Last updated: July 3, 2026
Entropy Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Quick Answer
The entropy calculator computes standard reaction entropy as ΔS°rxn = ΣS°products − ΣS°reactants and reversible heat-transfer entropy as ΔS = qrev/T. Positive ΔS indicates greater system entropy; negative ΔS indicates lower system entropy. Entropy connects to spontaneity through ΔG = ΔH − TΔS.
Entropy change is calculated either by subtracting the reactant standard entropy sum from the product standard entropy sum, or by dividing reversible heat by absolute temperature.
Key Takeaways
- Standard reaction entropy equals product S° sums minus reactant S° sums.
- Use stoichiometric coefficients when adding tabulated standard molar entropies.
- For reversible heat transfer at constant temperature, ΔS = qrev/T.
- Temperature must be absolute temperature in kelvin.
- Entropy influences spontaneity through ΔG = ΔH − TΔS.
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
ΔS°rxn = ΣS°products − ΣS°reactants; ΔS = qrev / T; ΔG = ΔH − TΔS
Where:
- ΔS°rxn=Standard reaction entropy change(J/(mol·K))
- ΣS°products=Sum of standard molar entropies of products(J/(mol·K))
- ΣS°reactants=Sum of standard molar entropies of reactants(J/(mol·K))
- qrev=Reversible heat transferred(J)
- T=Absolute temperature(K)
- ΔG=Gibbs free energy change(J/mol)
Worked Examples
Standard reaction entropy from sums
Products have a larger standard entropy sum than reactants.
- 1Add product standard molar entropies to get ΣS°products = 400 J/(mol·K).
- 2Add reactant standard molar entropies to get ΣS°reactants = 300 J/(mol·K).
- 3Subtract: ΔS°rxn = 400 − 300 = 100 J/(mol·K).
Reversible heat transfer
Find the entropy change when 5000 J of reversible heat is absorbed at 250 K.
- 1Use the reversible heat formula ΔS = qrev / T.
- 2Substitute qrev = 5000 J and T = 250 K.
- 3Calculate ΔS = 5000 ÷ 250 = 20 J/K.
Methane combustion entropy check
Use tabulated S° values for CH₄ + 2 O₂ → CO₂ + 2 H₂O(g).
- 1Products: CO₂ + 2 H₂O = 213.7 + 2×188.8 = 591.3 J/(mol·K).
- 2Reactants: CH₄ + 2 O₂ = 186.3 + 2×205.0 = 596.3 J/(mol·K).
- 3Subtract: ΔS°rxn = 591.3 − 596.3 = −5.0 J/(mol·K).
Introduction
Entropy measures how energy and matter are dispersed among microscopic states. This entropy calculator handles two common chemistry tasks: standard reaction entropy from tabulated standard molar entropies and entropy change for reversible heat transfer. Use it alongside the Gibbs free energy calculator when evaluating ΔG = ΔH − TΔS, or compare reaction direction with the equilibrium constant calculator. The sign convention and units follow the IUPAC Gold Book entropy definition and standard thermodynamics texts.
What entropy means in chemistry
Entropy, S, is a state function that quantifies energy dispersal and the number of accessible microscopic arrangements. A positive ΔS means the final state has greater entropy than the initial state; a negative ΔS means entropy decreases for the system. Phase changes, gas production, dissolving, mixing, and changes in molecule count often dominate the sign.
Entropy is extensive: double the amount of material and S doubles.
Standard molar entropy S° is usually tabulated at 298.15 K and 1 bar.
Reaction entropy ΔS°rxn uses stoichiometric coefficients just like enthalpy calculations.
For heat transfer, reversible conditions are required for the simple ΔS = qrev/T equation.
Standard reaction entropy formula
For a balanced chemical equation, multiply each species standard molar entropy by its stoichiometric coefficient, add the products, add the reactants, then subtract: ΔS°rxn = ΣνS°products − ΣνS°reactants. The result is reported in J/(mol·K) for the reaction as written. If you double every coefficient in the equation, ΔS°rxn doubles too.
