Question

The \(E^{\circ}\) values for two low-spin iron complexes in acidic solution are as follows: $$ \begin{aligned} \left[\mathrm{Fe}(o \text { -phen })_{3}\right]^{3+}(a q)+\mathrm{e}^{-} \rightleftharpoons\left[\mathrm{Fe}(o \text { -phen })_{3}\right]^{2+}(a q) & E^{\circ}=1.12 \mathrm{~V} \\\ \left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}(a q)+\mathrm{e}^{-} \rightleftharpoons\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}(a q) & E^{\circ}=0.36 \mathrm{~V} \end{aligned} $$ (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

(a) Yes, it is thermodynamically favorable to reduce both Fe(III) complexes to their Fe(II) analogs since both E° values are positive (1.12 V and 0.36 V). (b) The complex [Fe(CN)_6]³⁻ is more difficult to reduce compared to [Fe(o-phen)_3]³⁺ due to its lower E° value (0.36 V). (c) The difference in reduction potential can be attributed to the ligands: Cyanide (CN⁻) ligands in [Fe(CN)_6]³⁻ create a stronger ligand field, resulting in stronger bonding interactions with the metal center, making the complex more difficult to reduce compared to [Fe(o-phen)_3]³⁺ with o-phenanthroline ligands.

Step-by-step solution

Understand Reduction Process

In a redox reaction, the species with higher E° tends to be reduced, while the species with lower E° tends to be oxidized. A positive E° value implies that the reduction reaction is thermodynamically favorable, while a negative E° value implies that the reaction is not thermodynamically favorable.

Analyze thermodynamic favorability

In this exercise, we have two iron complexes [Fe(o-phen)_3]³⁺ and [Fe(CN)_6]³⁻ with their corresponding standard reduction potentials of E° = 1.12 V and E° = 0.36 V, respectively. Since both E° values are positive, the reduction of both Fe(III) complexes to their Fe(II) analogs is thermodynamically favorable.

Determine the more difficult to reduce complex

As mentioned earlier, the complex with a higher E° value is more favorable to be reduced. Thus, when comparing the two given complexes, [Fe(o-phen)_3]³⁺ has a higher E° value of 1.12 V, suggesting that it is more easily reduced than [Fe(CN)_6]³⁻ with an E° value of 0.36 V. Therefore, the complex [Fe(CN)_6]³⁻ is more difficult to reduce than [Fe(o-phen)_3]³⁺.

Explain the reason for the observed trend

The difference in reduction potential between the two complexes can be attributed to the differences in the ligands surrounding the iron center. In [Fe(o-phen)_3]³⁺, the o-phenanthroline ligands are organic compounds with nitrogen atoms that can donate electron density to the metal center. On the other hand, in [Fe(CN)_6]³⁻, the cyanide (CN⁻) ligands are stronger field ligands, which create a stronger bonding interaction with the metal center, making it more difficult to reduce the complex. Therefore, the complex [Fe(CN)_6]³⁻ is more difficult to reduce than [Fe(o-phen)_3]³⁺ due to the stronger ligand field created by the cyanide ligands.

Key concepts

Thermodynamics in Redox Reactions

Understanding thermodynamics in redox reactions is essential for students studying chemistry. In the context of redox reactions, the concept of standard reduction potential, denoted as \(E^\circ\), plays a pivotal role in predicting the spontaneity of a reaction.

When examining a redox reaction, the species with a higher \(E^\circ\) value is more likely to gain electrons and be reduced, while the species with a lower \(E^\circ\) value is more apt to lose electrons and be oxidized. Importantly, a positive standard reduction potential indicates that the reduction process is thermodynamically favorable, hinting at a reaction’s natural tendency to proceed without the input of additional energy. However, it's crucial to remember that standard reduction potentials are measured under standard conditions, and actual conditions may alter the spontaneity of the process.

To illustrate, the given exercise shows two iron complexes with their respective \(E^\circ\) values being positive, which tells us that the reduction of Fe(III) to Fe(II) in both complexes is favored in thermodynamic terms. The higher the \(E^\circ\) value, the greater the tendency of the complex to accept an electron, making its reduction process energetically more favorable.

Low-Spin Iron Complexes

The behavior of low-spin complexes, particularly those of transition metals such as iron, is influenced by the intricacies of electronic structure and ligand interactions. A low-spin complex forms when the transition metal has a strong ligand field, which leads to a larger energy gap between the d-orbitals. This causes the electrons to pair up in the lower energy orbitals first, thereby resulting in fewer unpaired electrons——a state termed 'low-spin'.

The exercise refers to low-spin iron complexes, which are characterized by their intricate electronic configurations that affect their chemical properties, including their standard reduction potentials. In low-spin complexes, the reduced spin states often result from the presence of strong-field ligands, which subsequently can influence the ease with which the complexes undergo reduction. For instance, the complex with a stronger ligand field is generally more difficult to reduce, as the iron is held more tightly within the ligand's grasp due to the lower energy and higher stabilization of its d-electrons. This principle helps explain why one iron complex may have a higher standard reduction potential than another, reflecting differences in their ease of reduction linked to their spin states.

Ligand Field Strength

Ligand field strength is a critical factor that determines the color, magnetism, and reactivity of transition metal complexes. It is essentially a measure of a ligand’s ability to split the d-orbital energies of the central metal ion. Strong-field ligands, such as cyanide in the exercise, can cause a significant splitting of the metal's d-orbitals, leading to low-spin electron configurations that result in greater stability of the complex. In contrast, weaker field ligands result in lesser splitting and often higher spin configurations.

Ligand field strength, therefore, underpins the explanation for why different iron complexes display varying standard reduction potentials. The more robust the ligand field, the more energetically unfavorable it becomes to remove an electron, because doing so would disturb the stable low-spin configuration. Thus, as exemplified by the complex [Fe(CN)_6]³⁻ from the exercise, a strong-field cyanide ligand creates a high stabilization energy, heightening the difficulty of reducing the complex compared to [Fe(o-phen)_3]³⁺, which has weaker field ligands and a correspondingly less energetically favorable electron configuration for reduction.