabilization of the Fe(III) complex and making it more likely to be reduced. In contrast, the negatively charged CN ligands in the Fe(CN) complex help stabilize the positive charge on the Fe center, making the Fe(III) complex less prone to reduction, resulting in a lower $E^\circ$ value.

Step-by-step solution

Identify the redox couple equations

We have the following redox couples with their standard reduction potentials: $$ \begin{aligned} (i)~~\left[\mathrm{Fe}(o-p h e n)_{3}\right]^{3+}(a q)+\mathrm{e}^{-} &\rightleftharpoons\left[\mathrm{Fe}(o-p h e n)_{3}\right]^{2+}(a q) & E^{\circ}=1.12 \mathrm{~V} \\\ (ii)~~\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}(a q)+\mathrm{e}^{-} &\rightleftharpoons\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}(a q) & E^{\circ}=0.36 \mathrm{~V} \end{aligned} $$

Identify the meaning of the standard reduction potentials

The standard reduction potential (\(E^\circ\)) of a redox couple indicates how likely a reaction is to proceed in the direction of reduction (gaining an electron). A larger \(E^\circ\) value means that the reduction is more likely to occur, resulting in a more stable reduced species. In these redox couples, we have Fe(III) being reduced to Fe(II). So, larger \(E^\circ\) values mean that the Fe(III) complex is more likely to be reduced to the Fe(II) complex and yield a stabilized Fe(II) complex.

Compare the standard reduction potentials and determine the stability of Fe(II) and Fe(III) complexes

Now, comparing the two values \(E^\circ\): \(E^{\circ}_{(o-phen)} = 1.12~V > E^{\circ}_{(CN)} = 0.36~V\) (a) This tells us that Fe(III) in the o-phen complex is more likely to be reduced to Fe(II) than the Fe(III) in the Fe(CN) complex. This implies that the relative stability of Fe(II) complexes is higher in the o-phen complex than in the Fe(CN) complex. Conversely, the Fe(III) in the o-phen complex is less stable than the Fe(III) in the Fe(CN) complex.

Explain the more positive Eº value for the o-phen complex

(b) The difference in \(E^\circ\) values can be explained by considering the charges carried by the ligands in each complex. In the o-phen complex, there are no charged o-phen ligands. Therefore, the overall charge of the complex is determined by the charge on the Fe center. This leads to a relative destabilization of the Fe(III) species, making it more likely to be reduced to the Fe(II) form. On the other hand, in the Fe(CN) complex, the ligands hold negative charges (-1 on each of the six CN ligands). These negative charges help stabilize the positive charge on the Fe center, making the Fe(III) complex less likely to be reduced to the Fe(II) form. This difference in charge stabilization affects the \(E^\circ\) values and results in a more positive value for the o-phen complex.

Key concepts

Understanding Redox Reactions

Redox reactions are fundamental processes in chemistry that involve the transfer of electrons between two species. The term 'redox' is a portmanteau of reduction and oxidation. In this context, reduction refers to the gain of electrons by a molecule, atom, or ion, while oxidation describes the loss of electrons. The substance that donates electrons gets oxidized, and the one that accepts electrons gets reduced. Understanding redox reactions is crucial for grasping a wide range of chemical phenomena, including metabolic processes, industrial applications, and the function of batteries.

In our explored problem, we dealt with the redox reactions of iron complexes. The use of standard reduction potentials (\(E^\text{o}\) values) allows us to predict the direction in which a redox reaction is inclined to proceed. In the given example, the complex with the higher potential is the more stable Fe(II) state upon reduction, indicating a greater tendency for the Fe(III) species to gain an electron and get reduced to Fe(II). Such insights have practical implications, helping chemists design reactions and understand redox processes in various environments.

Chemical Stability and Standard Reduction Potentials

Chemical stability, in the context of redox chemistry, often relates to the ease with which a compound can gain or lose electrons. The stability of a chemical species can be inferred from its standard reduction potential (\(E^\text{o}\)); more positive values suggest a greater likelihood of the species gaining electrons and becoming reduced. This is a measure of the driving force behind the redox reaction. Generally, a compound with a higher \(E^\text{o}\) value is more chemically stable under standard conditions when it serves as an oxidizing agent.

When it comes to the iron complexes discussed in our exercise, the one with a higher \(E^\text{o}\) value for the Fe(III) to Fe(II) reduction suggests that the Fe(III) state is more unstable, or more precisely, less favored, compared to the Fe(II) state. Therefore, the \(E^\text{o}\) values provide us with comparative insight into the stability of the oxidized and reduced forms of a species.

Impact of Ligand Charge Effects

The charge carried by ligands within a complex can significantly affect the complex's overall stability and its redox behavior. Ligands are ions or molecules that donate electron pairs to a central atom to form a coordination complex. Depending on the charge and the electron-donating ability of the ligands, they can either stabilize or destabilize the central metal ion.

In the exercise we analyzed, the ligand charge plays a critical role. For the [Fe(o-phen)\textsubscript{3}]\textsuperscript{3+} complex, the neutral o-phen ligands do not contribute to the stabilization of the Fe center's positive charge. On the contrary, in the [Fe(CN)\textsubscript{6}]\textsuperscript{3-} complex, each CN\textsuperscript{-} ligand brings a negative charge that helps to compensate for the positive charge on the Fe, thus stabilizing the Fe(III) state to a greater extent than in the o-phen complex. Such charge stabilization is a factor responsible for the differing \(E^\text{o}\) values observed. This demonstrates an important concept in coordination chemistry: ligand charge effects must be considered to understand the reductive and oxidative behavior of metal complexes.