# Coupled Reactions

> AP Chemistry · AP Chemistry 2024-2027 Curriculum
> Source: https://www.owlsprep.com/study/ap-chemistry-u9-coupled-reactions/

We define coupled reactions, practice calculating total Gibbs free energy for valid paired processes, connect the concept to biological energy transfer, and work through AP-style exam problems.

**Prerequisites:** [Spontaneity and Gibbs Free Energy Calculations](https://www.owlsprep.com/study/ap-chemistry-u9-gibbs-free-energy/); [Hess's Law for Enthalpy Summation](https://www.owlsprep.com/study/ap-chemistry-u6-hess-law/)

## Learning objectives

- Define coupled reactions and explain their core requirement of a shared common intermediate
- Calculate total Gibbs free energy change for valid coupled reaction pairs using Hess's law-style summation
- Connect coupled reaction principles to biological energy transfer via ATP hydrolysis
- Identify valid vs invalid coupled reaction pairs to avoid common AP exam distractors

## Core Definition and Validity Rules for Coupled Reactions

Many non-spontaneous reactions with positive \(\Delta G\) cannot proceed on their own, even if they are kinetically stable. Coupling these processes to a highly spontaneous reaction with a very negative \(\Delta G\) creates a single overall process that can proceed spontaneously, as long as the two reactions share a common intermediate to transfer free energy.

**Coupled Reactions** — Two or more sequential reactions that share a common intermediate, where a highly exergonic reaction provides the free energy required to drive an endergonic reaction forward.

**Worked example:** Reaction 1 (non-spontaneous): A → B, \(\Delta G = +22 \, \text{kJ/mol}\); Reaction 2 (spontaneous): C → D, \(\Delta G = -35 \, \text{kJ/mol}\), no shared intermediate. Can these two reactions be coupled to produce a spontaneous overall process?

1. Step 1: Verify if the reactions share a common intermediate. In this case, no shared intermediate exists.
2. Step 2: Even though the sum of \(\Delta G\) values is -13 kJ/mol, there is no mechanism for free energy transfer between the two unrelated processes.
3. Step 3: Final conclusion: The paired process cannot be classified as a valid coupled reaction, and will not proceed spontaneously.

> **tip**
>
> AP exam questions almost always include a distractor pair of reactions with no shared intermediate to test if you remember this requirement, rather than just summing \(\Delta G\) values blindly.

## Calculating Total Gibbs Free Energy for Coupled Reactions

Once you confirm a shared intermediate exists, you sum the individual \(\Delta G\) values of each reaction exactly the same way you sum enthalpy values in Hess's law. Since \(\Delta G\) is an extensive property, you must scale individual values by their stoichiometric coefficients before summing if the overall balanced reaction requires multiple equivalents of a single process.

$$\Delta G_{\text{total}} = n_1 \Delta G_1 + n_2 \Delta G_2 + ... + n_k \Delta G_k$$

**Worked example:** The non-spontaneous formation of glucose-6-phosphate from glucose has \(\Delta G = +13.8 \, \text{kJ/mol}\). ATP hydrolysis to ADP has \(\Delta G = -30.5 \, \text{kJ/mol}\), and the two reactions share a phosphate intermediate. Calculate the total \(\Delta G\) for the coupled process.

1. Step 1: Confirm the shared phosphate intermediate exists, so coupling is valid.
2. Step 2: No stoichiometric scaling is required, so sum the two \(\Delta G\) values directly.
3. $$\Delta G_{\text{total}} = +13.8 \, \text{kJ/mol} + (-30.5 \, \text{kJ/mol})$$
4. Step 4: Final result: \(\Delta G_{\text{total}} = -16.7 \, \text{kJ/mol}\), a negative value confirming the coupled process is spontaneous.

**Check your understanding**

Test your understanding of the summation rule

1. Reaction X has \(\Delta G = +42 \, \text{kJ/mol}\), Reaction Y has \(\Delta G = -55 \, \text{kJ/mol}\), they share a common intermediate. What is the overall \(\Delta G\)?

   - +97 kJ/mol
   - -13 kJ/mol
   - -42 kJ/mol
   - +13 kJ/mol

   *Why:* Sum the two values directly: +42 + (-55) = -13 kJ/mol, confirming a spontaneous coupled process.

## Biological Coupled Reactions: ATP as Universal Energy Currency

Virtually all endergonic cellular reactions, including amino acid synthesis, muscle contraction, and active transport across cell membranes, are coupled to ATP hydrolysis. This highly exergonic reaction is the primary driver of non-spontaneous processes in all living systems, measured at standard biological conditions of pH 7.

