Entropy S measures how many microscopic arrangements are consistent with the state of a system – loosely, how spread out its energy and matter are. Gases have far higher molar entropies than liquids, and liquids higher than solids; warming a substance, letting a gas expand or dissolving a crystal all increase entropy. The second law of thermodynamics says the total entropy of the universe increases in every spontaneous process.
For chemical reactions, chemists use standard molar entropies S° (in J/(mol·K), tabulated at 25 °C and 1 bar). Subtract the sum for the reactants from the sum for the products – each multiplied by its stoichiometric coefficient – to get the reaction entropy ΔS°. A reaction that produces more moles of gas usually has a positive ΔS°. Combined with the enthalpy change through ΔG = ΔH − TΔS, the sign of the entropy change tells you whether temperature helps or hinders the reaction.
For physical processes there are simple closed forms: ΔS = nR ln(V₂/V₁) for an ideal gas at constant temperature, q/T for heat added reversibly at a fixed temperature (such as melting or boiling), and n·Cp·ln(T₂/T₁) for heating without a phase change.
How to use the Entropy Calculator
- Process
- Sum of S° of products (× coefficients)
- Sum of S° of reactants (× coefficients)
- Reaction enthalpy ΔH (for ΔG, optional)
- Amount of gas or substance n
- Initial volume V₁
- Final volume V₂
- Initial pressure P₁
- Final pressure P₂
- Heat absorbed by the system q (negative if released)
- Molar heat capacity Cp
- Initial temperature T₁
- Temperature T (°C or K)
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose the kind of process. The calculator applies the matching formula, keeping temperatures in kelvin and converting every unit through its menu. In reaction mode, enter the coefficient-weighted sums of S° and, optionally, ΔH to get ΔG and the temperature at which the reaction changes direction.
Worked example
For the Haber process N₂(g) + 3H₂(g) → 2NH₃(g), standard molar entropies are S°(N₂) = 191.61, S°(H₂) = 130.68 and S°(NH₃) = 192.77 J/(mol·K). Products: 2 × 192.77 = 385.54; reactants: 191.61 + 3 × 130.68 = 583.65. ΔS° = −198.11 J/K – four moles of gas become two. With ΔH° = −91.88 kJ at 298.15 K, ΔG° = −91.88 − 298.15 × (−0.19811) = −32.81 kJ, so the reaction is spontaneous at 25 °C, and it stops being favourable above ΔH/ΔS = 463.8 K (190.6 °C) under standard conditions.
Typical standard molar entropies at 25 °C
| Substance | S° (J/(mol·K)) |
|---|---|
| C (diamond) | 2.38 |
| C (graphite) | 5.74 |
| H₂O (l) | 69.95 |
| H₂O (g) | 188.84 |
| H₂ (g) | 130.68 |
| N₂ (g) | 191.61 |
| O₂ (g) | 205.15 |
| CO₂ (g) | 213.79 |
| NH₃ (g) | 192.77 |
Values from the NIST Chemistry WebBook / CODATA key values. Note the jump from liquid to gaseous water: about 119 J/(mol·K).
Tips
- Use kelvin for every temperature in thermodynamic formulas – the unit menus convert for you.
- Watch the units: ΔH is usually in kJ/mol and ΔS in J/(mol·K).
- Tabulated values are for standard conditions (1 bar, usually 25 °C).
- Everything is calculated in your browser.
Common mistakes to avoid
- Mixing kJ and J between ΔH and ΔS.
- Assuming ΔH and ΔS do not change with temperature over large ranges.
- Using Celsius in ln(T₂/T₁).
