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Ch.20 - Electrochemistry
Brown - Chemistry: The Central Science 15th Edition
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBrown 15th EditionCh.20 - ElectrochemistryProblema 113b
Capitolo 20, Problema 113b

Cytochrome, a complicated molecule that we will represent as CyFe2+, reacts with the air we breathe to supply energy required to synthesize adenosine triphosphate (ATP). The body uses ATP as an energy source to drive other reactions (Section 19.7). At pH 7.0 the following reduction potentials pertain to this oxidation of CyFe2+: O21g2 + 4 H+1aq2 + 4 e- ¡ 2 H2O1l2 Ered ° = +0.8 (b) If the synthesis of 1.00 mol of ATP from adenosine diphosphate (ADP) requires a ∆G of 37.7 kJ, how many moles of ATP are synthesized per mole of O2?

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Identify the relevant half-reaction for the reduction of oxygen: \( \text{O}_2(g) + 4 \text{H}^+(aq) + 4 \text{e}^- \rightarrow 2 \text{H}_2\text{O}(l) \) with \( E_{\text{red}}^\circ = +0.8 \text{ V} \).
Use the Nernst equation to relate the Gibbs free energy change (\( \Delta G \)) to the cell potential (\( E_{\text{cell}} \)): \( \Delta G = -nFE_{\text{cell}} \), where \( n \) is the number of moles of electrons transferred, and \( F \) is Faraday's constant (approximately 96485 C/mol).
Calculate \( \Delta G \) for the reduction of oxygen using the given \( E_{\text{red}}^\circ \) and the number of electrons transferred (\( n = 4 \)).
Determine the number of moles of ATP synthesized per mole of \( \text{O}_2 \) by dividing the \( \Delta G \) for the reduction of oxygen by the \( \Delta G \) required for the synthesis of 1 mole of ATP (37.7 kJ/mol).
Express the final result as the number of moles of ATP synthesized per mole of \( \text{O}_2 \).

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Reduction Potentials

Reduction potentials indicate the tendency of a chemical species to acquire electrons and be reduced. A higher reduction potential means a greater likelihood of reduction occurring. In the context of cytochrome and oxygen, the given reduction potential helps determine the feasibility of the electron transfer process that ultimately contributes to ATP synthesis.
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Standard Reduction Potentials

Gibbs Free Energy (∆G)

Gibbs Free Energy (∆G) is a thermodynamic quantity that represents the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. In biochemical reactions, a negative ∆G indicates that a reaction can occur spontaneously. The synthesis of ATP from ADP is coupled with the energy released from the oxidation of cytochrome, making it essential to understand how ∆G relates to the energy yield of the reaction.
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Gibbs Free Energy of Reactions

Stoichiometry of Reactions

Stoichiometry involves the calculation of reactants and products in chemical reactions based on balanced equations. In this context, it is crucial to determine how many moles of ATP can be synthesized per mole of O2 consumed. By using the stoichiometric relationships derived from the reduction potentials and Gibbs Free Energy, one can quantify the efficiency of energy conversion in biological systems.
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Stoichiometry Concept
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Cytochrome, a complicated molecule that we will represent as CyFe2+, reacts with the air we breathe to supply energy required to synthesize adenosine triphosphate (ATP). The body uses ATP as an energy source to drive other reactions (Section 19.7). At pH 7.0 the following reduction potentials pertain to this oxidation of CyFe2+: O21g2 + 4 H+1aq2 + 4 e- ¡ 2 H2O1l2 Ered ° = +0.82 V CyFe3+1aq2 + e- ¡ CyFe2+1aq2 E°red = +0.22 V (a) What is ∆G for the oxidation of CyFe2+ by air? (b) If the synthesis of 1.00 mol of ATP from adenosine diphosphate (ADP) requires a ∆G of 37.7 kJ, how many moles of ATP are synthesized per mole of O2?

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