5.2.2(a)-(c) - Entropy and entropy change

Entropy as energy dispersal

In chemistry, a system is the chemical reaction or physical process you are focusing on. For this lesson, entropy means the entropy of that system, not the surroundings.

The word "disordered" is useful, but it is not the whole definition. OCR's wording puts energy dispersal first: the more ways energy can be spread among particles and arrangements, the higher the entropy.

This model helps explain thermodynamic stability. Greater entropy can favour thermodynamic stability when other factors are comparable because more arrangements are available. Entropy alone does not determine feasibility; the next lesson combines entropy with enthalpy and temperature. For example, particles in a gas can move through a large volume and have many possible positions and speeds, so the energy is more dispersed than in a rigid solid.

Do not treat entropy as a judgement about neatness. A tidy-looking beaker of gas still has high entropy compared with a solid because the particles and their energy are much more spread out.

Comparing entropy magnitudes

The physical state of a substance has a large effect on its entropy. For the same substance, entropy usually increases in this order:

In a solid, particles vibrate around fixed positions, so the particles and energy have relatively few arrangements. In a liquid, particles are still close together but can move past each other, so there are more arrangements. In a gas, particles are far apart and move freely, so there are many more possible arrangements and much greater energy dispersal.

[DIAGRAM: asset_name: Lesson 5.2.2a-c: Entropy and entropy change - diagram 01; asset_slug: 05_02_02a_entropy_and_entropy_change__diagram_01; recommended_method: drawn_chem; description: Deterministic teaching diagram comparing solid, liquid and gas particle arrangements and showing that a reaction forming more gaseous molecules usually has a positive entropy change for the system.]

A standard molar entropy compares one mole of each substance. If you compare $S^\circ$ of a gas with $S^\circ$ of a solid, explain particle freedom and energy dispersal; do not use the coefficients of a reaction as the reason. Coefficients enter only when finding the entropy change for the whole balanced reaction. Elements also have non-zero standard molar entropies at ordinary temperatures: do not confuse $S^\circ$ with the zero standard enthalpy of formation convention.

For reactions, changes in the number of gaseous molecules are especially important. If a reaction forms more moles of gas than it uses, the entropy of the system usually increases. If it uses up gas molecules and forms fewer gas molecules, the entropy of the system usually decreases.

Worked reasoning:

$\ce{N2O4(g) -> 2NO2(g)}$

One mole of gaseous molecules becomes two moles of gaseous molecules. The products have more independently moving gas particles, so the entropy change of the system is likely to be positive.

Now compare:

$\ce{2SO2(g) + O2(g) -> 2SO3(g)}$

Three moles of gaseous molecules become two moles of gaseous molecules. The products have fewer gas particles, so the entropy change of the system is likely to be negative.

This is a prediction rule, not a replacement for calculation. When entropy values are supplied, use the values.

Calculating entropy change

Entropy values for substances are usually given as standard molar entropies. Their unit is: