What this calculator does
The entropy formula for a chemical reaction is ΔS = ΣS(products) − ΣS(reactants): the total entropy of everything that comes out, minus the total entropy of everything that goes in. A positive result means the reaction increases disorder, often because a solid or liquid turns into a gas; a negative result means the products are more ordered than the reactants, such as when gas molecules combine into a liquid or solid.
Like the enthalpy calculator, this tool works from totals that are usually built up first from standard molar entropy values (S°) for each substance, multiplied by its moles in the balanced equation and summed for each side. This calculator does the subtraction and the per-mole conversion once those two totals are known, rather than supplying the underlying S° figures itself.
The formula
Sum each product's standard entropy times its moles to get the products total, do the same for the reactants, then subtract: ΔS = ΣS(products) − ΣS(reactants). Dividing by the moles of reaction as written in the balanced equation gives the entropy change per mole.
| Term | Meaning |
|---|---|
| ΔS | Entropy change of the reaction, in joules per kelvin. |
| ΣS(products) | The sum of each product's standard molar entropy, multiplied by its stoichiometric coefficient. |
| ΣS(reactants) | The same sum for the reactants side of the balanced equation. |
| Positive / negative ΔS | A positive ΔS means the system becomes more disordered; a negative ΔS means it becomes more ordered, most commonly when gas is consumed. |
The inputs explained
| Field | What to enter |
|---|---|
| Total entropy of products (sum of S° × moles for each product) (J/K) | The combined standard entropy of all the products, each multiplied by its number of moles in the balanced equation, summed together. |
| Total entropy of reactants (sum of S° × moles for each reactant) (J/K) | The same combined figure for the reactants side. |
| Moles of reaction (as written) | The number of moles of reaction as the balanced equation is written, used only to work out the per-mole figure. |
When to use it
Working out whether a reaction increases or decreases disorder
Reactions that produce more gas molecules than they consume typically have a strongly positive ΔS, while reactions that consume gas to form a liquid or solid, such as condensation or many synthesis reactions, typically have a negative ΔS.
Feeding entropy change into a spontaneity check
ΔS is one of the two figures, alongside ΔH, needed to work out Gibbs free energy and decide whether a reaction is thermodynamically favourable at a given temperature.
Comparing entropy change across scaled-up batches
Multiplying the products and reactants totals by the batch size before entering them scales the whole calculation, while the per-mole result stays a fixed property of the reaction regardless of batch size.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the entropy change varies with the products total
The same reactants total compared against a range of products totals, showing how ΔS moves from strongly negative toward less negative as the products become more disordered.
| Total entropy of products | Entropy change (ΔS) | Entropy |
|---|---|---|
| 50 J/K | -183.300 J/K | Decreases (system becomes more ordered, ΔS negative) |
| 69.9 J/K | -163.400 J/K | Decreases (system becomes more ordered, ΔS negative) |
| 100 J/K | -133.300 J/K | Decreases (system becomes more ordered, ΔS negative) |
| 150 J/K | -83.300 J/K | Decreases (system becomes more ordered, ΔS negative) |
| 200 J/K | -33.300 J/K | Decreases (system becomes more ordered, ΔS negative) |
How the per-mole entropy change scales with reaction size
The same total entropy change, expressed as written for different multiples of the balanced equation.
| Moles of reaction | Entropy change (ΔS) | Entropy change per mole of reaction |
|---|---|---|
| 0.5 | -163.400 J/K | -326.800 J/(mol·K) |
| 1 | -163.400 J/K | -163.400 J/(mol·K) |
| 2 | -163.400 J/K | -81.700 J/(mol·K) |
| 3 | -163.400 J/K | -54.467 J/(mol·K) |
| 5 | -163.400 J/K | -32.680 J/(mol·K) |
Questions
What is the entropy formula?
ΔS = ΣS(products) − ΣS(reactants): the total standard entropy of the products minus the total standard entropy of the reactants, using each substance's standard molar entropy multiplied by its moles in the balanced equation.
How do I calculate entropy for a reaction I don't have S° values for?
You need to look up the standard molar entropy for each substance involved, from a chemistry data table or reference source. This calculator does the subtraction and per-mole conversion once those totals are known; it does not supply the underlying S° figures.
Why is entropy change often negative when gas is consumed?
Gas molecules are far more disordered than the same substance as a liquid or solid, since they occupy much more space and move far more freely. A reaction that turns gas into liquid or solid, or reduces the total number of gas moles, usually loses entropy overall.
What is the difference between entropy and enthalpy?
Enthalpy (ΔH) measures the heat released or absorbed by a reaction. Entropy (ΔS) measures the change in disorder or the number of ways energy can be arranged. Both feed into Gibbs free energy, which combines them to predict whether a reaction is spontaneous at a given temperature.
For the enthalpy change of the same reaction, see the enthalpy of reaction calculator. To combine both into a spontaneity check, see the Gibbs free energy calculator.