Entropy Calculator
Enter coefficients and standard molar entropies (S°) for up to two reactants and two products to compute ΔS_rxn, and see whether the reaction increases or decreases entropy.
Reviewed by the ToolNestr Editorial Team — July 2026
Leave a species' S° blank to exclude it (useful for single-reactant or single-product reactions). All standard molar entropies are in J/(mol·K).
Reactants
Products
Two ideas that trip students up
1. Ordered vs disordered arrangements
On the left, particles sit in a tight, repeating grid — low entropy, like a crystalline solid. On the right, the same number of particles are scattered at random, widely spaced — high entropy, like a gas. Entropy counts how many such arrangements are possible.
2. Solid < liquid < gas
A rigid cube of tightly packed spheres (solid) sits at the smallest entropy, a loosely packed cluster (liquid) in the middle, and widely scattered spheres (gas) at the largest — the standard ordering S°(solid) < S°(liquid) < S°(gas).
Entropy graphs
How it works
The core idea in one line: reaction entropy is the same bookkeeping as enthalpy — add up the standard molar entropies of everything you end with, subtract the standard molar entropies of everything you started with.
ΔSrxn = ΣS°(products) − ΣS°(reactants)
each S° weighted by its stoichiometric coefficient, in J/(mol·K)
ΔS > 0 → entropy increases
ΔS < 0 → entropy decreases
Each S° is weighted by its stoichiometric coefficient before summing. A positive ΔS_rxn means the products have more accessible microstates than the reactants — often because moles of gas increased, a solid became a liquid or gas, or a substance dissolved into solution. A negative ΔS_rxn means the products are more ordered — often because gas moles decreased or a gas condensed into a liquid or solid.
Worked example 1 — decomposition of N₂O₄
Given: N₂O₄(g) → 2 NO₂(g). S°: N₂O₄(g) = 304.3, NO₂(g) = 240.1 J/(mol·K).
ΔS_rxn ≈ +175.9 J/(mol·K) — positive, because one mole of gas splits into two moles of gas, increasing the number of accessible microstates.
Worked example 2 — condensation of water vapor
Given: H₂O(g) → H₂O(l). S°: H₂O(g) = 188.8, H₂O(l) = 69.9 J/(mol·K), both with coefficient 1.
ΔS_rxn = −118.9 J/(mol·K) < 0 — negative, because a gas (high entropy, widely spaced, fast-moving molecules) condenses into a liquid (much more ordered), decreasing entropy of the system.
Standard molar entropies (S°) for common substances
Reference values at 25°C, 1 atm, used in the worked examples above. Notice S°(solid) < S°(liquid) < S°(gas) for water, and how graphite (a looser layered structure) has higher entropy than the rigid diamond lattice of the same element, carbon.
| Substance | S° (J/(mol·K)) |
|---|---|
| H₂O(s), ice | 48 |
| H₂O(l), liquid water | 70 |
| H₂O(g), steam | 189 |
| O₂(g) | 205 |
| N₂(g) | 192 |
| CO₂(g) | 214 |
| C(graphite) | 5.7 |
| C(diamond) | 2.4 |
Values are standard reference data (approximate, rounded) — always confirm against a current data table for precision work.
Where reaction entropy actually matters
🧭 Predicting spontaneity via Gibbs free energy
Combining ΔH and ΔS through ΔG = ΔH − TΔS lets chemists predict whether a reaction will be spontaneous at a given temperature, and whether raising or lowering temperature could flip the outcome — critical for designing industrial processes that must run efficiently at scale.
❄️ Refrigeration and heat engine limits
The second law of thermodynamics — entropy of system plus surroundings always increases — sets a hard theoretical ceiling on how efficient any refrigerator, heat pump, or heat engine can ever be, no matter how well it is engineered.
🔥 Why some exothermic reactions do not run
A reaction can release heat (ΔH < 0) yet still fail to be spontaneous at a given temperature if it also strongly decreases entropy (ΔS < 0) enough that TΔS outweighs ΔH — entropy is why enthalpy alone never tells the whole story.
🧬 Biology and local entropy decrease
Living cells build highly ordered structures — proteins, DNA, membranes — locally decreasing entropy. This does not violate the second law: cells pay for that local order by releasing heat and disordered waste, increasing the entropy of their surroundings by even more.
