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

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McMurry 8th Edition

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

Problem 21.134b

Chapter 18, Problem 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.)

Verified step by step guidance

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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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.

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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Related Practice

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Consider the gas-phase reaction of AB3 and A2 molecules:

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Consider the following endothermic reaction of gaseous AB3 molecules with A2 molecules.

Identify the true statement about the spontaneity of the reaction. (a) The reaction is likely to be spontaneous at high temperatures. (b) The reaction is likely to be spontaneous at high temperatures. (c) The reaction is always spontaneous.(d) The reaction is always spontaneous.

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Consider the following graph of total free energy of reactants and products versus reaction progress for the general reaction, Reactants -> Products. At which of the four points (labeled a, b, c, and d) is Q < K?

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Ideal gases A (red spheres) and B (blue spheres) occupy two separate bulbs. The contents of both bulbs constitute the initial state of an isolated system. Consider the process that occurs when the stopcock is opened.

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Textbook Question

Ammonium hydrogen sulfide, a stink bomb ingredient, decomposes to ammonia and hydrogen sulfide: Calculate the standard free-energy change for the rection at 25 °C if the total pressure resulting from the solid NH4S placed in an evacuated container is 0.658 atm at 25 °C.(a) -43.8 kJ(b) +1.04 kJ(c) -462 kJ(d) +5.51 kJ

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Formation constants for the ammonia and ethylenediamine complexes of nickel(II) indicate that Ni(en)₃²⁺ is much more

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(1) <REACTION>

(2) <REACTION>

The enthalpy changes for the two reactions, ΔH°₁ and ΔH°₂, should be about the same because both complexes have six Ni﹣N bonds.

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