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Tips on when to use Differential Rate Laws and Integrated Rate Laws - Concept

Teacher/Instructor Kendal Orenstein
Kendal Orenstein

Rutger's University
M.Ed., Columbia Teachers College

Kendal founded an academic coaching company in Washington D.C. and teaches in local area schools. In her spare time she loves to explore new places.

Tips on when to use differential Rate Law versus the Integrated Rate Law. So you have two different types of rate laws. You have the Differential Rate Law, which is on the first column and which we're used to. Rate equals k times the concentration of A for first order. We have second order reaction rate equals k times the concentration of A². You can find this using data, or your mechanism.

Then we have this thing called Integrated Rate Law. You have three separate rate laws, and they don't look anywhere near like the differential rate law. We have to figure out when we are to use each separate one. And what can each one of those tell us, and why they're used.

Well the Differential Rate law talks about the overall rate. How long it takes to go from beginning fully to the end from just reactants to just products. On average how long does it take? So that's what the Differential Rate Law is telling us.

We, basically from the beginning, how does something go from all reactants to all products, and how long does it take. Not only does it do that, it tells us how influential that particular reactant is, and the speed of the reaction.

In the second order reaction, the concentration is much more important to how fast the reaction goes. I did the first order rate law. There is this squared, so this has more of an impact on the rate than in the first order reaction. So also discuss this.

Also shows how impactful the concentration is to the rate; the speed of the reaction. So this is basic and this is the overall rate, from beginning to end. You can't talk about how long it will take to get to a certain point. This is just from the beginning, just the reactants, to when it goes to just the products. It gives us an idea of how important the particular reactants are into the speed of the reaction.

Integrated Rate Laws is different. The integrated rate law is the rate of the reaction at a speed of time. Actually it's not even the rate, it's basically discussing how a particular moment in time, how many reactants do we have, from the beginning versus at that particular moment. So it uses time.

Notice in the differential rate law, we don't have a variable for time, but here we do. Everything else is exactly the same. We have the concentration of the reactants, we have k, our rate constant. We also included time into our equation.

So anytime you have something like, how many reactants do we have after this particular moment in time, that's when you're going to use Integrated Rate Law. It can find concentration of reactants at a particular moment in time. The Differential Rate Law cannot do this.

If I said how is my reaction going for 5 minutes? I initially had a certain amount of concentration of A, and I had my reaction going for 5 minutes. How much A do I have left? Well, integrated rate law can tell me that. Differential Rate Law cannot tell me that. Differential Rate Law can say how long it's going to take for the whole reaction to occur, but the Integrated Rate Law talks about the reaction at a specific moment in time.

So that's the big difference between differential and integrated. If you're asking for a specific moment in time, you cannot use Differential Rate Law. So hopefully that helps you in determining when do you use which equation, because I know that it can sometimes get confusing. Hope that helped.