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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 (c) Calculate the time in half-lives when the inÂ­tegrated rate law is no longer valid, that is, when [A] t = 0.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.
To derive the form of the half-life expression for a first order reaction, we start with its integrated rate law, and then substitute the value 0.5 for the ratio of [A] to [A]o: Using the same techniques with the different integrated rate laws, you can derive the half-life expression for a reaction of any order. Summarized below are the half-lives for reactions of orders zero through two.