Integrated Rate Laws Time and Concentration

So far, we have used only instantaneous data in the rate expression. These expressions allow us to answer questions concerning the speed of the reaction at a particular moment, but not questions like about how long it might take to use up a certain reactant. However, if we take into account changes in the concentration of reactants or products over time, as expressed in the integrated rate laws, we can answer these types of questions. 

Assuming this reaction is first order, we can express the rate of reaction as the change in concentration of reactant A with time  

Setting these terms equal gives —= k[A] and integrating over time gives  

If the reaction is second order in A, we can derive the following equation using the same procedure  

Hydrogen iodide, HI, decomposes through a second-order process to the elements. The rate constant is 2.40 X 10 21/M s at 25°C. How long will it take for 

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