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# The first-order integrated rate law for a reaction A h products is derived from the rate

## Problem 112 Chapter 13

Chemistry: A Molecular Approach | 3rd Edition

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Problem 112

The first-order integrated rate law for a reaction A h products is derived from the rate law using calculus: Rate = k[A] (first@order rate law) Rate = - d[A] dt d[A] dt = -k[A] The equation just given is a first-order, separable differential equation that can be solved by separating the variables and integrating: d[A] [A] = -kdt L [A] [A]0 d[A] [A] = - L t 0 kdt In the integral just given, [A]0 is the initial concentration of A. We then evaluate the integral: [ln[A]]3A4 3A40 = -k[t] t 0 ln[A] - ln[A]0 = -kt ln[A] = -kt + ln[A]0 (integrated rate law) a. Use a procedure similar to the one just to derive an integrated rate law for a reaction A h products, which is one-half order in the concentration of A (that is, Rate = k[A]1>2 ). b. Use the result from part a to derive an expression for the half-life of a one-half-order reaction

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Solution = Solvent + Solutes 2) It helps regulate body temperature. 3) It is a good lubricant. 4) It is involved in many of the body’s chemical reactions. 2. Acids, Bases, pH a. Acids and bases are compounds that dissociate in water and create ions. + b. Acid H + some...

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The first-order integrated rate law for a reaction A h products is derived from the rate

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