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i believe if you tried to write the differential rate law as a function of time, you would have to manipulate it into the integrated rate law. the differential rate law equation as is relates rate to concentration
The integrated rate law tells us how much reactant concentration changes over time. The differential rate law tells us the rate as a function of concentration. In other words, it is the overall reaction as a function of reactant concentration. The differential rate law can help us figure out the integrated rate law.
The integrated rate law is the differential rate law written as a function of time. In other words, rather than rate being a function of concentration, rate is a function of time. This can be seen with the graphs of zero order, first order, and second order reactions, in which [A], ln[A], and 1/[A] are plotted against time, giving linear slopes (values for k)
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