Question

Spinach contains a lot of iron but is not a good source of dietary iron because nearly all the iron is tied up in the oxalate complex \(\left[\mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{3-}\) (a) The formation constant \(K_{\mathrm{f}}\) for \(\left[\mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{3-}\) is \(3.3 \times 10^{20}\). Calculate the equilibrium concentration of free \(\mathrm{Fe}^{3+}\) in a \(0.100 \mathrm{M}\) solution of \(\left[\mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{3-}\). (Ignore any acid-base reactions.) (b) Under the acidic conditions in the stomach, the \(\mathrm{Fe}^{3+}\) concentration should be greater because of the reaction $$ \begin{aligned} \left[\mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{3-}(a q) &+6 \mathrm{H}_{3} \mathrm{O}^{+}(a q) \\ \mathrm{Fe}^{3+}(a q)+3 \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(a q)+6 \mathrm{H}_{2} \mathrm{O}(l) \end{aligned} $$ Show, however, that this reaction is nonspontaneous under standard-state conditions. (For \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}, K_{\mathrm{a} 1}=5.9 \times 10^{-2}\) and \(\left.K_{\mathrm{a} 2}=6.4 \times 10^{-5} .\right)\) (c) Draw a crystal field energy-level diagram for \(\left[\mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{3-}\), and predict the number of unpaired electrons. \(\left(\mathrm{C}_{2} \mathrm{O}_{4}^{2-}\right.\) is a weak-field bidentate ligand.) (d) Draw the structure of \(\left[\mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{3-}\). Is the complex chiral or achiral?

Short answer

(a) [Fe^{3+}] = 3.03 × 10^{-22} M. (b) Nonspontaneous reaction. (c) High-spin complex with 5 unpaired electrons. (d) Achiral structure.

Step-by-step solution

Calculate the equilibrium concentration of Fe^{3+}

To find the concentration of \( \mathrm{Fe}^{3+} \) in a \( 0.100 \mathrm{M} \) solution of \( \left[\mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{3-} \), we can use the formation constant, \( K_{\mathrm{f}} = 3.3 \times 10^{20} \). The reaction is \( \mathrm{Fe}^{3+} + 3 \mathrm{C}_2\mathrm{O}_4^{2-} \rightleftharpoons \left[\mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{3-} \). The equation for the formation constant is: \( K_{f} = \frac{1}{[\mathrm{Fe}^{3+}]} \). Therefore, \( [\mathrm{Fe}^{3+}] = \frac{1}{K_f \times (0.100)} = 3.03 \times 10^{-22} \mathrm{M} \).

Analyze the reaction under acidic conditions

When \( \left[\mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{3-} \) is in acidic conditions, we'll use the equation: \( \Delta G = \Delta G^0 + RT\ln Q \). Since \( K_f \) is high, it implies that \( \Delta G^0 \) is large and negative. To make the reaction \( \left[\mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{3-} + 6\mathrm{H}_3\mathrm{O}^{+} \rightarrow \mathrm{Fe}^{3+} + 3\mathrm{H}_2\mathrm{C}_2\mathrm{O}_4 + 6\mathrm{H}_2\mathrm{O} \) proceed, \( \Delta G \) would need to be positive. However, because \( K_{a1} = 5.9 \times 10^{-2} \) and \( K_{a2} = 6.4 \times 10^{-5} \) are relatively small, this indicates that the oxalate protonation does not significantly shift the equilibrium. Hence, the reaction is nonspontaneous.

Draw a crystal field splitting diagram

For \( \left[\mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{3-} \), note that \( \mathrm{C}_2\mathrm{O}_4^{2-} \) is a weak-field ligand, leading to high-spin complexes. \( \mathrm{Fe}^{3+} \) has a \( d^5 \) configuration. The crystal field splitting diagram will have 5 unpaired electrons because the energy splitting \( \Delta \) is small in the presence of a weak field ligand, leading to electrons occupying all \( d \) orbitals singly first, according to Hund's rule.

