The Integrated Rate Law: The Dependence of Concentration on Time

A rate law used to determine the reaction rate from reactant concentrations and rate constants can be converted into rate laws demonstrating the dependence of reaction rate on reactant concentration and time.

These rate laws can be used to study how slowly or quickly a reactant is consumed, or how much time is necessary to reach half the concentration of a reactant.

To begin, examine the differential rate law, which expresses the reaction rate as a change in reactant concentration during a specific time interval. Integration of this law leads to the integrated rate law, which expresses the reaction rate as a relation between a reactant’s initial concentration and its concentration after a specific duration.

The integrated rate law is dependent on the overall reaction order and, hence, varies for each reaction type. However, irrespective of the overall order, all integrated rate laws take the form of a standard linear equation with distinct y, m, x, and b components, and can be plotted to generate a straight line.

In a zero-order integrated rate law, [A]_t is the reactant concentration at the time t, k is the rate constant, t is the time, and [A]₀ is the initial reactant concentratio