Differential and Integrated Rate Laws

[Ju-Wei Wang 1I]

How do you know when to use a differential rate law versus an integrated rate law? Are there specific things you can look for in the question that direct you to use a certain equation over the other?

[Samantha Joseph 1F]

The main difference between differential and integrated rate laws are that differential rate laws are used to describe a reaction rate as a function of the change in concentration over a time period, whereas integrate rate laws show the initial and actual concentration values after a period of time. For example, the differential law means rate = -d[A]/dt, showing that the change in value needs to be provided to answer the question. For integrated (example when n=1), ln[A] = -kt + ln[A₀], so you need to know t and the initial and/or final concentration values.

[Ridhi Ravichandran 1E]

You use integrated rate laws when you need to find the time or final/initial concentrations. Most problems involve using the integrated rate law; we deal with the differential rate law when we need to find reaction orders, etc.

[Diego Zavala 2I]

For our class most, if not all, problems will use the integrated rate law. The differential rate law is used to derive the integrated rate law