9.1 Entropy

Entropy & Microstates

Cycle through every microstate arrangement for N particles and compare a small vs. large container. Solid, liquid, and gas phases animate below.

S = kB ln WMicrostatesBoltzmannW = C(N,k)
Topic 9.1

Introduction to Entropy

Identify the sign and relative magnitude of the entropy change associated with chemical or physical processes.

Entropy increases when matter becomes more dispersed. The CED gives three specific cases:

  • Phase change. Solid → liquid → gas results in a dispersal of matter as individual particles become freer to move and generally occupy a larger volume.
  • Volume increase. For a gas at constant temperature, entropy increases with volume because the molecules can move within a larger space.
  • Moles of gas. For reactions involving gas-phase species, entropy generally increases when the total moles of gas-phase products exceeds the total moles of gas-phase reactants.

Entropy also increases when energy is dispersed. By kinetic molecular theory, the distribution of kinetic energy among gas particles broadens as temperature increases — so the entropy of a system increases with temperature. This is the Maxwell–Boltzmann curve of topic 3.5 read thermodynamically.

The practical checklist for predicting the sign of ΔS:

  • Look at gas moles first — it dominates everything else. More gas on the right means ΔS > 0.
  • If gas moles are unchanged, look at phase changes: melting, boiling, and subliming all increase entropy.
  • Dissolving a solid generally increases entropy (the ordered lattice breaks up).
  • Heating anything increases entropy.
  • More complex molecules have higher entropy than simpler ones at the same phase.

Relative magnitude matters too. Vaporization produces a far larger entropy increase than melting, because the volume change is enormous by comparison.

Key points

  • Count moles of gas first — it dominates the sign of ΔS for reactions.
  • Solid → liquid → gas always increases entropy, with vaporization by far the largest step.
  • Raising temperature increases entropy by broadening the kinetic-energy distribution.
  • Entropy is about dispersal of matter and energy, not about “disorder” or “messiness”.

Common mistakes

  • Calling entropy “disorder”. The CED language is dispersal of matter and energy — use it.
  • Counting all moles instead of gas moles. Aqueous and solid species matter far less.
  • Assuming dissolving always increases entropy. Dissolving a gas in a liquid decreases it sharply.
  • Assuming ΔS > 0 means favorable. Favorability needs ΔG, which weighs entropy against enthalpy.

Worked example

Predict the sign of ΔS° for each and justify: (a) 2 NH₃(g) → N₂(g) + 3 H₂(g) (b) H₂O(g) → H₂O(l) (c) NaCl(s) → Na⁺(aq) + Cl⁻(aq) (d) CO₂(g) → CO₂(aq)

(a) ΔS° > 0. Gas moles increase from 2 to 4. More gas-phase particles means matter is more dispersed and there are more ways to distribute the system's energy.

(b) ΔS° < 0. Condensation takes widely separated, freely moving gas molecules and confines them to close contact in the liquid. Matter becomes far less dispersed.

(c) ΔS° > 0. A highly ordered crystalline lattice breaks apart into ions free to move throughout the solution. (The effect is partly offset by water molecules ordering themselves into hydration shells around each ion, so the increase is smaller than you might expect — and for small, highly charged ions such as Al³⁺ that ordering can even make ΔS negative.)

(d) ΔS° < 0. Dissolving a gas confines molecules that previously roamed the whole container into the much smaller volume of the solution. This is why gases become less soluble as temperature rises.

Full notes for topic 9.1 →