A reaction-rate equation is an ordinary differential equation for continuously varying species concentrations. Under the law of mass action, its reaction rates are monomials in those concentrations.
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A rate equation, also known as a rate law or rate expression, is a mathematical equation that relates the rate of a chemical reaction to the concentration of the reactants. It is derived from experimental data and expresses how the rate of the reaction depends on the concentrations of the reactants raised to specific powers, which are known as the reaction orders.