Use standard states consistently. Mixing data for gases at 1 bar with older 1 atm tables usually creates small but avoidable differences.
Entropy from reversible heat transfer
When heat qrev is transferred reversibly at a constant absolute temperature T, the entropy change is ΔS = qrev/T. Heat absorbed by the system gives positive qrev and positive ΔS; heat released gives negative qrev and negative ΔS. Temperature must be in kelvin, never degrees Celsius.
A larger temperature produces a smaller entropy change for the same amount of reversible heat because the energy is added to a more thermally dispersed system.
Connection to Gibbs free energy
Entropy is central to spontaneity through ΔG = ΔH − TΔS. A positive ΔS lowers ΔG at higher temperature, while a negative ΔS makes ΔG less favorable as temperature rises. After computing entropy, combine it with reaction enthalpy using the Gibbs free energy calculator or relate ΔG° to K with the reaction quotient calculator.
Common entropy sign patterns
The table gives quick expectations before doing a numeric calculation. These patterns are helpful sanity checks, but tabulated values and the balanced equation decide the final number.
| Process | Typical ΔS sign | Reason |
|---|---|---|
| Solid melting | Positive | Liquid has more accessible arrangements |
| Gas molecules produced | Positive | More gas particles disperse energy and matter |
| Gas condenses | Negative | Molecules become more ordered |
| Ions crystallize from solution | Often negative | Solvated ions enter an ordered lattice |
Using reliable entropy data
Good ΔS°rxn calculations depend on consistent tabulated S° values. Prefer authoritative data sets such as the NIST Chemistry WebBook or curated teaching tables such as LibreTexts thermodynamics resources. Check whether water is liquid or gas, whether ions are aqueous, and whether the equation coefficients match the intended reaction.
Quick Reference Card
Entropy — Quick Reference
Quick reference • Entropy Calculator
ΔS°rxn = ΣS°products − ΣS°reactants; ΔS = qrev/TValid range: Reaction entropy may be positive or negative; heat-transfer entropy uses T > 0 K
Common Values
⚠ Watch Out
- •Do not forget stoichiometric coefficients when summing S° values.
- •Use kelvin for ΔS = qrev/T, not Celsius.
- •Keep phases consistent; H₂O(l) and H₂O(g) have very different entropies.
- •The reaction entropy is for the balanced equation exactly as written.
Pro Tips
- →Check the sign against gas molecule counts before trusting a result.
- →Use the same temperature and standard-state convention for every tabulated value.
- →Convert kJ to J before combining entropy with ΔG = ΔH − TΔS.
- →Report enough significant figures to match the entropy table precision.
FAQs
What does a positive entropy change mean?
A positive entropy change means the system's final state has greater entropy than its initial state. In reactions this often happens when more gas molecules are produced, a solid melts, or particles become more dispersed.
How do I calculate standard reaction entropy?
Add the stoichiometric standard molar entropies of all products, add those of all reactants, then subtract reactants from products: ΔS°rxn = ΣS°products − ΣS°reactants.
What units should I use for entropy?
Reaction entropy is commonly reported as J/(mol·K) for the reaction as written. Entropy from heat transfer qrev/T is reported as J/K for the system or process amount specified.
Can entropy change be negative?
Yes. A negative ΔS means the system entropy decreases, such as gas condensation or some reactions that reduce the number of gas molecules. The surroundings may still make the total entropy of the universe increase.
Why must temperature be in kelvin?
Thermodynamic equations use absolute temperature. Celsius values can be zero or negative and would make qrev/T physically meaningless in entropy calculations.
How is entropy related to Gibbs free energy?
Gibbs free energy combines enthalpy and entropy as ΔG = ΔH − TΔS. Positive entropy changes become more favorable at higher temperature because the TΔS term subtracts more from ΔH.