Cold packs get cold. Ice melts on a warm day. Ammonium nitrate soaks up heat and still dissolves happily. If reactions only ever went downhill in energy, none of that should happen. So something else must be pushing, and that something is entropy.
📚 What you need to know
Entropy, S, measures how spread out the matter and the energy in a system are.
The more ways the particles and their energy can be arranged, the higher the entropy.
For the same substance the order is always solid < liquid < gas, and the gas value is far bigger than the other two.
Entropy goes up when you make more gas, dissolve a solid, or turn a few particles into many.
Units of S are J K−1 mol−1 — joules, not kilojoules, and per kelvin.
Entropy is the reason endothermic reactions can still happen: spreading out can pay for taking heat in.
A change with a positive ΔS has become more spread out; a negative ΔS has become more ordered.
Why enthalpy on its own is not enough
At SL you learned that exothermic reactions give heat out and are the ones that usually “want” to happen. That rule takes you a long way, and then it breaks. Sports cold packs work because ammonium nitrate dissolving in water is endothermic — it pulls heat from your skin. Nobody has to force it. Tear the pack, and it happens on its own.
So the energy going downhill cannot be the whole story. There is a second thing nature keeps score of, and it has nothing to do with heat given out. It is about how spread out things end up.
Think of it as two questions a reaction has to answer, not one. “Do I release energy?” and “Do I spread things out?” A yes to either one can carry the reaction. This page is all about the second question.
What entropy actually measures
Entropy is a counting idea. Take a system and ask: in how many different ways could I arrange these particles and share out their energy, and still have the same overall thing? Lots of ways means high entropy. Very few ways means low entropy.
Entropy in one lineS = a measure of how many ways the particles and their energy can be arranged
Here is the everyday version. There is exactly one way for your books to be stacked neatly in the right order on the shelf. There are thousands of ways for them to be scattered across your bedroom floor. Both are possible, but “scattered” has far more versions of itself, so if things get shuffled at random you end up scattered nearly every time. That is entropy: spread-out states are more likely simply because there are more of them.
Energy behaves the same way. Heat never gathers itself back into one hot spot in a cold room, because there are vastly more ways for that energy to be shared among all the particles than to be piled into a few.
The particles are identical in all three boxes. What changes is how many different positions and speeds they are allowed to have — and that is what entropy counts.
Solid, liquid, gas: look at the real numbers
You do not have to take this on trust. The data booklet lists a standard molar entropy, S°, for hundreds of substances: the entropy of one mole in its standard state at 298 K and 100 kPa. Line up the same substance in different states and the pattern jumps out.
Ice to water adds 22 units. Water to steam adds 119. That gap is why the gases in an equation matter more than anything else when you are judging the sign of ΔS.
Why is boiling such a big deal? In a liquid the particles are still touching, so they are stuck with their neighbours. In a gas each particle can be almost anywhere in the container, moving at almost any speed. The number of possible arrangements explodes, and so does S.
What pushes entropy up
You will be asked to predict the sign of ΔS without a calculator, so learn the things that move it. In order of how much they matter:
Making more moles of gas. This beats everything else. Solid or liquid turning into gas, or 2 moles of gas becoming 4.
Melting or dissolving a solid. A neat lattice becomes free particles moving through a liquid.
Making more particles overall. One molecule splitting into three has more ways to be arranged than one.
Heating anything. More energy to share out means more ways to share it, so S creeps up with temperature.
Bigger, floppier molecules. A long chain has more ways to bend and vibrate than a small tight molecule.
Run those in reverse and entropy falls: gases being used up, gases turning into liquids, many particles joining into few.
🧩 How to predict the sign of ΔS in ten seconds
Count moles of gas on the left using the balancing numbers.
Count moles of gas on the right the same way.
More gas on the right? ΔS is positive. Less gas on the right? Negative.
Same gas count on both sides? Now look at solids melting or dissolving, and at the total number of particles.
