Calculate entropy change for chemical reactions, phase transitions, and mixing processes. Covers ΔS°rxn from standard molar entropies and Boltzmann entropy.
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.
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. This entropy calculator helps you compare outcomes quickly and reduce avoidable mistakes when making day-to-day care decisions. Use the estimate as a planning baseline and confirm final decisions with a qualified professional when risk is high.
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)
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.
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.
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 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.
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.