# What is an integrated rate law?

##### 1 Answer

An integrated rate law is an equation that expresses the concentrations of reactants or products as a function of time.

An integrated rate law comes from an ordinary rate law.

Consider the first order reaction

A → Products

The rate law is: rate =

But

If you don't know calculus, don't worry. Just skip ahead 8 lines to the final result.

If you know calculus, you know that, as the Δ increments become small, the equation becomes

If we integrate this differential rate law, we get

At

So the **integrated rate law** for a first order reaction is

This equation is often written as

In the same way, we can derive the integrated rate law for any other order of reaction.