Common misconceptions
"Entropy always increases in every process, everywhere, all the time."
Only the TOTAL entropy of a system plus its surroundings must increase for a spontaneous process (the second law). LOCAL entropy can and does decrease — water freezing into ice, a cell organizing molecules into proteins, or a reaction with negative ΔS_rxn. What is forbidden is the sum decreasing.
"Entropy is just a fancy word for messiness."
The disorder analogy is a useful first mental picture, but it is imprecise. Entropy more precisely counts the number of accessible microstates (energetically equivalent arrangements) consistent with a system's observable state — a subtly different and more rigorous idea than everyday "messiness."
"A negative ΔS_rxn means the reaction is impossible."
A negative ΔS_rxn only describes the system's own entropy change. The reaction can still be spontaneous overall if it is sufficiently exothermic (very negative ΔH) — the heat released raises the surroundings' entropy by more than the system loses, so ΔG = ΔH − TΔS is still negative.
"Solids always have lower entropy than any liquid or gas, without exception."
The general trend S°(solid) < S°(liquid) < S°(gas) holds for the same substance across its phases, but it is not a universal ranking across different substances — a complex gas is not automatically compared meaningfully to an unrelated solid, and structural factors (like graphite vs diamond, both solids of carbon) also matter.
Formula sources & further reading
The formulas here are standard, traceable to:
- • OpenStax, Chemistry 2e — Chapter 16, Entropy and Free Energy (free, peer-reviewed). openstax.org
- • Brown, LeMay & Bursten, Chemistry: The Central Science — Chapter 19, Chemical Thermodynamics.
- • Zumdahl & Zumdahl, Chemistry — entropy, standard molar entropies, and the second law of thermodynamics.
ΔS_rxn = Σ(coefficient × S°)products − Σ(coefficient × S°)reactants. Results are rounded for display.
How to use this calculator
Enter reactants
Coefficient and S° for reactant 1; optionally reactant 2.
Enter products
Coefficient and S° for product 1; optionally product 2.
Read the result
ΔS_rxn solves live, with an entropy-increasing/decreasing label and the static order/disorder diagrams.
Related tools
Frequently asked questions
What is entropy?
Entropy (S) is a measure of how spread out energy and matter are among the possible microscopic arrangements (microstates) of a system. Loosely, it tracks disorder or randomness — but more precisely, higher entropy means there are more ways for a system's particles to be arranged while looking the same at the macroscopic level. It is measured in J/(mol·K).
What does the second law of thermodynamics say about entropy?
The second law states that for any spontaneous process, the total entropy of the system plus its surroundings always increases (or stays the same for a perfectly reversible process). It never decreases. This is why heat flows from hot to cold and not the reverse, and why some reactions proceed in one direction but not spontaneously in the other.
Why does entropy increase when a solid melts or a liquid boils?
Melting and boiling both give particles more freedom of motion and more possible arrangements. A solid has particles locked into a rigid, ordered lattice (low entropy). A liquid lets particles slide past each other (more entropy). A gas lets particles move almost independently through a huge volume with widely spaced, fast-moving molecules (much more entropy). So S°(solid) < S°(liquid) < S°(gas) is the standard ordering.
How does ΔS relate to spontaneity via ΔG = ΔH − TΔS?
Gibbs free energy combines both enthalpy and entropy: ΔG = ΔH − TΔS. A reaction is spontaneous when ΔG < 0. A positive ΔS (entropy increasing) makes the −TΔS term more negative, favoring spontaneity, especially at higher temperature. A negative ΔS works against spontaneity unless ΔH is negative enough (exothermic) to compensate. This is why some exothermic reactions with negative ΔS become non-spontaneous at high temperature, and some endothermic reactions with positive ΔS become spontaneous at high temperature.
Does a negative ΔS_rxn mean the reaction cannot happen?
No. A negative ΔS_rxn only means the reaction, by itself, decreases entropy in the system. The reaction can still be spontaneous overall if it releases enough heat (sufficiently negative ΔH) to increase the entropy of the surroundings by more than the system loses — the total entropy change (system + surroundings) is what the second law actually requires to be positive.