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The integrated rate law for the zero-order reaction A âB is [A] t = [A] 0 â kt. (a) Sketch the following plots: (i) rate versus [A] t and. (ii) [A] t versus t. (b) Derive an expression for the half-life of the reacÂ­tion. (c) Calculate the time in half-lives when the inÂ­tegrated rate law is no longer valid, that is, when [A] t = 0. STEP-BY-STEP SOLUTION. JavaScript Not Detected. JavaScript is required to view textbook solutions.
Due to the mathematical complexities of the problem, we will only consider rate laws of the form rate = [A] n. However, with some experimental tricks I will explain below, that treatment does allow us to use the method of integrated rates for a reaction with any arbitrary rate law. By integrating the differential rate law (the simple rate law from Heading ), we derive the integrated rate law for a reaction. Without proof, we present below the forms of the integrated rate laws for reaction orders zero through two: