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Why is rate law important?
The is a cool window into how a chemical reaction takes place.
On the surface, the rate law explicitly tells you how fast a reaction will go given particular concentrations of each reagent (partial pressures for gases). In other words, if you know the concentrations of your reagents, you can figure out the likely reaction rate.
In a deeper sense, rate laws tell you about what's happening in the rate-determining-step of the reaction. In other words, if a reaction takes place in several stages, the rate law will help you to figure out what they are. (The fancy way of saying this is that the rate law can help you figure out the mechanism of a reaction). This is not only interesting because it gives you information about this reaction, but also because you can use this knowledge to extrapolate to other reactions.