23.3 Entropy change, ΔS

Entropy, S, describes the number of possible arrangements of particles and their energy. More accessible microstates correspond to greater entropy.

It is a system property, not simply “disorder”. Particle number, phase, temperature and mixing all affect the number of accessible arrangements.

A gas has much higher entropy than the same substance as a solid because particles can occupy many more positions and energy distributions.

Entropy is not a synonym for messiness and a reaction can increase one part of a system while decreasing another.

Entropy increases on melting, boiling, dissolving and heating, and decreases for the reverse changes. A reaction forming more gaseous molecules usually has positive ΔS; forming fewer has negative ΔS.

Use the strongest structural change first: gas count often dominates, while phase and temperature changes provide additional evidence. The sign prediction is qualitative unless data are supplied.

H₂O(s) → H₂O(l) gives ΔS>0; 2SO₂(g)+O₂(g) → 2SO₃(g) gives a negative gas-count contribution because three gas molecules become two.

A positive entropy change does not by itself prove spontaneity; Gibbs free energy also depends on enthalpy and temperature.

For a reaction, ΔS° = ΣS°(products) − ΣS°(reactants). Multiply each standard molar entropy by its stoichiometric coefficient before summing.

Keep units consistent, usually J K⁻¹ mol⁻¹, and interpret the sign after the subtraction. A positive result means the system has more accessible arrangements overall.

For A + 2B → C, ΔS° = S°(C) − [S°(A)+2S°(B)]. The coefficients belong inside the brackets, not only in the balanced equation.

Do not reverse the subtraction or use ΔS° = ΔSsurr + ΔSsys when the syllabus only asks for the tabulated-state calculation.