Problem 74 - Chemistry Central Science

Question

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

Step-by-Step Solution

Answer

(a) The relative \(E^{\circ}\) values indicate that the Fe(III) complex \([\mathrm{Fe}(\mathrm{o}-\mathrm{phen})_{3}]^{3+}\) is less stable compared to its Fe(II) counterpart, while the Fe(III) complex \([\mathrm{Fe}(\mathrm{CN})_{6}]^{3-}\) is more stable than its Fe(II) counterpart compared to the first couple. (b) The more positive \(E^{\circ}\) value for the \([\mathrm{Fe}(\mathrm{o}-\mathrm{phen})_{3}]^{3+}/[\mathrm{Fe}(\mathrm{o}-\mathrm{phen})_{3}]^{2+}\) couple can be attributed to stronger bonding interactions with o-phenanthroline ligands in Fe(II) compared to Fe(III) ions, making the reduced Fe(II) complex more difficult to oxidize.

Step 1: Interpreting the \(E^{\circ}\) values

The \(E^{\circ}\) values are measures of the tendency for a redox couple to undergo oxidation or reduction. A more positive \(E^{\circ}\) value indicates a greater tendency for reduction, while a less positive (more negative) \(E^{\circ}\) value indicates a greater tendency for oxidation.

Step 2: Analyzing the relative stabilities

For the first redox couple, the \(E^{\circ}\) value is 1.12 V, which indicates a strong tendency for the complex to be reduced, meaning that the Fe(III) complex, \([\mathrm{Fe}(\mathrm{o}-\mathrm{phen})_{3}]^{3+}\), is less stable than the Fe(II) complex, \([\mathrm{Fe}(\mathrm{o}-\mathrm{phen})_{3}]^{2+}\). For the second redox couple, the \(E^{\circ}\) value is 0.36 V. This indicates a weaker tendency for reduction than the first redox couple. Therefore, the Fe(III) complex, \([\mathrm{Fe}(\mathrm{CN})_{6}]^{3-}\), is more stable compared to the Fe(II) complex, \([\mathrm{Fe}(\mathrm{CN})_{6}]^{4-}\), than in the first couple.

Step 3: Explaining the difference in \(E^{\circ}\) values

The difference in the \(E^{\circ}\) values between the two redox couples can be explained by the effect of the ligands (o-phen and CN) on the central iron atom. The o-phenanthroline ligands form stronger bonds with Fe(II) ions than with Fe(III) ions. This stronger bonding interaction stabilizes the reduced Fe(II) complex, making it more difficult to oxidize, and resulting in a more positive \(E^{\circ}\) value for the \([\mathrm{Fe}(\mathrm{o}-\mathrm{phen})_{3}]^{3+}/[\mathrm{Fe}(\mathrm{o}-\mathrm{phen})_{3}]^{2+}\) couple. On the other hand, the cyanide ligands form strong bonds with both Fe(II) and Fe(III) ions, with a smaller difference in bonding strength between the two oxidation states compared to o-phenanthroline. This results in a smaller difference in stability between the Fe(III) and Fe(II) complexes of the cyanide ligands, and thus a less positive \(E^{\circ}\) value for the \([\mathrm{Fe}(\mathrm{CN})_{6}]^{3-}/[\mathrm{Fe}(\mathrm{CN})_{6}]^{4-}\) couple.

Key Concepts

Redox Reactions

Redox reactions are chemical processes where oxidation and reduction occur simultaneously. In these reactions, one substance loses electrons (oxidation) while another gains electrons (reduction). The standard reduction potential, denoted as \(E^{\circ}\), is a measure of the tendency of a chemical species to be reduced. A more positive \(E^{\circ}\) value implies a stronger tendency for the reduction process.

For example, in the given exercise, the \([\text{Fe(o-phen)}_{3}]^{3+}/[\text{Fe(o-phen)}_{3}]^{2+}\) redox couple has an \(E^{\circ}\) value of 1.12 V, which is more positive compared to the \([\text{Fe(CN)}_{6}]^{3-}/[\text{Fe(CN)}_{6}]^{4-}\) couple's value of 0.36 V. This indicates that the former has a much greater tendency to gain electrons and undergo reduction.

The relative \(E^{\circ}\) values help us understand the likelihood of the respective redox reactions taking place under standard conditions, shedding light on the stability of the complexes involved.

Stability of Complexes

The stability of complexes in redox reactions is intricately linked to their \(E^{\circ}\) values. From the given problem, we can determine the stability by analyzing these values. A higher tendency for one form to be reduced typically signals that it is less stable compared to its reduced form.

Taking the example of \([\text{Fe(o-phen)}_{3}]^{3+}\) with an \(E^{\circ}\) value of 1.12 V, the complex has a high tendency to be reduced to \([\text{Fe(o-phen)}_{3}]^{2+}\). This means \([\text{Fe(o-phen)}_{3}]^{3+}\) is less stable, while the reduced form, \([\text{Fe(o-phen)}_{3}]^{2+}\), is more stable.

In contrast, the \([\text{Fe(CN)}_{6}]^{3-}/[\text{Fe(CN)}_{6}]^{4-}\) couple shows that \([\text{Fe(CN)}_{6}]^{3-}\) is more stable than the \([\text{Fe(o-phen)}_{3}]^{3+}\). The stability can directly influence how these complexes behave in various chemical reactions.

Ligand Bonding Effects

Ligand bonding has a significant impact on the stability and redox behavior of metal complexes. Different ligands can stabilize different oxidation states of a metal, affecting their \(E^{\circ}\) values. In this case, two different ligands, o-phenanthroline and cyanide, show distinct bonding interactions with iron.

o-Phenanthroline forms stronger bonds with the Fe(II) ion, resulting in greater stability of the reduced form, \([\text{Fe(o-phen)}_{3}]^{2+}\). This strong interaction translates to a higher \(E^{\circ}\) value, as seen in the exercise.

• Stronger bonding with Fe(II) implies less stability in its oxidized state.
• The result is a higher tendency to be in its reduced form.

On the other hand, cyanide forms robust bonds with both Fe(III) and Fe(II).

• The bonding strength difference is minor between the two oxidation states.
• This results in a smaller \(E^{\circ}\) value difference, showing less influence on stability between forms.

The variation in ligand bonding directly affects the electrochemical behavior of these complexes, highlighting the critical role ligands play in redox chemistry.