Spontaneity gets oversimplified into "exothermic reactions happen and endothermic ones don't," which is wrong often enough to be a real problem. Gibbs free energy is what actually settles the question.
The equation and what it means
Formula
Interpreting the sign of ΔG
The four sign combinations
| ΔH | ΔS | Result |
|---|---|---|
| Negative | Positive | Always spontaneous, at every temperature |
| Positive | Negative | Never spontaneous, at any temperature |
| Negative | Negative | Spontaneous only at low temperature |
| Positive | Positive | Spontaneous only at high temperature |
The middle two rows are where temperature genuinely decides the outcome, and they're exactly the cases that a simple "exothermic is spontaneous" rule gets wrong.
Connecting to the equilibrium constant and cell potential
Standard free energy change relates directly to the equilibrium constant through ΔG° = −RT ln K, meaning a very favorable reaction corresponds to a very large K. It also connects to electrochemistry through ΔG = −nFE°, linking a cell's voltage directly to how thermodynamically favorable its underlying reaction is.
Where students actually lose points here
Assuming exothermic always means spontaneous
That's only guaranteed when entropy is also increasing. A reaction that's exothermic but decreases entropy is only spontaneous below a certain temperature, not automatically.
Ignoring temperature's role entirely
For two of the four sign combinations, temperature is the deciding factor, not enthalpy or entropy alone. Treating favorability as fixed regardless of temperature misses exactly what those two cases test.
Mixing up ΔG and ΔG°
ΔG° describes standard conditions specifically. ΔG describes the actual conditions of a real system, which can be spontaneous or not independent of what the standard value predicts.
The unifying idea of Unit 9
Free energy is the concept that ties enthalpy, entropy, equilibrium, and electrochemistry together into one coherent picture by the end of the course.
Common questions
Does a negative ΔH always mean a reaction is spontaneous?
No. Spontaneity depends on both enthalpy and entropy together, along with temperature. An exothermic reaction with a decrease in entropy is only spontaneous below a certain temperature, not automatically.
How does Gibbs free energy relate to the equilibrium constant?
Through the equation ΔG° = −RT ln K. A very negative ΔG° corresponds to a very large equilibrium constant, meaning the reaction strongly favors products at equilibrium.
What's the difference between ΔG and ΔG°?
ΔG° describes the free energy change under standard conditions specifically. ΔG describes the free energy change under the actual, real conditions of a system, which can differ from the standard prediction.