23.3 Entropy Change, ΔS

2026 Syllabus Objectives

By the end of these notes, you should be able to:

  1. Define the term entropy, S, as the number of possible arrangements of the particles and their energy in a given system.
  2. Predict and explain the sign of entropy changes that occur:
    • (a) During a change in state (e.g. melting, boiling, dissolving, and their reverse)
    • (b) During a temperature change
    • (c) During a reaction in which there is a change in the number of gaseous molecules
  3. Calculate the entropy change for a reaction, ΔS⦵, using standard entropies: ΔS⦵ = ΣS⦵(products) − ΣS⦵(reactants)

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1. What is Entropy?

Entropy (S) is defined as the number of possible arrangements of the particles and their energy in a given system.

Let's break that down in simple terms:

  • Think of particles (atoms, molecules, or ions) in a substance. They can be arranged in many different ways, and their energy can be spread out in many different ways too.
  • The more ways there are to arrange those particles and their energy, the higher the entropy.
  • A system with high entropy is disordered — the particles are spread out, moving freely, and arranged randomly.
  • A system with low entropy is ordered — the particles are fixed in position and arranged regularly.

Simple analogy: Imagine a box of Lego bricks. If they are all neatly sorted by colour and size in separate compartments, that is ordered — low entropy. If you shake the box and the bricks end up scattered randomly, that is disordered — high entropy. There are far more ways to be "scrambled" than to be "sorted."

Key point: When a system becomes more disordered, its entropy increases. When it becomes more ordered, entropy decreases.

General Rules About Entropy Values

It helps to know a few patterns about entropy:

  • All elements and compounds have positive standard molar entropy values — entropy is always greater than zero (except at absolute zero temperature).
  • The state of matter strongly affects entropy:

Gas > Liquid > Solid (in terms of entropy)

  • Gas particles move around freely and randomly — highest entropy

  • Liquid particles are close together but can slide around each other — medium entropy

  • Solid particles are locked in fixed positions and can only vibrate — lowest entropy

  • More complex substances (with more atoms per molecule) tend to have higher entropy than simpler ones. For example, calcium carbonate (CaCO₃) has a higher entropy than calcium oxide (CaO), because CaCO₃ has more atoms and therefore more ways to arrange its energy.

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