Short on time? This page is the recap. For explanations and worked examples, use the full study guide.
Recap
- ΔG° is the Gibbs free energy change with everything in its standard state: pure solids and liquids, 1 M solutions, gases at 1 bar (about 1 atm).
- ΔG° < 0 means the process is thermodynamically favoured (older books say “spontaneous”). ΔG° > 0 means the reverse is favoured.
- ΔG° says which direction is favoured, never how fast.
- ΔG° combines two drives: releasing energy (ΔH° < 0) and dispersing matter and energy (ΔS° > 0).
Key relationships
| Relationship | Units and notes | Use it to |
|---|---|---|
| ΔG° = ΣnΔG°f(products) − ΣnΔG°f(reactants) | kJ mol⁻¹; ΔG°f = 0 for elements in standard states | find ΔG° from a data table |
| ΔG° = ΔH° − TΔS° | ΔH° in kJ mol⁻¹, ΔS° ÷ 1000 to kJ K⁻¹ mol⁻¹, T in K | find ΔG° at any temperature |
| T = ΔH° ÷ ΔS° | same units top and bottom | find the changeover temperature (ΔG° = 0) |
| ΔH° | ΔS° | Favoured at |
|---|---|---|
| − | + | all T |
| + | − | no T |
| + | + | high T |
| − | − | low T |
Assumptions
- ΔH° and ΔS° are treated as constant with temperature, so ΔG° at a new temperature is an estimate.
- Every species is in its standard state. Different concentrations or pressures change ΔG (later in the unit).
Mistakes to avoid
- J and kJ mixed. Divide ΔS° by 1000 first. An answer of tens of thousands of kJ is a warning sign.
- °C instead of K. 25 °C is 298 K.
- Reactants minus products. It is always products minus reactants.
- Coefficients dropped. Multiply each ΔG°f by its coefficient.
- “Exothermic, so favoured.” Check ΔS° too: freezing water is exothermic but not favoured above 273 K.
- “Favoured, so fast.” Rate is a kinetics question.
Quick self-check
- ΔH° = −50 kJ mol⁻¹ and ΔS° = +100 J K⁻¹ mol⁻¹. When is the process favoured? (At all temperatures: both terms make ΔG° negative.)
- ΔH° = +30.0 kJ mol⁻¹, ΔS° = +80.0 J K⁻¹ mol⁻¹. Find ΔG° at 500 K. (30.0 − 500 × 0.0800 = −10.0 kJ mol⁻¹, favoured)
- ΔH° = +45.0 kJ mol⁻¹, ΔS° = +150 J K⁻¹ mol⁻¹. Above what temperature is it favoured? (45 000 ÷ 150 = 300 K)
Next: practice questions.