Reaction Entropy

Reaction entropy: ΔS = ΣS°(products) − ΣS°(reactants)

Entropy S counts the microstates available to a system, which is another way of describing its disorder: ΔS = S_products − S_reactants. When ΔS > 0 the disorder grew; when ΔS < 0 it shrank. The second law of thermodynamics says the entropy of an isolated system never falls, so the universe keeps drifting toward ΔS_total > 0. A gas spreads through a container on its own because the expanded state opens up far more microstates to occupy. Freezing a substance lowers S, while vaporizing it raises S. Standard entropy S° at 25°C is tabulated for thousands of substances. Combustion usually pushes S up, since gaseous products carry more freedom of movement. Boltzmann pinned this down at the microscopic level with S = k·ln Ω, where Ω is the number of microstates and k = 1.38×10⁻²³ J/K. The formula is carved into his tombstone in Vienna.

Applications

Entropy drives the prediction of chemical equilibrium and spontaneity through Gibbs free energy ΔG = ΔH − TΔS, where a negative ΔG flags a spontaneous process. It accounts for the entropy of mixing in alloys, solutions, and pharmaceutical formulations. It anchors information theory too, where Shannon entropy underpins compression and cryptography. Living things lean on it as well: organisms burn external energy to hold their local entropy low, the puzzle Schrödinger framed in "What Is Life?" back in 1944. And it reaches all the way out to cosmology and the heat death of the universe.

FAQ

Can entropy decrease locally? It can, as long as the system is open. A refrigerator drops the entropy inside, but it dumps even more into the surrounding room. Living things pull off the same trick, building order in one spot by shipping entropy out as heat.

Why does S° have a positive value, not zero? The third law reserves S = 0 for a perfect crystal sitting at 0 K. Warm anything up to 25°C and thermal motion has already piled on a fair amount of entropy.

Does ΔS alone determine spontaneity? Across the whole system plus its environment, yes. For the reaction on its own, no, and you reach for Gibbs instead: ΔG = ΔH − TΔS. That is how an endothermic reaction can still run spontaneously, once TΔS grows large enough to beat ΔH.