> **Coupling Mnemonic**
>
> Endergonic + Exergonic = Spontaneous: E + E = S, remember you need one negative \(\Delta G\) large enough to cancel out the positive \(\Delta G\) of the non-spontaneous process.

**Exam command terms**

Common AP exam command terms for this topic

- **Justify** — You must explicitly state that ATP hydrolysis provides enough negative \(\Delta G\) to offset the positive \(\Delta G\) of the non-spontaneous biosynthetic reaction *(Justify why glucose phosphorylation proceeds in cells even though it is non-spontaneous alone.)*

## Industrial Electrochemical Coupled Reactions

Many industrial metallurgy processes use spontaneous combustion or redox reactions to drive non-spontaneous metal ore reduction. For example, iron smelting pairs the non-spontaneous reduction of iron(III) oxide with the highly exergonic combustion of carbon, sharing a gaseous oxygen intermediate to create a spontaneous overall process at high temperature.

**Worked example:** Reduction of iron(III) oxide to iron metal has \(\Delta G = +148 \, \text{kJ/mol}\) per mole of \(\text{Fe}_2\text{O}_3\). Combustion of carbon to CO has \(\Delta G = -272 \, \text{kJ/mol}\) per 2 moles of C. The two reactions share a gaseous oxygen intermediate. Calculate the total \(\Delta G\) for the coupled smelting process.

1. Step 1: Confirm shared oxygen intermediate exists, so coupling is valid.
2. $$\Delta G_{\text{total}} = +148 \, \text{kJ/mol} + (-272 \, \text{kJ/mol})$$
3. Step 3: Final result: \(\Delta G_{\text{total}} = -124 \, \text{kJ/mol}\), confirming the smelting process proceeds spontaneously at operating temperatures.

## Common pitfalls

- **Wrong:** Summing \(\Delta G\) values for two unrelated reactions with no shared intermediate
  - Why it fails: No shared intermediate means there is no mechanism to transfer free energy between the two processes
  - Correct: Always confirm a common intermediate exists before adding \(\Delta G\) values to claim a process is coupled.
- **Wrong:** Using \(\Delta G\) values measured at different temperatures for summation
  - Why it fails: \(\Delta G\) is temperature dependent, so mismatched conditions produce invalid total values
  - Correct: Only add \(\Delta G\) values specified for identical pressure, temperature, and concentration conditions.
- **Wrong:** Adding standard cell potential \(E^\circ\) values directly the same way you add \(\Delta G\)
  - Why it fails: \(E^\circ\) is an intensive property that does not scale with reaction stoichiometry, so it cannot be summed directly
  - Correct: Convert \(E^\circ\) values to \(\Delta G\) using \(\Delta G = -nFE^\circ\) before combining for coupled processes.
- **Wrong:** Claiming a reaction with total \(\Delta G = 0\) is a valid spontaneous coupled process
  - Why it fails: Coupled processes require net negative \(\Delta G\) to proceed at measurable rates
  - Correct: Ensure the sum of \(\Delta G\) values is strictly negative to confirm the coupled reaction is spontaneous.
- **Wrong:** Forgetting to multiply \(\Delta G\) values by molar coefficients when balancing the overall coupled reaction
  - Why it fails: \(\Delta G\) is an extensive property that scales with reaction stoichiometry
  - Correct: Adjust individual \(\Delta G\) values by their stoichiometric multipliers before summing the total.

## Cheatsheet

| Rule | Formula / Requirement |
| --- | --- |
| Coupling Validity Check | Must share at least one common reaction intermediate |
| Total ΔG Calculation | \(\Delta G_{\text{total}} = n_1 \Delta G_1 + n_2 \Delta G_2\) |
| Spontaneity Condition | \(\Delta G_{\text{total}} < 0\) |
| Biological Standard Condition | \(\Delta G^{\circ '}\) at pH = 7, 298 K |

## What's next

Mastering coupled reactions is a critical bridge between Gibbs free energy concepts and real-world applications you will encounter in the electrochemistry portion of Unit 9, including electrolytic cells that use external electrical energy to drive non-spontaneous redox processes. This topic is also frequently paired with reaction kinetics questions about activation energy in multi-step reaction pathways on AP exam free response sections, so you will see it referenced repeatedly as you review for your test. Make sure you practice identifying shared intermediates across different reaction types to avoid the most common distractors on exam day.

---

From [OwlsPrep](https://www.owlsprep.com) — free study guides for A-Level, IB, AP and IGCSE, written against the official syllabus. Canonical page: https://www.owlsprep.com/study/ap-chemistry-u9-coupled-reactions/