Still tied? Then ΔS is small — say so, and say why. That is worth the mark.
Notice the third row. Two moles of gas become two moles of gas, so nothing dramatic happens — the small positive value comes from turning two identical molecules into two different ones.
Common changes and their entropy sign
Change
What happens to the particles
Sign of ΔS
Ice melting
Fixed lattice becomes a liquid that can flow
Positive
Water boiling
Touching particles become free and far apart
Positive, and large
Salt dissolving in water
Lattice breaks up, ions spread through the solution
Positive
A carbonate decomposing
Solid gives off a gas
Positive
Steam condensing
Free gas particles get trapped in a liquid
Negative
Ammonia being made from N2 and H2
4 mol of gas becomes 2 mol of gas
Negative
H2 and Cl2 making HCl
2 mol of gas becomes 2 mol of gas
Near zero
Worked examples
WORKED EXAMPLE
Predict, with a reason, whether ΔS is positive or negative for N2(g) + 3H2(g) → 2NH3(g).
Count the gas on the left
1 mol N2 + 3 mol H2 = 4 mol of gasCount the gas on the right2 mol of gasCompare
4 mol of gas becomes 2 mol, so the particles have fewer ways to be arranged.
ΔS is negativeThe mark is for the reason, not the word. Write “the number of moles of gas falls from 4 to 2”.
WORKED EXAMPLE
Ammonium nitrate dissolving in water takes heat in from its surroundings. Explain why it dissolves anyway.
What the enthalpy says
ΔH is positive, so on energy grounds alone this change looks unfavourable.
What happens to the arrangement
An ordered ionic lattice breaks apart and the NH4+ and NO3− ions spread right through the water.
So the entropy change is
Strongly positive — a huge gain in ways to arrange the ions.
The entropy gain outweighs the energy costThis is the whole reason the next three pages exist. Two competing effects need one number to settle them, and that number is ΔG.
WORKED EXAMPLE
Put these in order of increasing entropy, all at 298 K: 1 mol of CO2(g), 1 mol of H2O(l), 1 mol of NaCl(s).
Sort by state first
Solid is lowest, then liquid, then gas — state beats everything else here.
Put them in lineNaCl(s) < H₂O(l) < CO₂(g)Check against the booklet
72, then 70… careful. Those two are almost the same, so quote the values: NaCl(s) 72 and H2O(l) 70 J K−1 mol−1.
H₂O(l) ≈ NaCl(s), both well below CO₂(g) at 214A useful reminder: solid < liquid < gas is a rule for the same substance. Across different substances you need the real numbers.
💡 Exam tip
Say the words “moles of gas”. Examiners want the reason, and gas count is the reason they are looking for.
Watch the units. Entropy is in J K−1 mol−1 while enthalpy is in kJ mol−1. This trips people up on the next pages.
“More disordered” is fine, “more spread out” is better. Talk about the number of ways particles and energy can be arranged.
Entropy is never negative for a substance — only a change in entropy can be negative.
Look for state symbols before anything else. (s), (l), (g) and (aq) are doing the real work in these questions.
If asked “explain in terms of entropy”, always name the two things being spread: the particles and their energy.
⚠ Common mix-up
Thinking entropy is just “messiness”. It is a count of possible arrangements. Messiness is only the picture that helps you remember it.
Assuming exothermic means it will happen. Plenty of endothermic changes happen on their own because entropy pays the bill.
Counting molecules instead of moles of gas. 2H2O(l) is not gas. Only the (g) species count in step one.
Ignoring the balancing numbers. Two moles of gas on the left is not the same as one.
Mixing up ΔS and S°.S° is a value for one substance; ΔS is the change for a whole reaction.
Saying a reaction “has entropy” when you mean the entropy has increased. Be precise about change.
You can now say whether entropy goes up or down. Next you will put a number on it, straight from the data booklet. Up next: Calculating Standard Entropy Changes.
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