Rate Law Calculator

A differential rate law states the instantaneous reaction rate as a function of concentrations, rate = k[A]^m[B]^n. The exponents m and n are the orders with respect to each reactant and their sum is the overall order. They are determined experimentally and do not follow from the balanced equation, except in the special case of a genuinely elementary step, where order coincides with molecularity. The units of k follow from the overall order, given generally by molar to the power one minus n, per second, which yields per second for a first-order reaction and per molar per second for a second-order one. Rates are conventionally reported per unit stoichiometric coefficient, so for 2 NO2 going to products the rate of reaction is half the rate at which NO2 disappears. Orders are not restricted to small positive integers. Radical chain reactions frequently show half-integer orders because initiation contributes a square root of an initiator concentration. Enzyme-catalysed reactions become zero order in substrate once the enzyme is saturated, as do surface-catalysed reactions at full coverage. Negative orders appear when a species inhibits the catalyst or reverses an early step. A common experimental device is to flood the system with one reactant so its concentration stays effectively constant, folding it into an observed pseudo-order constant. The main limitation of any rate law is its range of validity: a mechanism change with concentration, temperature or pH can alter the exponents, so the expression should not be pushed far beyond the conditions it was fitted to.

The concentration dependence of chemical change was first formalised by Cato Maximilian Guldberg and Peter Waage in Christiania, now Oslo, in 1864. Their law of mass action expressed chemical behaviour in terms of what they called active masses, with the driving force proportional to a product of concentrations raised to powers, and they restated it more rigorously in 1879. Although they framed the law around equilibrium, the product-of-powers structure is the direct ancestor of the modern rate expression. Jacobus Henricus van't Hoff, in Etudes de dynamique chimique of 1884, made the decisive separation of reaction order from stoichiometry and classified processes as mono-, bi- and trimolecular; he received the first Nobel Prize in Chemistry in 1901. Wilhelm Ostwald's isolation method then made individual orders measurable by holding all but one reactant in large excess. The distinction between order, an empirical exponent, and molecularity, a mechanistic count of molecules in an elementary step, was sharpened through the twentieth century as multi-step mechanisms were unravelled. Leonor Michaelis and Maud Menten's 1913 treatment of enzyme kinetics supplied the classic case of a rate law that shifts continuously from first order to zero order in substrate as the enzyme saturates, demonstrating that a single fixed exponent describes only a limited regime.