Draw the structure and determine chirality

In the structure of \( \left[\mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{3-} \), \( \mathrm{Fe}^{3+} \) is coordinated in an octahedral geometry by three bidentate oxalate ligands. Each \( \mathrm{C}_2\mathrm{O}_4^{2-} \) ligand forms a 5-membered ring with \( \mathrm{Fe}^{3+} \), resulting in a highly symmetric structure. Since the structure is symmetric and there are mirror images that superimpose, it does not have a non-superimposable mirror image and is, therefore, achiral.

Key concepts

Formation Constant

The formation constant, often denoted as \( K_{f} \), is an equilibrium constant that quantifies the stability of a complex ion in solution. For the iron oxalate complex, \( \left[\mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{3-} \), this is a significant value. A higher \( K_{f} \) indicates a more stable complex, implying the complex forms readily and disassociates reluctantly.
The value for this complex is very high, \( 3.3 \times 10^{20} \), which means that once the complex forms, very little free \( \mathrm{Fe}^{3+} \) remains in the solution.

• This stability is crucial when considering the availability of iron in dietary sources like spinach.
• The calculation of free \( \mathrm{Fe}^{3+} \) concentration involves inverting the \( K_{f} \) value.

Therefore, knowing the formation constant can help us understand why iron in spinach is not readily bioavailable for absorption by our bodies.

Crystal Field Theory

Crystal field theory helps explain the electronic structure of metal complexes, including the color, magnetism, and energy of the iron oxalate complex. In our complex \( \left[\mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{3-} \), \( \mathrm{Fe}^{3+} \) has a \( d^5 \) electron configuration.
The oxalate acts as a ligand creating a crystal field that splits the \( d \)-orbitals in the iron atom. This leads to high-spin or low-spin configurations depending on the ligand's field strength.

• Weak-field ligands like oxalate result in a smaller splitting energy \( \Delta \).
• This causes the electrons to spread across all \( d \)-orbitals according to Hund’s rule, maximizing the number of unpaired electrons.

Hence, in the crystal field splitting diagram for this complex, we see all five electrons are unpaired, leading to magnetic properties.

Ligand Field Strength

The strength of a ligand field impacts the electronic transitions and properties of a complex. Ligands can be classified as strong or weak field based on their ability to split the \( d \)-orbitals. In the case of the iron oxalate complex, \( \mathrm{C}_{2}\mathrm{O}_{4}^{2-} \) is a weak-field ligand.
Weak-field ligands lead to smaller energy differences between the \( t_{2g} \) and \( e_g \) orbitals.

• This results in high-spin configurations with a maximum number of unpaired d-electrons.
• The complexes tend to have a lower crystal field stabilization energy (CFSE).

The ligand field strength plays a role in the expression of magnetism (as it implies several unpaired electrons) and contributes to the color observed in these complexes.

Chirality

Chirality in chemistry refers to the geometric property of a structure having a non-superimposable mirror image. In analyzing the iron oxalate complex, \( \left[\mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{3-} \), its structure needs to be assessed.
The oxalate ligands form a symmetric, octahedral geometry around the iron center.

• The 5-membered rings created by each bidentate oxalate ligand result in a structure where mirror images superimpose perfectly.
• This symmetry makes the structure achiral, meaning it does not have any optical isomers.

The lack of chirality is important in applications and experimental settings where optical activity might otherwise be a consideration.

Acid-Base Equilibrium

Acid-base equilibrium describes how acids and bases interact in solutions, affecting solubility and reaction pathways. In the context of the iron oxalate complex, acidic stomach conditions can shift equilibriums.
The reaction with hydronium ions \( \left(\mathrm{H}_{3}\mathrm{O}^{+}\right) \) could theoretically release \( \mathrm{Fe}^{3+} \) ions by protonating the oxalate ligands.

• However, the relatively low \( K_{a1} \) and \( K_{a2} \) values for oxalic acid show that oxalate does not protonate easily.
• This makes the displacement of iron with acids in the stomach nonspontaneous.

Understanding the acid-base equilibrium helps clarify why dietary iron from such complexes remains less bioavailable.