Short on time? This page is the recap. For explanations, particle diagrams and worked examples, use the full study guide.
Recap
- Entropy, S, measures how dispersed the matter and the energy of a system are. ΔS > 0 means more dispersal; ΔS < 0 means less.
- Matter dispersal: particles spread over more space or become freer to move.
- Energy dispersal: the particles’ kinetic energies spread over a wider range of values, which happens when the temperature rises.
- Entropy is a separate idea from enthalpy. It explains why some endothermic changes, such as ice melting on a warm day, still happen.
Key relationships
| Change | Sign of ΔS | Particle-level reason |
|---|---|---|
| Solid → liquid | + (small) | particles can now move past each other |
| Liquid → gas | + (large) | particles separate and fill a far larger volume |
| Gas expands, same T | + | each particle has more space to move in |
| Temperature rises | + | kinetic-energy distribution becomes lower and wider |
| More moles of gas in products | usually + | more freely moving gas particles |
| Fewer moles of gas in products | usually − | fewer freely moving gas particles |
| Same moles of gas on both sides | small; sign not predictable by counting | details of the molecules decide |
Reverse any change and the sign of ΔS reverses.
Assumptions behind the rules
- The “count moles of gas” rule assumes the gas term outweighs everything else. That is usually true, but when the moles of gas are equal the rule says nothing about the sign.
- The volume rule for gases assumes the temperature is constant. If both volume and temperature change, judge each effect separately.
- States matter: H₂O(l) and H₂O(g) are different species with very different entropies.
Mistakes to avoid
- Counting solids and liquids as well as gases when comparing the two sides of an equation.
- Saying ΔS = 0 when the moles of gas are equal. Say “small, sign not predictable from moles of gas”.
- Linking the sign of ΔS to the sign of ΔH. They are independent.
- Forgetting temperature. A hotter sample of the same substance has higher entropy, even with no phase change.
- Writing “disorder” with no particle detail. Name what spreads out: the particles, their energy, or both.
- Treating melting and boiling as equal steps. Vaporisation gives the much larger increase.
Quick self-check
- Sign of ΔS for CO₂(g) → CO₂(s)? (Negative: gas to solid, matter far less dispersed.)
- Sign of ΔS for 2 N₂O(g) → 2 N₂(g) + O₂(g)? (Positive: 2 mol of gas → 3 mol of gas.)
- A sealed steel cylinder of helium is warmed. What happens to S, and why? (Increases: energy is spread over a wider range of kinetic energies.)
- Which is larger, ΔS for melting or for boiling the same substance? (Boiling.)
Next: practice questions.