Rate Law Calculator
Compute rate law using validated scientific equations. See step-by-step derivations, unit analysis, and reference values.
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The rate law relates reaction rate to the rate constant k and reactant concentrations [A] and [B] raised to their respective orders m and n. The overall reaction order is m + n. The rate constant k incorporates temperature dependence via the Arrhenius equation.
Last reviewed: December 2025
Worked Examples
Example 1: First Order Reaction
Example 2: Second Order Two-Reactant Reaction
Background & Theory
The Rate Law 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 Rate Law 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
rate = k [A]^m [B]^n
The rate law relates reaction rate to the rate constant k and reactant concentrations [A] and [B] raised to their respective orders m and n. The overall reaction order is m + n. The rate constant k incorporates temperature dependence via the Arrhenius equation.
Frequently Asked Questions
What is a rate law in chemistry?
A rate law is a mathematical expression that relates the rate of a chemical reaction to the concentrations of its reactants raised to specific powers called reaction orders. The general form is rate = k[A]^m[B]^n, where k is the rate constant, [A] and [B] are molar concentrations, and m and n are the reaction orders with respect to each reactant. Rate laws must be determined experimentally and cannot be predicted from the balanced equation alone. The overall reaction order is the sum of all individual orders (m + n).
How do you determine the rate constant k?
The rate constant k is determined experimentally by measuring how the reaction rate changes when reactant concentrations are varied. Using the method of initial rates, you run multiple experiments where only one reactant concentration changes at a time. By comparing the ratios of rates to the ratios of concentrations, you can solve for the exponents and then calculate k. The units of k depend on the overall reaction order: for zeroth order k has units of M/s, for first order 1/s, and for second order 1/(M*s).
How does temperature affect the rate law?
Temperature does not change the form of the rate law or the reaction orders, but it significantly affects the rate constant k. According to the Arrhenius equation, k = A * exp(-Ea/RT), where A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is temperature in Kelvin. A 10-degree Celsius increase typically doubles or triples the rate constant. Higher temperatures provide more molecules with sufficient energy to overcome the activation energy barrier.
What is the ideal gas law and when does it apply?
PV = nRT, where P is pressure, V is volume, n is moles, R is the gas constant (0.0821 L-atm/mol-K), and T is temperature in Kelvin. It applies to gases at low pressure and high temperature relative to their boiling point. Real gases deviate at high pressures and low temperatures.
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.
What inputs do I need to use Rate Law Calculator accurately?
Each field is labelled with the required unit (metric or imperial). Gather your source values before starting — for example, a weight measurement in kilograms, a distance in metres, or a dollar amount — and enter them exactly as measured. The formula section on this page lists every variable and explains what each represents.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy