## Differential vs Integrated Rate Law

$aR \to bP, Rate = -\frac{1}{a} \frac{d[R]}{dt} = \frac{1}{b}\frac{d[P]}{dt}$

Angela Wu-2H
Posts: 50
Joined: Fri Aug 30, 2019 12:16 am

### Differential vs Integrated Rate Law

What is the difference between differential and integrated rate law? When do we use each one?

Maggie Eberhardt - 2H
Posts: 97
Joined: Sat Jul 20, 2019 12:16 am

### Re: Differential vs Integrated Rate Law

I know that the two equations can de derived from each other, but I was wondering about when each is used as well. I think the differential is simply a mathematically derived version of the rate law, and the integrated one is a mathematically integrated version of the rate law.

Skyllar Kuppinger 1F
Posts: 52
Joined: Thu Jul 25, 2019 12:16 am

### Re: Differential vs Integrated Rate Law

You use the integrated rate law when you're trying to find how much of a species will be remaining after a certain amount of time, or trying to find k or t based on the final and initial concentrations of a species. Here's an example from the book where you use the integrated rate law: "for the first order reaction A--> 3B + C, when the initial conc of A is 0.015M, the conc of B increases to 0.018M in 3.0 min. What is the rate constant for the reaction expressed as the rate of loss of A?"

You would plug your numbers into the integrated rate law to solve for k.