Entropy Calculator
Compute entropy using validated scientific equations. See step-by-step derivations, unit analysis, and reference values.
Calculator
Adjust values & calculateFormula
For a reversible process, entropy change equals heat transferred divided by absolute temperature. For chemical reactions, entropy change is the difference between total standard molar entropies of products and reactants, weighted by stoichiometric coefficients.
Last reviewed: December 2025
Worked Examples
Example 1: Entropy Change of Ice Melting
Example 2: Reaction Entropy for Combustion of Carbon
Background & Theory
The Entropy Calculator applies the following established principles and formulas. Chemistry is the science of matter's composition, structure, properties, and transformations. At the heart of quantitative chemistry lies the mole concept. One mole of any substance contains exactly 6.022×10²³ entities (Avogadro's number, Nₐ), and the molar mass of an element or compound in grams per mole is numerically equal to its atomic or molecular mass in atomic mass units. This allows chemists to convert between measurable mass and the number of reacting particles. Stoichiometry uses balanced chemical equations to relate the amounts of reactants and products. A balanced equation conserves both mass and charge. Molarity, the most common concentration unit, is defined as M = n/V, where n is moles of solute and V is volume of solution in liters, giving units of mol/L. Acidity and basicity are quantified by the pH scale, defined as pH = −log₁₀[H⁺], where [H⁺] is the molar concentration of hydrogen ions. Pure water at 25°C has pH 7.00; acids have lower values and bases higher values. Each unit change represents a tenfold change in hydrogen ion concentration. Gas behavior is described by the ideal gas law PV = nRT, where P is pressure in pascals, V is volume in cubic meters, n is moles, R = 8.314 J/(mol·K), and T is temperature in kelvin. Special cases include Boyle's Law (P₁V₁ = P₂V₂ at constant temperature) and Charles's Law (V₁/T₁ = V₂/T₂ at constant pressure). Thermochemistry quantifies heat changes in reactions through enthalpy, H. Hess's Law states that the total enthalpy change for a reaction is the sum of enthalpy changes for any sequence of steps leading to the same overall reaction, making it possible to calculate enthalpies for reactions that cannot be measured directly. Electron configuration describes the distribution of electrons in atomic orbitals according to the Aufbau principle, Pauli exclusion principle, and Hund's rule. Periodic trends including atomic radius, ionization energy, and electronegativity arise systematically from electron configuration and nuclear charge, enabling chemists to predict and rationalize chemical behavior across the periodic table.
History
The history behind the Entropy Calculator traces back through the following developments. Chemistry's roots lie in alchemy, the medieval practice combining proto-scientific experimentation with mystical aims. Alchemists developed practical techniques including distillation, calcination, and the preparation of acids, building a body of empirical knowledge despite their theoretical misunderstandings. Modern chemistry is conventionally dated to Antoine Lavoisier (1743–1794), often called the father of modern chemistry. Lavoisier demonstrated the law of conservation of mass in 1789, showing that matter is neither created nor destroyed in chemical reactions. He identified oxygen's role in combustion, dismantling the phlogiston theory, and co-authored the first systematic chemical nomenclature, establishing the language still used today. John Dalton proposed the first modern atomic theory in 1803, asserting that all matter is composed of indivisible atoms, that atoms of the same element are identical in mass, and that compounds form from fixed ratios of different atoms. This provided a physical basis for Lavoisier's conservation law and Proust's law of definite proportions. Dmitri Mendeleev published his periodic table in 1869, arranging the 63 known elements by atomic mass and revealing repeating patterns of chemical behavior. He boldly left gaps for undiscovered elements and predicted their properties with remarkable accuracy, predictions confirmed by the subsequent discovery of gallium, scandium, and germanium. Ernest Rutherford's gold foil experiment in 1911 revealed the nuclear model of the atom: a tiny, dense, positively charged nucleus surrounded by electrons. Niels Bohr refined this in 1913 with a quantized model of electron orbits that explained the hydrogen emission spectrum. Quantum chemistry and molecular orbital theory, developed through the 1920s and 1930s, provided the full quantum mechanical description of chemical bonding. The latter 20th century saw the rise of computational chemistry, enabling molecular simulation at unprecedented scale. The green chemistry movement, articulated in the 12 Principles of Green Chemistry in 1998, reoriented the field toward sustainability, waste reduction, and benign chemical design, reflecting chemistry's growing awareness of its environmental responsibilities.
