Processes with a positive entropy change (ΔS > 0) are those that increase the disorder or number of possible arrangements of particles in a system. The most common examples you’ll see on an exam include melting, vaporization, sublimation, dissolving a solid in a liquid, gas expansion, and reactions that produce more gas molecules than they consume. If a process spreads particles out, gives them more room to move, or converts them from an ordered state to a less ordered one, entropy increases.
Phase Changes That Increase Entropy
For any substance, the entropy of a gas is greater than the entropy of a liquid, which is greater than the entropy of a solid: S(gas) > S(liquid) > S(solid). This hierarchy means three phase transitions always have ΔS > 0:
- Melting (solid → liquid): Particles break free from their fixed positions in the crystal lattice and gain the ability to flow past one another.
- Vaporization (liquid → gas): Particles escape the liquid surface and spread out to fill their container, dramatically increasing the number of possible arrangements.
- Sublimation (solid → gas): Particles jump directly from a rigid, ordered solid into the gas phase, which is the largest single-step entropy increase of any phase change.
The numbers make this concrete. Liquid water has a standard molar entropy of about 70 J/mol·K, while steam sits at roughly 189 J/mol·K. That nearly threefold jump reflects how many more ways water molecules can be arranged once they’re free to move independently in the gas phase. The reverse processes (freezing, condensation, deposition) all have ΔS < 0 because they force particles into more ordered arrangements.
Reactions That Produce More Gas Molecules
In any chemical reaction involving gases, compare the total moles of gas on the product side to the total moles of gas on the reactant side. If the number of gaseous moles increases, ΔS is positive. Gases dominate the entropy calculation because their particles occupy far more volume and have far more accessible arrangements than solids or liquids.
A combustion reaction is the classic example. Burning a hydrocarbon like propane (C₃H₈) converts one large molecule into multiple molecules of CO₂ and H₂O vapor. You go from fewer gas molecules to many more, so ΔS > 0. On the other hand, a synthesis reaction like nitrogen combining with hydrogen to form ammonia (N₂ + 3H₂ → 2NH₃) takes four total moles of gas down to two. That decrease means ΔS < 0.
A quick shortcut: count the gas molecules on each side of the equation. If products have more, entropy increases. If they have fewer, entropy decreases. If the count is the same, ΔS will be small and you’ll need more information to determine the sign.
Dissolving a Solid or Liquid in a Solvent
When you dissolve a solid like table salt or sugar in water, entropy typically increases. Before dissolving, the solute particles are locked in an ordered crystal and the solvent molecules are separate from them. After dissolving, solute and solvent particles are completely interspersed, creating a far greater number of possible arrangements. That mixing effect drives ΔS positive.
The same logic applies to mixing two liquids that are miscible. Combining ethanol and water, for instance, produces a solution where the molecules are more randomly distributed than they were in two separate containers.
There is one important exception: dissolving a gas in a liquid typically decreases entropy. A gas molecule in the atmosphere has enormous freedom of movement. Once it dissolves into a liquid, it becomes confined to a much smaller volume and interacts closely with solvent molecules. Think of carbonation: CO₂ molecules forced into liquid water are more constrained than they were in the gas phase, so ΔS < 0 for that step.
Gas Expansion and Temperature Increases
When a gas expands into a larger volume at constant temperature, entropy increases. The relationship is logarithmic: ΔS = nR·ln(V₂/V₁), where V₂ is the final volume and V₁ is the initial volume. As long as V₂ is larger than V₁, the natural log is positive and so is ΔS. This applies whether the expansion is controlled (like a piston moving outward) or spontaneous (like a gas rushing into a vacuum).
Heating a substance also increases entropy. Raising the temperature gives particles more kinetic energy, which means they can access a greater number of energy states. A cold brick warming up has a positive ΔS, while a hot brick cooling down has a negative ΔS. When two objects at different temperatures are brought together and reach thermal equilibrium, the total entropy of the system increases because the gain by the cold object outweighs the loss by the hot object.
Increasing Molecular Complexity
Larger, more structurally complex molecules have higher standard entropies than smaller, simpler ones. A molecule with more atoms has more ways to vibrate, rotate, and bend, and each additional mode of motion increases the number of accessible energy arrangements. A polyatomic nonlinear molecule like ethanol has significantly more entropy than a diatomic molecule like O₂ at the same temperature and pressure.
This matters for reactions. If a process breaks a simple molecule into a more complex mixture of products, or if it creates molecules with more internal degrees of freedom, that contributes positively to ΔS. Molecular mass plays a role too: heavier molecules at the same temperature have more closely spaced energy levels, giving them access to more microstates and higher entropy.
How to Identify ΔS > 0 on an Exam
When you see a list of processes and need to pick which ones have positive entropy change, run through these checks in order:
- Phase change direction: Solid → liquid, liquid → gas, or solid → gas all have ΔS > 0. The reverse directions have ΔS < 0.
- Gas molecule count: More moles of gas in the products than the reactants means ΔS > 0.
- Dissolving: A solid or liquid dissolving in a solvent is typically ΔS > 0. A gas dissolving in a liquid is typically ΔS < 0.
- Volume change: Expansion of a gas into a larger volume is ΔS > 0.
- Temperature change: Heating a substance raises its entropy.
Most exam questions test phase changes and gas molecule counts, since those produce the most clear-cut answers. If a process combines multiple factors (say, a reaction that produces more gas molecules and involves vaporization), both factors point in the same direction and you can be confident ΔS > 0. When factors conflict, such as a reaction that produces fewer but more complex molecules, the gas molecule count usually dominates unless the question specifically asks about molecular complexity.