Waiting for answer This question has not been answered yet. You can hire a professional tutor to get the answer.
What is an integrated rate law?
An integrated 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.
See .
Consider the first order reaction
A → Products
The rate law is: rate = ##r = k["A"]##
But ##r = -(Δ["A"])/(Δt)##, so
##-(Δ["A"])/(Δt) = k["A"]##
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
##-(d["A"])/(dt) = k["A"]## or
##(d["A"])/(["A"]) = -kdt##
If we integrate this differential rate law, we get
##ln["A"]_t = -kt## + constant
At ##t## = 0, ##["A"]_t = ["A"]_0##, and ##ln["A"]_0## = constant
So the integrated rate law for a first order reaction is
##ln ["A"] = ln["A"]_0 - kt ##
This equation is often written as
##ln((["A"])/["A"]_0) = -kt## or
##(["A"])/(["A"]_0) = e^(-kt)## or
In the same way, we can derive the integrated rate law for any other order of reaction.