Frequently Asked Questions
Formula
deltaS = Q_rev / T; deltaS_rxn = sum(S_products) - sum(S_reactants)
For a reversible process, entropy change equals heat transferred divided by absolute temperature. For chemical reactions, entropy change is the difference between total standard molar entropies of products and reactants, weighted by stoichiometric coefficients.
Worked Examples
Example 1: Entropy Change of Ice Melting
Problem: Calculate the entropy change when 1 mole of ice melts at 273.15 K. The enthalpy of fusion is 6,010 J/mol.
Solution: deltaS = Q / T\ndeltaS = 6010 J / 273.15 K\ndeltaS = 22.00 J/(mol*K)\n\nThis is positive because melting increases molecular disorder — liquid water has more microstates than solid ice.
Result: deltaS = 22.00 J/(mol*K) — entropy increases during melting
Example 2: Reaction Entropy for Combustion of Carbon
Problem: Find deltaS for C(s) + O2(g) -> CO2(g). Standard entropies: C(s) = 5.7, O2(g) = 205.2, CO2(g) = 213.8 J/(mol*K).
Solution: deltaS_rxn = S(products) - S(reactants)\ndeltaS_rxn = [213.8] - [5.7 + 205.2]\ndeltaS_rxn = 213.8 - 210.9\ndeltaS_rxn = 2.9 J/(mol*K)
Result: deltaS = 2.9 J/(mol*K) — slight entropy increase (1 mol gas produces 1 mol gas)
Frequently Asked Questions
What is entropy in chemistry?
Entropy (S) is a thermodynamic quantity that measures the degree of randomness or disorder in a system. In statistical mechanics, entropy is defined as S = k_B * ln(W), where k_B is Boltzmann constant and W is the number of microstates available to the system. A higher entropy means more possible arrangements of particles and energy. Entropy always increases for the universe as a whole (Second Law of Thermodynamics), though individual systems can decrease in entropy if a greater increase occurs elsewhere. In chemistry, entropy changes during reactions help determine whether a process is spontaneous by contributing to the Gibbs free energy equation deltaG = deltaH - T*deltaS.
How do you predict the sign of entropy change for a reaction?
Several qualitative rules help predict whether entropy increases or decreases in a chemical reaction. Entropy generally increases when: solids dissolve into solution, liquids vaporize to gases, the number of gas molecules increases (e.g., 1 mol gas producing 2 mol gas), temperature increases, or complex molecules decompose into simpler ones. Entropy generally decreases when: gases condense or are absorbed, molecules combine to form larger molecules, or crystallization occurs from solution. For example, the reaction 2H2O(l) producing 2H2(g) + O2(g) has a large positive entropy change because liquid water becomes three moles of gas, dramatically increasing the number of possible microstates.
Is my data stored or sent to a server?
No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.
How do I verify Entropy Calculator's result independently?
The Formula section on this page shows the equation used. You can reproduce the calculation manually or in a spreadsheet using those steps. Compare your answer against the worked examples in the Examples section, which use known reference values so you can confirm the calculator is behaving as expected.
How accurate are the results from Entropy Calculator?
All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.
Why might my result differ from another tool or reference?
Differences typically arise from rounding conventions, the specific version of a formula (for example, simple vs compound interest), or unit inconsistencies between inputs. Check that both tools are using the same formula variant and the same units. The References section links to the authoritative source behind the formula used here.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy