Second Order Integrated Rate Law

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: State Functions in Thermochemistry

You're on a roll. Keep up the good work!

Take Quiz Watch Next Lesson
Your next lesson will play in 10 seconds
  • 0:00 Differential Rate Law
  • 1:33 Second Order…
  • 2:10 How to Graph the Equation
  • 2:46 An Example Calculation
  • 3:56 Lesson Summary
Save Save Save

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Log in or Sign up

Speed Speed

Recommended Lessons and Courses for You

Lesson Transcript
Instructor: LaRita Williams

LaRita holds a master's degree and is currently an adjunct professor of Chemistry.

In this lesson, we will give the equation for the second order integrated rate law. We'll discuss its graph and then set up and solve a simple example problem.

Differential Rate Law

Today's technology makes it possible for almost anything to happen fast. Breaking news can be at your fingertips with the click of a button. Full meals can be microwaved in a just a couple of minutes. Cross-country travel might only take a few short hours. In a society obsessed with getting things done quickly, why not also be concerned with the speed of your chemical reactions? The investigation of kinetics allows us to do just that. Kinetics is the study of the rate at which chemical reactions occur.

In kinetics, reactions are classified according to their order. The order of a reaction is the experimentally determined exponent to which each reactant concentration must be raised in the differential rate law equation. If a reaction is second order with respect to a certain reactant, then that reactant is being raised to a power of 2 in its differential rate law equation.

For the generic reaction you can see below (Equation 1), where reactant A goes to products B and C, the differential rate law is given. Note, that in the differential rate law equation, the concentration of reactant A is raised to a power 2, indicating that this reaction is second order with respect to A.

General Reaction Equation
Generic Reaction Equation

Second Order Differential Rate Law
Second Order Rate Law

The differential rate law models how the rate of a reaction depends on the concentrations of species in that reaction. On the other hand, the integrated rate law shows how the concentrations of species in a reaction depend on time.

Second Order Integrated Rate Law Equation

An integration of the second order differential rate law that we looked at a moment ago gives us the second order integrated rate law equation, shown on your screen below:

Second Order Integrated Rate Law Equation
__Second Order Integrated Rate Law Equation__

In this equation, Asub0 represents the initial concentration of reactant A; t is the variable for time; k is the rate constant of the reaction, and A represents the concentration of reactant A at time, t. If the values of k and Asub0 are known, we can calculate the concentration of A at any given time, t, thus modeling how the concentration of that reactant is affected by time.

How to Graph the Equation

Look carefully, and you'll notice that the equation for the second order integrated rate law is in the form y = mx +b, where y = 1/A; m = k; x = t; and b = 1/Asub0. We learned in other lessons that y = mx +b is the equation for a line. So, if we plot our x and y coordinates from the equation (t and 1/A), we will produce the graph of a straight line. Moreover, the slope of that line (m) will be equal to the rate constant of our reaction (k).

To unlock this lesson you must be a Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use

Become a member and start learning now.
Become a Member  Back
What teachers are saying about
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!
Create an account