Inputs explained
| Field | What to enter |
|---|---|
| Process | Choose one: Chemical reaction (standard entropies), Ideal gas at constant T – volume change, Ideal gas at constant T – pressure change, Heat transferred reversibly at constant T (q/T) … |
| Sum of S° of products (× coefficients) | Units: J/(mol·K), kJ/(mol·K), cal/(mol·K) |
| Sum of S° of reactants (× coefficients) | Units: J/(mol·K), kJ/(mol·K), cal/(mol·K) |
| Reaction enthalpy ΔH (for ΔG, optional) | Units: kJ/mol, J/mol, kcal/mol, cal/mol, eV (per particle) |
| Amount of gas or substance n | Units: mol, mmol, µmol, nmol, kmol |
| Initial volume V₁ | Units: L, mL, µL, m³, dm³, cm³ … |
| Final volume V₂ | Units: L, mL, µL, m³, dm³, cm³ … |
| Initial pressure P₁ | Units: atm, kPa, bar, hPa (mbar), mmHg (Torr), psi … |
| Final pressure P₂ | Units: atm, kPa, bar, hPa (mbar), mmHg (Torr), psi … |
| Heat absorbed by the system q (negative if released) | Units: J, kJ, cal, kcal |
| Molar heat capacity Cp | Units: J/(mol·K), cal/(mol·K) |
| Initial temperature T₁ | Units: °C, K, °F |
| Temperature T (°C or K) | Units: °C, K, °F |
What each result means
- Entropy change ΔS (per mole of reaction in reaction mode) = [dS]
- Gibbs energy change ΔG = ΔH − TΔS = [Reaction enthalpy ΔH (for ΔG, optional)] – ([Temperature T (°C or K)] + 273.15)×[dS]÷1000
Formula
Reaction: ΔS° = ΣS°(products) − ΣS°(reactants) · ΔG = ΔH − TΔS · Isothermal ideal gas: ΔS = nR·ln(V₂/V₁) = −nR·ln(P₂/P₁) · Reversible heat: ΔS = q/T · Heating: ΔS = n·Cp·ln(T₂/T₁)Worked example
Inputs — Process: Chemical reaction (standard entropies); Sum of S° of products (× coefficients): 385.54 J/(mol·K); Sum of S° of reactants (× coefficients): 583.65 J/(mol·K); Reaction enthalpy ΔH (for ΔG, optional): -91.88 kJ/mol; Temperature T (°C or K): 25 °C.
Results — Entropy change ΔS (per mole of reaction in reaction mode) = -198.11 J/K; Gibbs energy change ΔG = ΔH − TΔS = -32.8135 kJ/mol; Spontaneity at this temperature = Spontaneous (ΔG < 0); Crossover temperature ΔH/ΔS (ΔG = 0) = 190.63 °C; What drives the reaction = Enthalpy-driven (ΔH < 0, ΔS < 0) – spontaneous below the crossover temperature; Sign of ΔS = Negative – the system becomes more ordered.
Key terms
- Entropy (S)
- A state function measuring the number of microscopic arrangements available to a system, S = k ln W.
- Standard molar entropy (S°)
- The entropy of one mole of a substance at 1 bar and a given temperature (usually 298.15 K).
- Second law of thermodynamics
- In any spontaneous process the total entropy of the system and its surroundings increases.
- Reversible process
- An idealised process that passes through equilibrium states and can be reversed by an infinitesimal change.
Frequently asked questions
How do I calculate the entropy change of a reaction?
Multiply each standard molar entropy S° by its coefficient, add up products and reactants separately, and subtract: ΔS° = ΣS°(products) − ΣS°(reactants). For N₂ + 3H₂ → 2NH₃ this is 385.5 − 583.7 = −198.1 J/K.
What is the entropy change when an ideal gas doubles its volume?
ΔS = nR ln 2 = 5.76 J/K per mole at constant temperature.
What is the entropy of fusion of ice?
ΔS = ΔHfus/T = 6,010 J/mol ÷ 273.15 K = 22.0 J/(mol·K).
Can entropy decrease?
The entropy of a system can decrease (water freezing, gas compressed), but only if the surroundings gain at least as much, so the total never decreases.
Why must temperature be in kelvin?
Entropy formulas divide by T or take ln(T₂/T₁); both are only meaningful on an absolute scale. 25 °C is 298.15 K.
What is the unit of entropy?
J/K for a system and J/(mol·K) for molar entropies. 1 cal/(mol·K) = 4.184 J/(mol·K).
Does a positive ΔS mean a reaction is spontaneous?
Not by itself. Spontaneity depends on ΔG = ΔH − TΔS, so an exothermic reaction with negative ΔS can still be spontaneous at low temperature.