Spontaneity and entropy

A spontaneous process is one that goes on its own, once started, without outside help. It has a natural direction: a stone rolls downhill, not up; hot tea cools down, it does not warm up by itself.

Many spontaneous reactions are exothermic. But some endothermic changes are spontaneous too: ice melts on its own above 0 °C, taking in heat. So ∆H alone cannot decide whether a process is spontaneous. Something else matters.

That something is entropy, S, a measure of the disorder (randomness) of a system. For a reversible change at temperature T: ∆S = q_rev / T. Entropy increases when:

• a solid melts or a liquid boils (the particles move more freely);
• gases are produced, or the number of gas molecules increases;
• molecules split into smaller pieces;
• the temperature rises.

Entropy falls in the opposite cases: when a liquid freezes, or when gas molecules combine into fewer molecules, as in N₂(g) + 3H₂(g) → 2NH₃(g), where four gas molecules become two.

The second law of thermodynamics: in an isolated system, a spontaneous change always increases the total entropy. For a system and its surroundings together:

∆S_total = ∆S_system + ∆S_surroundings > 0 for a spontaneous change, where ∆S_surroundings = –∆H_system / T.

So an exothermic reaction (∆H negative) increases the entropy of the surroundings, by warming them, and this can make up for a fall in the system's own entropy.

The third law of thermodynamics: the entropy of a perfectly crystalline substance is zero at absolute zero (0 K), where everything is perfectly ordered and still.