Activation Energy Calculator
Calculate activation energy using the Arrhenius equation with two-temperature rate data. Supports Ea from rate constants, frequency factor estimation, and temperature dependence analysis.
Entropy Calculator
Calculate entropy change for chemical reactions, phase transitions, and mixing processes. Covers ΔS°rxn from standard molar entropies and Boltzmann entropy.
Presets
Reactants
Products
Entropy Change (ΔS)⧉
-242.80 J/(mol·K)
Negative: decrease in disorder
ΔS in kJ/(mol·K)⧉
-0.24280
Useful when combining with ΔH in kJ/mol
Direction⧉
Opposes Spontaneity
Positive ΔS contributes -TΔS < 0 to ΔG, favoring spontaneity
ΣnS° Products⧉
353.50 J/(mol·K)
Sum of (coefficient × S°) for all products
ΣnS° Reactants⧉
596.30 J/(mol·K)
Sum of (coefficient × S°) for all reactants
|ΔS| per mole⧉
242.80 J/(mol·K)
Absolute magnitude of entropy change
Entropy Change Visualization
Less Disorder
More Disorder
Standard Molar Entropies Reference
| Substance | S° (J/(mol·K)) | Relative |
|---|---|---|
| H₂(g) | 130.7 | |
| O₂(g) | 205 | |
| N₂(g) | 191.6 | |
| CO₂(g) | 213.7 | |
| H₂O(l) | 69.9 | |
| H₂O(g) | 188.7 | |
| CH₄(g) | 186.3 | |
| C₂H₆(g) | 229.6 | |
| NH₃(g) | 192.5 | |
| NaCl(s) | 72.1 | |
| C(graphite) | 5.7 | |
| Fe(s) | 27.3 | |
| CaCO₃(s) | 92.9 | |
| CaO(s) | 39.7 | |
| SO₂(g) | 248.2 |
Planning notes, formulas, and examples
About the Entropy Calculator
Entropy (S) is a thermodynamic quantity that measures the degree of disorder or the number of microstates available to a system. The second law of thermodynamics states that the total entropy of an isolated system always increases for spontaneous processes. Understanding entropy is crucial for predicting whether chemical reactions will occur spontaneously.
The standard entropy change of a reaction (ΔS°rxn) is calculated from the standard molar entropies of products and reactants: ΔS°rxn = ΣnS°(products) - ΣnS°(reactants). Standard molar entropies are tabulated at 298.15 K and 1 bar for thousands of substances. Unlike enthalpy, elements in their standard states do NOT have zero entropy (the third law assigns S = 0 only at 0 K for perfect crystals).
This calculator lets you compute ΔS°rxn by entering reactants and products with their molar entropies and stoichiometric coefficients. It also calculates entropy changes for phase transitions (ΔS = ΔH/T), isothermal expansion of ideal gases, and the Boltzmann statistical entropy (S = kB ln W). These tools cover the most common entropy calculations encountered in general and physical chemistry.
When This Page Helps
Entropy calculations require looking up standard values and correctly applying stoichiometric coefficients. This calculator handles the bookkeeping and provides results for reactions, phase changes, and gas expansions with clear explanations.
How to Use the Inputs
- Select the calculation mode: reaction, phase transition, or gas expansion.
- For reactions: enter standard molar entropies and coefficients for products and reactants.
- For phase transitions: enter the enthalpy of transition and the temperature.
- For gas expansion: enter initial and final volumes (or pressures).
- Use presets to load common examples with known values.
- Review the entropy change and spontaneity assessment.
- Check the reference table for standard molar entropies of common substances.
Formula used
Reaction: ΔS°rxn = Σ n·S°(products) - Σ n·S°(reactants)
Phase transition: ΔS = ΔH_transition / T
Ideal gas expansion: ΔS = nR·ln(V₂/V₁) = -nR·ln(P₂/P₁)
Boltzmann: S = kB × ln(W)
Where kB = 1.381×10⁻²³ J/K, R = 8.314 J/(mol·K)Example Calculation
Result: ΔS°rxn = -242.8 J/(mol·K)
For CH₄ + 2O₂ → CO₂ + 2H₂O(l): ΔS° = [213.7 + 2(69.9)] - [186.3 + 2(205.0)] = 353.5 - 596.3 = -242.8 J/(mol·K). The negative value makes sense: 3 moles of gas become 1 mole of gas + 2 moles of liquid, a decrease in disorder.
Tips & Best Practices
- Standard molar entropies (S°) are always positive — unlike ΔHf°, elements have nonzero S° values.
- Reactions that produce more gas molecules generally have positive ΔS°.
- At constant temperature and pressure, ΔG = ΔH - TΔS determines spontaneity.
- Entropy has units of J/(mol·K) — don't forget to match units with enthalpy (kJ/mol).
- Phase transitions at equilibrium: ΔG = 0, so ΔS = ΔH/T exactly.
- The entropy of vaporization of many liquids is approximately 88 J/(mol·K) at their normal boiling point (Trouton's rule).
Entropy and the Second Law
The second law of thermodynamics — arguably the most fundamental law in physics — states that the entropy of the universe always increases for spontaneous processes. This means heat flows from hot to cold, gases expand to fill their containers, and dissolved solutes don't spontaneously precipitate. The arrow of entropy defines the arrow of time.
Statistical Interpretation of Entropy
Ludwig Boltzmann showed that entropy has a microscopic interpretation: S = kB ln W, where W is the number of microstates consistent with the macroscopic properties. A deck of cards has more microstates when shuffled randomly than when sorted — this is why entropy tends toward the maximum.
Entropy in Everyday Chemistry
Entropy plays a decisive role in many familiar processes. The hydrophobic effect (why oil and water don't mix) is entropy-driven: water molecules near nonpolar surfaces are more ordered. Protein folding balances the entropy cost of ordering the chain against the entropy gain of releasing ordered water molecules.
Sources & Methodology
Last updated:
Frequently Asked Questions
Entropy is a measure of the number of microstates (W) available to a system. Higher entropy means more disorder and more ways to arrange the system's energy among its particles.
The entropy of a specific system can decrease (like freezing water), but the total entropy of the system plus surroundings always increases for spontaneous processes (second law). This keeps planning practical and lowers the chance of preventable errors.
Gas molecules are spread over a much larger volume with more possible positions and momenta, giving many more microstates. Typical S° values: gases ~200 J/(mol·K), liquids ~70-150 J/(mol·K), solids ~20-80 J/(mol·K).
A perfect crystal at absolute zero (0 K) has zero entropy. This provides the reference point for measuring absolute entropies.
A reaction is spontaneous when ΔG = ΔH - TΔS < 0. Even reactions with negative ΔS can be spontaneous if ΔH is sufficiently negative (exothermic).
When ideal gases mix, ΔS_mix = -nR Σ(xᵢ ln xᵢ), which is always positive. Mixing always increases entropy.
More in this topic
Arrhenius Equation Calculator
Solve the Arrhenius equation for rate constant, activation energy, frequency factor, or temperature. Includes Arrhenius plot data and multi-temperature analysis.
Combustion Analysis Calculator
Determine empirical and molecular formulas from combustion analysis data. Enter masses of CO₂ and H₂O produced to find percent composition and molecular formula.