Coupled Reactions (College Board AP Chemistry)

• A thermodynamically unfavorable reaction is one that does not occur spontaneously
  • It needs the additional input of energy after the reactants are mixed together 
  • It will have a positive ΔG° value.
•  We can make a thermodynamically unfavorable reaction favorable 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 
  • Light driving the overall conversion of carbon dioxide to glucose in photosynthesis 

• We can make a thermodynamically unfavorable reaction favorable by coupling it to a favorable reaction via an intermediate
• The sum of the two reactions will result in a reaction that overall has a negative ΔG° value.
• 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

• • • The equilibrium constant is less than 1 which means there are more reactants than products at equilibrium so not much copper would be produced
  • 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 will allow us to make a significant amount of copper because they share the common intermediate, sulfur 
  • 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 
  • Removing the sulfur from reaction 1 causes the equilibrium to shift to the right therefore producing more copper 
  • 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) 2Cu (s) + SO₂ (g)

• • • Adding the two ΔG°values together:
      • +85.1 +(-301.4) = –216.3  kJmol^-1 
      • A negative value shows now this overall reaction is thermodynamically favorable
      • It will have an equilibrium constant of above 1
      • Copper will be produced 
• 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 kJmol^-1

• • The reactions are coupled
  • The water cancels out to give:

alanine + glycine + ATP alanylglycine + ADP + Pi

• • Adding the two ΔG° values together gives an overall  ΔG° = –2  kJ mol^-1
  • The reaction is now thermodynamically favored