Enthalpy vs Entropy: What's the Difference?

Two-thirds of the way into every thermodynamics unit, the same question hits: "Wait — is enthalpy the disorder one, or is that entropy?" They're the two quantities that together decide whether a reaction happens, and mixing them up scrambles everything downstream.

The short answer: enthalpy change (ΔH) measures the heat a process releases or absorbs at constant pressure, in kJ/mol. Entropy change (ΔS) measures how much more spread out energy and matter become, in J/(mol·K). Nature favours lower enthalpy and higher entropy — and when the two disagree, temperature settles the argument.

Quick comparison at a glance

Feature	Enthalpy (H)	Entropy (S)
What it tracks	Heat content; energy released or absorbed	Dispersal of energy and matter; number of ways to arrange
Symbol for change	ΔH	ΔS
Units	kJ/mol	J/(mol·K) — note the joules, not kilojoules
Favourable direction	Negative (heat released)	Positive (more spread out)
Everyday signal	Flask feels hot or cold	Solid → liquid → gas; things mix and spread
Role in spontaneity	One vote	The other vote — temperature weights it

What is enthalpy?

ΔH is the heat exchanged at constant pressure — negative for exothermic processes, positive for endothermic ones, exactly as covered in [What Is Enthalpy?]. It's the quantity your hand detects on the outside of the beaker, and the one behind every "this reaction releases 890 kJ/mol" statement, like the exothermic reactions in Endothermic vs Exothermic Reactions Explained.

Falling to lower enthalpy is one thing nature "likes": a ball rolls downhill, and reacting particles tend toward stronger bonding and lower energy.

What is entropy?

Entropy is often introduced as "disorder", but the sharper picture is dispersal: entropy measures how spread out energy and matter are — equivalently, how many microscopic ways there are to arrange the particles and their energy while looking the same from outside. More arrangements = higher entropy.

Reliable rules of thumb for the sign of ΔS:

• Phase changes: solid → liquid → gas increases entropy sharply. Gas particles roam an entire container; particles locked in a crystal barely move.
• Counting gas moles: more moles of gas on the product side means ΔS > 0; fewer means ΔS < 0. This is the fastest exam check there is.
• Mixing and dissolving: usually increase entropy — particles gain places to be.
• Heating: always increases entropy — particles get more energy to spread across.

Increasing entropy is the other thing nature "likes": left alone, energy and matter spread out. Perfume crosses a room; ice in a warm drink never un-melts.

How the two decide what happens

Some processes are easy calls — burning propane releases heat and makes more gas (C₃H₈ + 5O₂ → 3CO₂ + 4H₂O: six moles of gas become seven): both votes say go. The interesting cases are the conflicts:

• Ice melting on a spring day: ΔH > 0 (absorbs heat — unfavourable) but ΔS > 0 (liquid beats solid — favourable). Above 0 °C, the entropy vote wins and ice melts anyway. Endothermic, yet it happens by itself.
• Water freezing in January: ΔH < 0 (releases heat — favourable) but ΔS < 0 (crystal is more ordered — unfavourable). Below 0 °C, the enthalpy vote wins.

Notice what settled both arguments: temperature. Entropy's vote counts for more when it's hot, less when it's cold. The exact formula that weighs the votes — ΔG = ΔH − TΔS — is the next post, [What Is Gibbs Free Energy?].

Worked examples

Predict the sign of ΔS before checking:

1. CaCO₃(s) → CaO(s) + CO₂(g). Zero moles of gas become one: ΔS > 0. Matter spreads dramatically when a gas is born from a solid.

2. N₂(g) + 3H₂(g) → 2NH₃(g). Four moles of gas shrink to two: ΔS < 0. The Haber process pays an entropy penalty — it runs because the enthalpy side is favourable enough under the right conditions.

3. Sugar dissolving in tea. Ordered crystal → molecules scattered through the liquid: ΔS > 0, and the drink barely changes temperature — a nearly pure entropy-driven process.

Common mistakes to avoid

• The units trap. ΔH comes in kJ/mol but ΔS in J/(mol·K) — a factor of 1000 apart. Every teacher sets at least one problem that punishes forgetting the conversion.
• "Entropy = messy room". The metaphor suggests entropy is about untidiness you can see. It's really about energy and particles having more microscopic arrangements — a bigger space of possibilities, not a value judgement.
• Using one quantity to predict spontaneity alone. Exothermic-therefore-spontaneous fails (ice melts endothermically); entropy-always-wins fails too (water freezes). Only the two together, weighted by temperature, predict correctly.

FAQ

Which one decides if a reaction is spontaneous?
Both. Gibbs free energy combines them: ΔG = ΔH − TΔS. Negative ΔG means spontaneous — see the next post in this series.

Can entropy ever decrease?
In a system, yes — water freezes, gases condense. The universe's total entropy still increases, because the heat released disperses into the surroundings and raises their entropy by more.

Why does entropy have kelvin in its units?
Because entropy tracks energy dispersed per degree of temperature — J/(mol·K). That K is also your reminder to use kelvin, never °C, in calculations.

Is enthalpy or entropy more important?
At low temperatures, enthalpy tends to dominate; at high temperatures, the TΔS term grows until entropy dominates. Neither is "more important" — temperature sets the exchange rate.

The takeaway

Enthalpy (ΔH, kJ/mol) is the heat story: negative is favourable. Entropy (ΔS, J/(mol·K)) is the dispersal story: positive is favourable. When they agree, the outcome is obvious; when they clash, temperature decides — which is exactly what Gibbs free energy calculates.

Next up: [What Is Gibbs Free Energy?] puts the two votes into one equation. Meanwhile [Kinetics vs Thermodynamics] explains why even a "spontaneous" reaction can take forever, and [What Is Enthalpy?] covers the ΔH half in detail.

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