Ch.18 - Thermodynamics: Entropy, Free Energy & Equilibrium

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McMurry 8th Edition

Ch.18 - Thermodynamics: Entropy, Free Energy & Equilibrium

Problema 21.134b

Capitolo 18, Problema 21.134b

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 [Fe(C₂O₄)₃]^3-.
(b) Under the acidic conditions in the stomach, the Fe³⁺ concentration should be greater because of the reaction
[Fe(C₂O₄)₃]^3-(aq) + 6 H₃O⁺(aq) ⇌ Fe³⁺(aq) + 3 H₂C₂O₄(aq) + 6 H₂O(l)
Show, however, that this reaction is nonspontaneous under standard-state conditions. (For H₂C₂O₄, K_a1 = 5.9 × 10^-2 and K_a2 = 6.4 × 10^-5.)

Guida verificata passo dopo passo

Identify the reaction given: \([\text{Fe(C}_2\text{O}_4)_3]^{3-}(aq) + 6 \text{H}_3\text{O}^+(aq) \rightleftharpoons \text{Fe}^{3+}(aq) + 3 \text{H}_2\text{C}_2\text{O}_4(aq) + 6 \text{H}_2\text{O}(l)\).

Determine the equilibrium constant \(K_{eq}\) for the reaction using the given \(K_{a1}\) and \(K_{a2}\) values for oxalic acid (\(\text{H}_2\text{C}_2\text{O}_4\)).

Calculate the \(K_{eq}\) for the reverse reaction by considering the dissociation of \(\text{H}_2\text{C}_2\text{O}_4\) into \(\text{H}^+\) and \(\text{C}_2\text{O}_4^{2-}\) using \(K_{a1}\) and \(K_{a2}\).

Use the relationship \(K_{eq} = \frac{1}{K_{sp}}\) to find the \(K_{sp}\) of the complex \([\text{Fe(C}_2\text{O}_4)_3]^{3-}\).

Conclude that if \(K_{eq} < 1\), the reaction is nonspontaneous under standard-state conditions.

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Complex Ion Formation

Complex ions are formed when metal ions bind to ligands, which are molecules or ions that can donate electron pairs. In the case of spinach, iron is complexed with oxalate ions to form [Fe(C2O4)3]3-, making the iron less bioavailable. Understanding complex ion formation is crucial for analyzing how metal ions interact with other species in biological systems.

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Percorso guidato

02:20

Complex Ions and Formation Constant

Acid-Base Equilibria

Acid-base equilibria involve the transfer of protons (H+) between species in solution, which can affect the solubility and availability of ions. The reaction provided shows how the acidic environment in the stomach can influence the concentration of Fe3+ ions by shifting the equilibrium. Knowledge of acid-base equilibria is essential for predicting how changes in pH can impact chemical reactions.

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02:00

Arrhenius Acids and Bases

Gibbs Free Energy and Spontaneity

Gibbs free energy (G) is a thermodynamic potential that helps predict whether a reaction will occur spontaneously. A reaction is spontaneous if the change in Gibbs free energy (ΔG) is negative. To determine the spontaneity of the given reaction, one must calculate ΔG using standard-state conditions and the equilibrium constants provided, which is fundamental in thermodynamics.

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01:51

Gibbs Free Energy of Reactions

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