Entropy and spontaneous changeEdexcel International A Level Chemistry: Revision notes

Many reactions that occur spontaneously are exothermic, but not all. Some endothermic reactions occur spontaneously at room temperature. Examples are ammonium nitrate dissolving in water, which makes the water cold, and citric acid reacting with sodium hydrogencarbonate with fizzing and cooling.

So the enthalpy change alone does not control whether a reaction occurs. We also need entropy.

Entropy, S, is a measure of the disorder of a system. More precisely it measures the number of ways the particles and the energy quanta can be arranged.

The more randomly dispersed the molecules are, and the more ways energy can be shared between them, the greater the entropy. Entropy has units of J K⁻¹ mol⁻¹.

This is why gases spread out to fill a container or a room: there are far more ways to arrange the molecules when they are dispersed than when they are all in one corner.

• Entropy increases with temperature, because particles have more energy and the quanta can be distributed in more ways.
• Entropy increases as a substance changes from solid to liquid to gas. A gas has by far the greatest entropy because its particles are widely dispersed and move randomly. There is a large jump at melting and a much larger one at boiling.
• A perfect crystal at 0 K has zero entropy, because there is only one arrangement and no energy to distribute.

Absolute entropy values are therefore never negative.

The natural direction of change is towards an increase in total entropy. Total entropy is the entropy change of the system plus that of the surroundings.

A reaction that releases heat increases the entropy of the surroundings, because the energy is dispersed there. An endothermic reaction takes heat from the surroundings and decreases their entropy.

A reaction occurs spontaneously if the total entropy increases. An endothermic reaction can occur because the entropy increase in the system outweighs the decrease in the surroundings.

Look for these features when predicting the sign of the entropy change of the system:

• Change of state: melting and boiling give an increase. Freezing and condensing give a decrease.
• Dissolving an ionic solid: the ordered lattice breaks up and the ions disperse randomly in solution, so entropy generally increases.
• Change in the number of moles, especially of gas: more moles of gas on the product side gives an increase. For N₂(g) + 3H₂(g) → 2NH₃(g), 4 mol of gas become 2 mol, so entropy decreases. For CaCO₃(s) → CaO(s) + CO₂(g), a gas forms from solids, so entropy increases.