Entropy

• Entropy (S) measures disorder / the number of ways particles and energy can be arranged. More disorder = higher entropy.
• Entropy increases going solid → liquid → gas, and increases whenever a gas is produced, a solid dissolves, or particles are freed up to move.
• The driving force of a reaction isn't just enthalpy (ΔH) — it's the total entropy change, which includes the surroundings too.
• ΔS°_total = ΔS°_system + ΔS°_surroundings — a reaction is spontaneous (feasible) when this is positive.
• ΔS°_system is calculated from standard entropies: ΔS°_system = ΣS°_products − ΣS°_reactants
• ΔS°_surroundings is calculated from the enthalpy change: ΔS°_surr = −ΔH / T
• Gibbs free energy, ΔG = ΔH − TΔS, combines both enthalpy and entropy into one number. A reaction is feasible when ΔG ≤ 0.
• Temperature controls whether some reactions are feasible — this is why iron extraction needs a blast furnace at ~1500°C.
• Feasible (thermodynamically favourable) ≠ fast. That's the difference between thermodynamic stability and kinetic stability.

Here's the puzzle this chapter solves: most reactions we see every day are exothermic — energy flows out, products end up more stable, lower in energy. That makes intuitive sense; things "want" to roll downhill to a lower-energy state, like a ball rolling down a slope.

But then you meet endothermic reactions — the products end up in a higher energy state than the reactants. If the driving force were purely "systems want to lose energy," these reactions shouldn't happen at all. And yet they do — ice melts at room temperature, ammonium nitrate dissolves in water and the water goes cold, thermal decompositions happen. So enthalpy (ΔH) clearly isn't the whole story.

The missing piece is entropy — and once you add it in, both exothermic and endothermic reactions make sense under one single rule.

Think of entropy (symbol S) as a measure of how many different ways you could arrange the particles and their energy in a system and have it look basically the same. The more possible arrangements, the higher the entropy.

Imagine your bedroom. There is exactly one way for it to be perfectly tidy — every item precisely in its spot. But there are thousands of ways for it to be messy — a sock here, a book there, endless combinations. Messiness (disorder) has vastly more possible arrangements than order. That's entropy in a nutshell: disordered states have more ways to exist, so they have higher entropy.

Classic example: melting ice.

there are vastly more ways for the molecules to be spread out than to stay bunched in one jar.

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