9.7 Coupled Reactions

A thermodynamically unfavorable reaction, with $\Delta G^\circ>0$, will not happen on its own, but you can drive it by adding an external energy source like electricity or light, or by coupling it to a favorable reaction with $\Delta G^\circ<0$ that shares a common intermediate. When you add the coupled reactions, their $\Delta G^\circ$ values add too, and if the total is negative the overall process is thermodynamically favored. For AP Chemistry, add the $\Delta G^\circ$ values before judging the coupled process.

Why This Matters for the AP Chemistry Exam

Coupled reactions tie together everything from Unit 9: Gibbs free energy, thermodynamic favorability, and how ΔG° values combine. The exam expects you to explain how an unfavorable process can still produce a desired product when it is paired with a favorable one or pushed by outside energy. This is a reasoning topic, so you should be ready to justify why an overall reaction works using the signs and sums of ΔG°, and to recognize real examples like electrolysis, photosynthesis, and ATP-to-ADP coupling in living systems.

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Key Takeaways

• A reaction with ΔG° > 0 is thermodynamically unfavorable and needs help to proceed.
• External energy sources can drive unfavorable processes: electrical energy runs an electrolytic cell or charges a battery, and light drives the conversion of carbon dioxide to glucose in photosynthesis.
• Coupling links an unfavorable reaction to a favorable one through a shared common intermediate so the overall ΔG° < 0.
• When you add coupled reactions, you add their ΔG° values; the sum determines if the overall process is favored.
• If you scale a reaction by a factor, multiply its ΔG° by the same factor.
• The conversion of ATP to ADP is the classic biological example of using a favorable reaction to drive an unfavorable one.

Thermodynamically Unfavorable Reactions

For most of Unit 9, you work with thermodynamically favorable reactions, meaning ΔG° < 0 and K > 1. This topic focuses on the opposite: thermodynamically unfavorable reactions, where ΔG° > 0 and K < 1. These do not proceed on their own and need an external push to happen.

One common push is electrical energy. By supplying electricity, you can drive nonspontaneous redox reactions. For example, a battery can be connected to an electrolytic cell (covered in 9.8) to force electrons in a direction they would not move on their own. This is also how a rechargeable battery gets charged back up.

Light is another external energy source. In photosynthesis, light drives the overall conversion of carbon dioxide to glucose, a process that would not happen without that energy input.

Coupled Reactions Explained

Another way to make an unfavorable reaction proceed is to couple it with a favorable one. Coupled reactions combine a reaction with ΔG° > 0 and a reaction with ΔG° < 0 that share a common intermediate.

From kinetics, recall that an intermediate is produced in one step and consumed in the next. When two reactions share a common intermediate, you can add them together to get a new overall reaction. Because ΔG° is a state function, the ΔG° values add too. If the sum is negative, the overall process is thermodynamically favored.

Here is a worked example. Consider this unfavorable reaction:

Cu2S → 2Cu + S (ΔG° = 86.2 kJ)

This reaction needs external energy to occur. But you can find a favorable reaction that involves S and add it in:

S + O2 → SO2 (ΔG° = -300.1 kJ)

Adding the two reactions:

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 kJ)

The S cancels because it is the common intermediate, and the favorable formation of SO2 outweighs the unfavorable decomposition of Cu2S. The overall reaction has ΔG° < 0, so it is thermodynamically favored.

This idea shows up constantly in biology. The conversion of ATP to ADP is favorable, and cells couple it to many reactions that would otherwise be unfavorable, which lets those reactions produce the products the cell needs.

Problem Solving

Given the following reactions and thermodynamic data, calculate ΔG° for the reaction Fe2O3 + 3CO → 2Fe + 3CO2:

Fe2O3 → 2Fe + 3/2O2 (ΔG° = 742.2 kJ)

CO + 1/2O2 → CO2 (ΔG° = -283.5 kJ)

The two reactions share O2 as a common intermediate. First, multiply the second reaction by 3 so the O2 amounts will cancel. When you scale a reaction, you scale its ΔG° by the same factor.

Fe2O3 → 2Fe + 3/2O2 (ΔG° = 742.2 kJ)

3CO + 3/2O2 → 3CO2 (ΔG° = -283.5 * 3 = -850.5 kJ)

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

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

How to Use This on the AP Chemistry Exam

Problem Solving

• Line up your reactions so the common intermediate cancels. If you have to reverse a reaction, flip the sign of its ΔG°. If you have to scale a reaction, multiply its ΔG° by the same factor.
• Add the adjusted ΔG° values to get the overall ΔG°. A negative total means the coupled process is thermodynamically favored.
• Watch your units and signs. A common slip is forgetting to scale ΔG° after multiplying a reaction through.

Free Response

• Be ready to explain in words why coupling works, not just compute a number. The key idea is that the favorable reaction's negative ΔG° outweighs the unfavorable reaction's positive ΔG°, giving a negative overall ΔG°.
• If asked about external energy, name a specific driver: electrical energy for an electrolytic cell or charging a battery, or light for the conversion of carbon dioxide to glucose.
• When citing biology, the ATP-to-ADP conversion is the standard example of a favorable reaction driving unfavorable ones.

Common Misconceptions

• "Unfavorable means impossible." An unfavorable reaction (ΔG° > 0) can still happen if you add external energy or couple it to a favorable reaction. It just will not go on its own.
• "Coupling changes the individual ΔG° values." Each reaction keeps its own ΔG°. Coupling just adds them; the favorable one offsets the unfavorable one.
• "Any two reactions can be coupled." They must share a common intermediate so it cancels when you add the reactions. Without that shared species, you cannot combine them into one overall process.
• "Scaling a reaction does not affect ΔG°." If you multiply a reaction by a factor, you must multiply its ΔG° by the same factor. Reversing a reaction flips the sign of ΔG°.
• "Thermodynamically favored means it happens fast." Favorability only tells you about direction, not speed. A favored reaction can still be slow if it is under kinetic control.

Related AP Chemistry Guides

• 9.1 Introduction to Entropy
• 9.3 Gibbs Free Energy and Thermodynamic Favorability
• 9.2 Absolute Entropy and Entropy Change
• 9.8 Galvanic (Voltaic) and Electrolytic Cells
• 9.4 Thermodynamic and Kinetic Control
• Unit 9 Review: Thermodynamics and Electrochemistry