Entropy Change Calculator

Free Entropy Change Calculator

This tool finds the entropy change, ΔS, of a physical or chemical process in three different situations. The Standard Solver handles heating or cooling a substance at constant pressure using ΔS = nCp,m ln(T2/T1), and phase changes like melting or boiling using ΔS = nΔH/T. The Advanced Tools tab handles a full chemical reaction, adding up tabulated standard molar entropies for every reactant and product to find ΔS°rxn.

Every mode shows whether entropy goes up (more disorder) or down (more order), walks through the full calculation step by step, and draws a simple before-and-after diagram so the idea of 'disorder' actually clicks visually. It's free, runs instantly in your browser, and needs no sign-up.

What Is Entropy Change (ΔS)?

Entropy, S, is a measure of how spread out energy and matter are within a system — loosely, how much 'disorder' or how many possible arrangements a system has. A neatly stacked deck of cards has low entropy; the same deck thrown in the air and scattered across the floor has high entropy, because there are vastly more disordered arrangements than ordered ones.

Entropy change, ΔS = S(final) − S(initial), tells you the direction that disorder moved during a process. The second law of thermodynamics says the total entropy of the universe never decreases on its own — it's the reason ice melts in a warm room, gases spread out to fill a container, and heat flows from hot objects to cold ones, never the other way around without outside help.

The Heating Formula: ΔS = nCp,m ln(T2/T1)

When you heat or cool a substance without changing its phase (still solid, still liquid, or still gas the whole time) and without changing the pressure, the entropy change follows ΔS = n × Cp,m × ln(T2/T1). Here n is the number of moles, Cp,m is the molar heat capacity at constant pressure in J/(mol·K), and T1 and T2 are the starting and ending absolute temperatures in kelvin.

The natural logarithm shows up because entropy depends on temperature in a curved, not straight-line, way — each additional degree matters a little less as the temperature gets higher, since the substance already has more thermal energy to spread around. Heating always gives a positive ΔS (T2 > T1 makes the ratio bigger than 1, and ln of a number bigger than 1 is positive); cooling always gives a negative ΔS.

The Phase-Change Formula: ΔS = ΔH / T

Melting, freezing, boiling, condensing, subliming, and depositing all happen at one fixed temperature — the melting point or boiling point of the substance — so the heating formula above doesn't apply here. Instead, entropy change during a phase transition is ΔS = n × ΔH(transition) / T, where ΔH(transition) is the molar enthalpy of fusion or vaporization (or similar), and T is the constant transition temperature in kelvin.

This comes directly from the definition ΔS = q(reversible) / T. A phase change at its exact transition temperature is about as close to a perfectly reversible process as chemistry gets, since a tiny nudge in either direction can push the substance to melt a little more or freeze a little more. Melting, vaporizing, and subliming always increase entropy; freezing, condensing, and depositing always decrease it.

How to Use This Calculator

On the Standard Solver tab, first pick 'Heating or cooling at constant pressure' or 'Phase change at constant temperature' from the dropdown. For heating, enter the moles, the molar heat capacity, and your starting and ending temperature. For a phase change, enter the moles, the molar enthalpy of the transition, and the fixed transition temperature.

The result updates instantly: total ΔS in J/K, the per-mole molar entropy change, and a plain-language read on whether the system became more ordered or more disordered. Click 'Jump to solution steps' to see the whole calculation broken down, ready to check against your own homework.

Positive vs Negative ΔS: What the Sign Means

A positive ΔS means the system ends up more disordered, with energy or particles spread across more possible arrangements. Heating a gas, melting a solid, boiling a liquid, dissolving a solid into solution, and any reaction that produces more moles of gas than it started with all tend to increase entropy.

A negative ΔS means the system ends up more ordered. Cooling something down, freezing a liquid, condensing a gas, and reactions where gas molecules combine into fewer moles of liquid or solid all tend to decrease entropy. Neither sign makes a process automatically 'good' or 'bad' — spontaneity actually depends on both ΔS and ΔH together, through Gibbs free energy, ΔG = ΔH − TΔS.

Worked Example: Heating Water from 25°C to 100°C

Take 500 g of liquid water heated from 25°C (298.15 K) to 100°C (373.15 K), just below boiling. That mass is 500 ÷ 18.02 = 27.75 mol, and water's molar heat capacity is about 75.3 J/(mol·K). The temperature ratio is 373.15 ÷ 298.15 ≈ 1.2515, and ln(1.2515) ≈ 0.2244.

Plugging in: ΔS = 27.75 × 75.3 × 0.2244 ≈ 469 J/K. That's a solidly positive number, exactly as expected — heating anything up always increases its entropy, since the water molecules now have access to a wider spread of vibrational and translational energy states.

Worked Example: Entropy of Vaporization

Now take 1 mole of liquid water vaporizing at its normal boiling point, 100°C (373.15 K), with a molar enthalpy of vaporization of 40.7 kJ/mol. Using ΔS = nΔH/T: ΔS = 1 × 40,700 J/mol ÷ 373.15 K ≈ 109.1 J/(mol·K).

