Coupled Reactions

AP Chemistry· 40 min read

1. Core Definition and Validity Rules for Coupled Reactions★★☆☆☆⏱ 8 min

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.

📘 Definition

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.

2. Calculating Total Gibbs Free Energy for Coupled Reactions★★★☆☆⏱ 10 min

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.

✓ Quick check

Test your understanding of the summation rule

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

3. Biological Coupled Reactions: ATP as Universal Energy Currency★★★☆☆⏱ 9 min

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.

4. Industrial Electrochemical Coupled Reactions★★★★☆⏱ 7 min

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.

5. Common Pitfalls

Wrong move:

Summing (\Delta G) values for two unrelated reactions with no shared intermediate

Why:

No shared intermediate means there is no mechanism to transfer free energy between the two processes

Correct move:

Always confirm a common intermediate exists before adding (\Delta G) values to claim a process is coupled.

Wrong move:

Using (\Delta G) values measured at different temperatures for summation

Why:

(\Delta G) is temperature dependent, so mismatched conditions produce invalid total values

Correct move:

Only add (\Delta G) values specified for identical pressure, temperature, and concentration conditions.

Wrong move:

Adding standard cell potential (E^\circ) values directly the same way you add (\Delta G)

Why:

(E^\circ) is an intensive property that does not scale with reaction stoichiometry, so it cannot be summed directly

Correct move:

Convert (E^\circ) values to (\Delta G) using (\Delta G = -nFE^\circ) before combining for coupled processes.

Wrong move:

Claiming a reaction with total (\Delta G = 0) is a valid spontaneous coupled process

Why:

Coupled processes require net negative (\Delta G) to proceed at measurable rates

Correct move:

Ensure the sum of (\Delta G) values is strictly negative to confirm the coupled reaction is spontaneous.

Wrong move:

Forgetting to multiply (\Delta G) values by molar coefficients when balancing the overall coupled reaction

Why:

(\Delta G) is an extensive property that scales with reaction stoichiometry

Correct move:

Adjust individual (\Delta G) values by their stoichiometric multipliers before summing the total.

6. Quick Reference 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.