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Unit 9

9.6 Coupled Reactions

3 min readjuly 9, 2021

sander-o

Sander Owens

fiveable-dylan

Dylan Black


AP Chemistry 🧪

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9.6: Coupled Reactions

Thermodynamically Unfavorable Reactions

For most of this unit, we’ve discussed thermodynamically favorable reactions or reactions for which ΔG° < 0 and that K > 1. However, this section looks at thermodynamically unfavorable reactions. These are reactions that do not occur spontaneously and therefore won’t happen without any sort of external energy source. The first part of this unit discusses how these external energy sources can be used to help nonspontaneous processes occur. 
A common source of energy for spurring nonspontaneous processes is electricity. By using electrical energy, nonspontaneous redox reactions can take place. For example, a battery can be connected to an electrolytic cell (a topic we’ll discuss in unit 9.7) to “push” electrons from a negatively charged ion to a positively charged one in a reaction of the form Y+ + Z- → Y + Z (assuming Y + Z → Y+ + Z- is spontaneous). These cells are also similar to the way a battery is charged.
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Coupled Reactions Explained

Another way to make nonspontaneous reactions spontaneous is through the use of coupled reactions. Coupled reactions are a combination of a nonspontaneous reaction and a spontaneous reaction that have a common intermediate. Recall from kinetics that an intermediate is a product of one part of a mechanism and a reactant in the next. For example, in the following mechanism, O is an intermediate:
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By using reactions with common intermediates, mechanisms for new reactions can form. By adding together these elementary steps, a new reaction results that is spontaneous. An example of this is clear in the following reaction:
Cu2S → 2Cu + S (ΔG° = 86.2 kJ)
We see that this reaction is nonspontaneous and therefore requires some external energy to occur. However, we can also find a spontaneous reaction with either Cu or S as a reactant that we can add to the reaction to create a spontaneous process overall. For example, let’s use the reaction S + O2 → SO2 (ΔG° = -300.1 kJ).
By adding these reactions together we find the following:
Cu2S → 2Cu + S (ΔG° = 86.2 kJ)
S + O2 → SO2 (ΔG° = -300.1 kJ)

Cu2S + O2 → 2Cu + SO2 (ΔG° = 86.2 + (-300.1) = -213.9)
As we see through adding these reactions together, we can use the spontaneous process of sulfur and oxygen forming sulfur dioxide to couple the reactions and form a process that is overall spontaneous.
This concept finds many applications in biology, including the conversion of ATP to ADP in biological systems. The example below comes from organic chemistry but is another example of reaction coupling. Don’t worry if you don’t understand terms like ATP, ADP, or what all the hexagons and pentagons mean:
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Resources:

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Practice Problem

Given the following reactions and thermodynamic data, calculate the ΔG° value for the reaction Fe2O3 + 3CO → 2Fe + 3CO2:
Fe2O3 → 2Fe + 3/2O2 (ΔG° = 742.2 kJ)
CO + 1/2O2 → CO2 (ΔG° = -283.5 kJ)
We can use reaction coupling to solve this problem because the two reactions have a common intermediate of O2. However, we first want to multiply the bottom reaction by 3 to make the O2s cancel out. When we do so we also multiply ΔG° by the same factor.
Fe2O3 → 2Fe + 3/2O2 (ΔG° = 742.2 kJ)
3CO + 3/2O2 → 3CO2 (ΔG° = -283.5 * 3 kJ = -850.5 kJ)

Fe2O3 + 3CO + 3/2O2 → 2Fe + 3CO2 + 3/2O2 (ΔG° = 742.2 kJ + -850.5 kJ = -108.3 kJ)
Fe2O3 + 3CO+ → 2Fe + 3CO2 (ΔG° = -108.3 kJ)

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