Short on time? This page is the recap. For explanations and worked examples, use the full study guide.
Recap
- “Thermodynamically favoured” (ΔG° < 0) means that, under standard conditions, products are favoured at equilibrium (K > 1).
- ΔG° and K carry the same information. One is an energy; the other is a ratio of concentrations or pressures.
- ΔG° > 0 means K < 1: reactants favoured, but some product still forms. K is small, never zero.
- If ΔG° is about the size of RT or smaller, K is close to 1. If ΔG° is many times RT, K is very far from 1.
- Temperature changes K mainly by changing ΔG° = ΔH° − TΔS°.
Key relationships
| Relationship | Symbols and units | Use it to |
|---|---|---|
| ΔG° = −RT ln K | ΔG° in J mol⁻¹; R = 8.314 J mol⁻¹ K⁻¹; T in K | find ΔG° from a known K |
| K = e^(−ΔG°/RT) | exponent has no unit | find K from a known ΔG° |
| RT at 298 K ≈ 2.48 kJ mol⁻¹ | compare with ΔG° | judge whether K is near 1 or far from 1 |
| 5.7 kJ mol⁻¹ ≈ factor of 10 in K (298 K) | from RT ln 10 | estimate K without a calculator |
| ΔG° = ΔH° − TΔS°, then K | ΔH° and ΔS° assumed constant | predict K at another temperature |
Assumptions behind the numbers
- ΔG° is for the balanced equation as written, and K is written for that same equation.
- “Standard conditions” means 1 atm for gases and 1 mol L⁻¹ for solutes; ΔG° describes those, not every possible mixture.
- When you use ΔH° − TΔS° at a new temperature, you assume ΔH° and ΔS° barely change with temperature.
Mistakes to avoid
- kJ with R in J. Multiply ΔG° in kJ by 1000 first.
- log instead of ln. The equation uses the natural log.
- Celsius instead of kelvin. Add 273 (or 273.15).
- Lost minus sign. K < 1 must give ΔG° > 0. Check that the signs agree.
- “ΔG° > 0 means no reaction.” It means a small K, not zero product.
- “Favoured means fast.” ΔG° and K say nothing about rate.
Quick self-check
- At 298 K, ΔG° = −11.4 kJ mol⁻¹. Roughly what is K? (about 100; the exact value is 99.6)
- What is ΔG° for a reaction with K = 1? (0 kJ mol⁻¹)
- Is a reaction with K = 1.0 × 10⁻³ at 298 K thermodynamically favoured? (No: ΔG° = +17.1 kJ mol⁻¹)
Next: practice questions.