12.5Free Energy
Section · module m71831
What this needs
Learn these first — this section will not make sense without them.
Nothing in the algebra book is a prerequisite for this section.
What this touches
Algebra that turns up here. Not a blocker, but this is where you will see it used.
- Applies2.4Models and Applications
ΔG° = ΔH° − TΔS° mixes units — ΔH° arrives in kJ while TΔS° comes out in J — so evaluating this literal equation correctly requires inserting a ×(1 kJ/1000 J) conversion mid-formula, a step the worked examples show explicitly and that is easy to drop.
- Applies4.2Linear Functions
ΔG = ΔH − TΔS is linear in T with slope −ΔS and intercept ΔH, which is why its sign — and hence spontaneity — can flip exactly once as T increases; reading ΔG this way alongside linear functions makes the sign-table in this section (ΔG<0 vs >0) feel like evaluating one line rather than memorizing three cases.
Coupled reactions reuse the Hess's-law addition trick from chapter 9 on ΔG instead of ΔH — decomposing ZnS (ΔG°=+201.3 kJ) is made spontaneous by adding the oxidation of sulfur (ΔG°=−300.1 kJ) so the shared S(s) cancels, the identical scale-and-add-to-eliminate-a-species move as solving a linear system by elimination.