23.3 Entropy Change
The universe’s obsession with mess — and how chemists put a number on it
🎯 Learning outcomes
Candidates should be able to:
- Define the term entropy, S, as the number of possible arrangements of the particles and their energy in a given system.
- Predict and explain the sign of the entropy changes that occur:
- during a change in state, e.g. melting, boiling, and dissolving (and their reverse)
- during a temperature change
- during a reaction in which there is a change in the number of gaseous molecules
- Calculate the entropy change for a reaction, ΔS, given the standard entropies, S⦵, of the reactants and products, using ΔS⦵ = ΣS⦵(products) − ΣS⦵(reactants).
1 Introduction to Entropy
Leave a tidy room empty for a week, and it doesn’t clean itself — but leave it, and it slowly drifts towards chaos. Ice melts, perfume spreads across a room, and iron rusts, but none of these ever reverse themselves. Chemistry has a precise way of explaining this one-way traffic: entropy. By the end of this guide, you’ll be able to predict, calculate, and explain why reactions happen — using nothing more than two equations.
📖 What is Entropy?
Entropy (S) is a measure of the number of possible arrangements of particles and their energy within a system. In simple terms, it measures how disordered or spread out a system is.
📖 System vs Surroundings
A system is the part under investigation — in chemistry, this is the chemical reaction itself, i.e. reactants being converted to products.
Surroundings are anything other than the chemical reactants and products, e.g. the solvent and reaction vessel. For magnesium reacting with sulfuric acid in a test tube, the surroundings include:
- the solvent (in this case, water)
- the air around the test tube
- the test tube itself
- anything dipping into the test tube (e.g. a thermometer)
✨ The Golden Rule of Entropy
The more disordered a system becomes, the higher its entropy, and the more energetically stable it is.
S(gas) > S(liquid) > S(solid)
Factors Affecting Entropy
Entropy is greater if there are more ways of arranging the energy in a molecule or atom, or more ways to arrange molecules or atoms in a given volume.
- State of matter: gases have the highest entropy; solids have the lowest.
- Temperature: higher temperature → more particle motion and more possible energy arrangements → higher entropy.
- Number of particles: more moles of gas molecules → more arrangements → higher entropy.
- For concentrated aqueous solutions of salts with highly charged ions, there may be considerable order in the solvent due to several hydration layers around these ions.
Changes that tend to continue happening naturally are called spontaneous changes. Once started, a spontaneous change will carry on — for example, when a spark is applied, methane gas reacts with oxygen spontaneously to form carbon dioxide and water, continuing until either the methane or the oxygen is used up. A reaction does not need to happen rapidly to be spontaneous; many spontaneous reactions are slow or need an input of energy to start them.
Entropy can also be thought of as a dispersal of energy, either from the system to the surroundings or from the surroundings to the system. The system becomes energetically more stable as it becomes more disordered.
- All elements and compounds have positive standard molar entropy values.
- Larger, more complex molecules generally have higher entropy because they have more ways of arranging energy, e.g. CH₄ < C₂H₆ < C₃H₈.
2 Signs of Entropy Changes
Changes of State
| Change | Effect on Entropy |
|---|---|
| Solid → Liquid (melting) | ↑ Increases — regular lattice → irregular arrangement; particles can rotate and slide |
| Liquid → Gas (boiling) | ↑ Increases significantly — particles now move freely, very disordered |
| Gas → Liquid (condensing) | ↓ Decreases — particles brought together, more ordered |
| Liquid → Solid (freezing) | ↓ Decreases — fixed lattice positions, least disorder |
| Dissolving a solid | ↑ Increases — particles spread out in solvent; more arrangements of energy |
| Crystallisation | ↓ Decreases — ions/molecules become locked in an ordered solid lattice |
Entropy Changes in Reactions
The key driver is the change in the number of gaseous molecules:
- More gas molecules in products → ΔS > 0 (entropy increases)
- Fewer gas molecules in products → ΔS < 0 (entropy decreases)
- If there is no change in moles of gas, ΔS is small and determined by other factors.
Worked Examples — Qualitative
✏️ Worked Example 1: CaCO₃ decomposition
CaCO₃ (s) → CaO (s) + CO₂ (g)
A solid reactant produces a gas. CO₂ can move freely, so the system becomes more disordered.
Result: ΔS > 0 (entropy increases) ✔
✏️ Worked Example 2: Haber Process — ammonia formation
N₂ (g) + 3H₂ (g) ⇌ 2NH₃ (g)
4 moles of gas (reactants) form 2 moles of gas (products). Fewer gas molecules means fewer ways of arranging energy, so the system is more ordered.
Result: ΔS < 0 (entropy decreases) ✔
3 Calculating Entropy Changes
When selecting entropy and free energy values from data tables, make sure to look carefully at the state symbols.
📖 The Formula
ΔSᵒ system = ΣSᵒ products − ΣSᵒ reactants
Units: J K⁻¹ mol⁻¹ (note: NOT kJ). Σ means ‘sum of’ — multiply each Sᵒ value by its stoichiometric coefficient.
Step-by-Step Method
- Write the balanced equation with state symbols.
- List all Sᵒ values (given in the data booklet or question).
- Multiply each Sᵒ value by its stoichiometric coefficient.
- ΔSᵒ = Σ(Sᵒ × coefficient)products − Σ(Sᵒ × coefficient)reactants
- Check the sign: ΔS > 0 means more disorder; ΔS < 0 means more order.
✏️ Worked Example
Calculate ΔSᵒ system for: 2Mg (s) + O₂ (g) → 2MgO (s)
Given:
Sᵒ [Mg (s)] = 32.60 J K⁻¹ mol⁻¹
Sᵒ [O₂ (g)] = 205.0 J K⁻¹ mol⁻¹
Sᵒ [MgO (s)] = 38.20 J K⁻¹ mol⁻¹
Solution:
ΔSᵒ = ΣSᵒ products − ΣSᵒ reactants
ΔSᵒ = (2 × 38.20) − (2 × 32.60 + 1 × 205.0)
ΔSᵒ = 76.40 − 270.20
ΔSᵒ = −193.8 J K⁻¹ mol⁻¹
Interpretation: ΔS < 0. Solid MgO is more ordered than Mg + O₂ gas. Entropy decreases. ✔
✔ DO remember
- Always use stoichiometric coefficients when calculating ΔSᵒ.
- Include correct state symbols — entropy values differ significantly between states.
- Units for Sᵒ are J K⁻¹ mol⁻¹, NOT kJ. Don’t mix up with enthalpy (ΔH).
- ΔS > 0 → products more disordered; ΔS < 0 → products more ordered.
❌ DO NOT confuse
- System vs surroundings: the system is the reacting molecules; surroundings are everything else.
- Entropy (S) with enthalpy (H) — they are different thermodynamic quantities.
- Forgetting to count moles of gas carefully in equations like the Haber process.
- Assuming that a positive ΔH always means entropy increases — these are independent.
🔁 Quick Summary
- Entropy = disorder/randomness: gas > liquid > solid
- Higher temperature → higher entropy
- Producing gases usually increases entropy
- More gas molecules → larger entropy
- Dissolving usually increases entropy
ΔSᵒ = ΣSᵒ(products) − ΣSᵒ(reactants)