Coupled Reactions (College Board AP® Chemistry): Study Guide

Making thermodynamically unfavorable processes occur

• A thermodynamically unfavorable reaction is one that does not occur spontaneously

  • It occurs only while an external source keeps supplying energy; this is not the same as supplying the activation energy to start a reaction

  • It has a positive ΔG° value

• A thermodynamically unfavorable process can be made to occur by:

  • Applying external energy sources

  • Coupling it with a thermodynamically favorable reaction that shares an intermediate 

• Examples of applying external energy include:

  • Electrical energy being used to drive an electrolytic cell or charge a battery

  • Light driving the overall conversion of carbon dioxide to glucose in photosynthesis 

Coupling reactions

• A desired product can be formed by coupling the thermodynamically unfavorable reaction that produces it to a favorable reaction

  • The two reactions share a common intermediate

• The sum of the two reactions is a reaction with a negative overall ΔG°

Coupling: decomposition of copper(I) sulfide

• For example, the decomposition of copper(I) sulfide to produce copper as the desired product and sulfur is thermodynamically unfavorable 

Cu₂S (s) ⇌ 2Cu (s) + S (s) ΔG° = +85.1 kJ mol⁻¹ K < 1

• ΔG° is positive, so K < 1 and the decomposition is not thermodynamically favored: on its own, very little copper forms

• This reaction can be coupled to a thermodynamically favorable reaction such as the reaction between sulfur and oxygen to give sulfur dioxide

S (s) + O₂ (g) ⇌ SO₂ (g) ΔG° = −301.4 kJ mol⁻¹ K > 1

• At equilibrium, the equilibrium constant is greater than 1 so there will be more products than reactants 

• Coupling these two reactions, which share the common intermediate sulfur, allows a significant amount of copper to form

• Even if only a small amount, sulfur will still be produced in reaction 1 when copper(I) sulfide decomposes

  • This will then be used up in reaction 2 by reacting with oxygen to produce sulfur dioxide 

• Adding the two reactions cancels the sulfur, and the overall reaction has a negative ΔG°, so copper forms

• The thermodynamically favorable second reaction is driving the thermodynamically unfavorable reaction 

• Adding the two reactions together, the sulfur will cancel out to give:

Cu₂S (s) + O₂ (g) $\rightleftharpoons$ 2Cu (s) + SO₂ (g)

• Adding the two ΔG°values together:

  • +85.1 + (−301.4) = −216.3 kJ mol⁻¹

  • The negative value shows that the overall reaction is thermodynamically favorable

  • It will have an equilibrium constant of above 1

  • Copper will be produced

Coupling: conversion of ATP to ADP

• Coupling reactions are also used in the conversion of ATP to ADP in the body, which helps drive protein synthesis

  • Amino acids alanine and glycine will produce alanylglycine (a dipeptide) and water: 

alanine + glycine ⇌ alanylglycine + H₂O ΔG° = +31 kJ mol⁻¹

• This is thermodynamically unfavorable due to the positive ΔG° 

• The hydrolysis of ATP is thermodynamically favorable:

ATP + H₂O ⇌ ADP + Pi ΔG° = −33 kJ mol⁻¹

• The reactions are coupled

• The water cancels out to give:

alanine + glycine + ATP $\rightleftharpoons$ alanylglycine + ADP + Pi

• Adding the two ΔG° values together gives an overall ΔG° = −2 kJ mol⁻¹

• The reaction is now thermodynamically favored