Living cells build proteins and sugars, and both have positive ΔG. They manage it by pairing each uphill reaction with a strongly downhill one. Free energies add the way enthalpies do in Hess’s law.
🔑 Key idea
When two reactions share an intermediate and run as one combined process, their free energies add: $\Delta G_\text{total} = \Delta G_1 + \Delta G_2$, and their constants multiply: $K_\text{total} = K_1K_2$. If the total is negative, the combined process is favored, even though one part alone is not.
💡 Why it works
$G$ is a state function, so the overall change does not depend on the path; adding the equations adds the $\Delta G$ values. Coupling is not a bookkeeping trick: the two reactions must be physically linked, usually through a shared intermediate. In cells, ATP transfers a phosphate group to the reactant, making an activated intermediate whose next step is downhill.
An uphill step (+14.2 kJ/mol) paired with ATP hydrolysis (−30.5 kJ/mol). The combined process is downhill by 16.3 kJ/mol.
Worked examples
✏️ Worked example: Making glutamine
Glutamate + $\mathrm{NH_4^+}$ → glutamine + water has $\Delta G^{\circ\prime} = +14.2\ \text{kJ/mol}$. ATP hydrolysis has $\Delta G^{\circ\prime} = -30.5\ \text{kJ/mol}$. Find the total and $K$ at $310\ \text{K}$ (body temperature).
Alone, the first reaction has $K = e^{-14\,200/(8.314 \times 310)} = 4.0 \times 10^{-3}$: coupling raises $K$ by more than 100 000 times.
Answer: $-16.3\ \text{kJ/mol}$; $K \approx 560$.
✏️ Worked example: Adding constants
Reaction 1 has $K_1 = 2.0 \times 10^{-3}$ and reaction 2 has $K_2 = 5.0 \times 10^{5}$ at the same temperature. Coupled, they add to the overall process. Find $K$ and the sign of $\Delta G^\circ$.
The $\circ\prime$ (degree-prime) marks the biochemists' standard state: pH 7 rather than $1\ \text{M}$ $\mathrm{H_3O^+}$, which suits reactions in cells. Other values you will meet: phosphoenolpyruvate hydrolysis, $-61.9\ \text{kJ/mol}$; glucose + phosphate → glucose 6-phosphate, $+13.8\ \text{kJ/mol}$. Industry couples reactions too: in smelting, carbon's reaction with oxygen pays for pulling oxygen out of a metal oxide.
A typical cell turns over its ATP many times a day, remaking it from ADP and phosphate with energy from food; the ATP is a carrier of free energy, not a store.
⚠️ Common mistake
Thinking coupling changes the $\Delta G$ of the unfavored step itself. That step still has $\Delta G = +14.2\ \text{kJ/mol}$; what changes is that it no longer runs alone. Check: the total is the sum, and each part keeps its own value.
Practice
Pass with 3 right answers, the last 2 in a row. Each right answer earns 2 XP.