This value, around 109 J/(mol·K), is close to what's known as Trouton's Rule — the observation that many ordinary liquids have a molar entropy of vaporization somewhere around 85–90 J/(mol·K), with water running a bit higher because of the extra order broken up by hydrogen bonding in liquid water that isn't present, at least not to the same extent, in the vapor.

Standard Reaction Entropy: Adding Up Absolute Entropies

For a full chemical reaction, the Advanced Tools tab uses ΔS°rxn = ΣS°(products) − ΣS°(reactants), where S° is the standard molar entropy of each species, tabulated in most chemistry textbooks and reference data sets. Every value gets multiplied by its coefficient in the balanced equation before you add the two sides together.

There's one important difference from a similar-looking Hess's Law calculation for enthalpy: standard molar entropies are never zero for elements. Unlike enthalpy of formation, where an element in its stable form is defined as the zero reference point, the third law of thermodynamics says every real substance — element or compound — has some positive entropy above absolute zero, so every single species in the equation contributes a nonzero term.

Worked Example: Standard Entropy of Methane Combustion

Take the same combustion reaction often used for enthalpy problems: CH4(g) + 2 O2(g) → CO2(g) + 2 H2O(l). Using standard molar entropies S°[CH4(g)] = 186.3 J/(mol·K), S°[O2(g)] = 205.2 J/(mol·K), S°[CO2(g)] = 213.8 J/(mol·K), and S°[H2O(l)] = 70.0 J/(mol·K): the product side sums to 213.8 + (2 × 70.0) = 353.8 J/K, and the reactant side sums to 186.3 + (2 × 205.2) = 596.7 J/K.

ΔS°rxn = 353.8 − 596.7 = −242.9 J/K. Notice this is negative, even though burning methane releases a huge amount of heat (a strongly exothermic, spontaneous reaction). That's because 3 moles of gas on the reactant side turn into just 1 mole of gas plus 2 moles of liquid water on the product side — far fewer gas particles bouncing around freely means a big drop in disorder, which is a perfect illustration of why ΔH and ΔS have to be considered separately.

Typical Molar Heat Capacity Values

For the heating and cooling mode, you'll need a molar heat capacity, Cp,m, in J/(mol·K). A few common reference values:

• Water (liquid): about 75.3 J/(mol·K)
• Water vapor (steam): about 33.6 J/(mol·K)
• Ice: about 38 J/(mol·K)
• Aluminum: about 24.2 J/(mol·K)
• Iron: about 25.1 J/(mol·K)
• Copper: about 24.4 J/(mol·K)
• Nitrogen gas (N2): about 29.1 J/(mol·K)

Common Mistakes to Avoid

The most frequent slip-up is using the heating formula, ΔS = nCp ln(T2/T1), across a phase change — for example trying to heat ice straight through to steam in one step. Each phase needs its own heating calculation, plus a separate phase-change calculation at the melting and boiling points in between.

• Always convert temperatures to kelvin before taking a logarithm or dividing by T — Celsius and Fahrenheit will silently give a wrong answer.
• Don't assume a negative ΔS means a reaction can't happen — check Gibbs free energy (ΔG = ΔH − TΔS) instead, since a large enough negative ΔH can still make the overall process spontaneous.
• Remember that elements do get a nonzero S° value in reaction entropy calculations, unlike in enthalpy-of-formation tables.
• Multiply each S° or Cp value by the correct coefficient or mole amount before adding — don't just sum the raw tabulated numbers.

Where Entropy Calculations Show Up in Real Life

Entropy calculations sit behind refrigeration and air-conditioning design, predicting how mixtures separate or blend, understanding why certain reactions run forward but never spontaneously in reverse, and combining with enthalpy through Gibbs free energy to predict whether a chemical process, a phase change, or even a biological reaction will happen on its own under given conditions.

Limitations to Keep in Mind

The heating formula assumes Cp,m stays roughly constant across the temperature range you're testing — in reality, heat capacity drifts slightly with temperature, so results across very wide ranges are good estimates rather than lab-grade precision.

The reaction entropy tab depends entirely on the accuracy of the S° values you enter. Always pull these from a trusted reference table, and make sure every formula's physical state (solid, liquid, gas, aqueous) matches your balanced equation, since the same substance can have very different entropy values depending on its state.

Quick Reference: Every Formula on This Page

ΔS = n × Cp,m × ln(T2/T1) — entropy change from heating or cooling at constant pressure. ΔS = n × ΔH(transition) / T — entropy change during a phase transition at constant temperature. ΔS°rxn = ΣS°(products) − ΣS°(reactants) — standard reaction entropy from tabulated absolute entropies. ΔG = ΔH − TΔS — how entropy connects back to spontaneity through Gibbs free energy.