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30A: Rates of Chemical Reactions 30A-3 Rate Laws for Second-Order and Pseudo-First Order Reactions: A +RP d[A] dt = k[A][R] The reaction is first order in each of the reactants and second order overall. If the concentration of R is chosen such that [R] >> A), the concentration of R changes very little during the reaction, and we can write k [R] =constant = k’ d[A k'[A] dt Hence, the reaction is said to be pseudo-first-order in A. Second-order or other higher order reactions can usually be made pseudo-first-order through control of experimental conditions.
MPLE For a pseudo-first-order reaction in which the reagent is present in 100-fold excess, find the relative error resulting from the assumption that k[R] is con- stant when the reaction is 40% complete. Solution The initial concentration of the reagent can be expressed as [R]. = 100[A I At 40% reaction, 60% of A remains. Thus, [A].on = 0.60[A]. [R]40% = [R]. - 0.40[A]. = 100[A] -0.40[A]. = 99.6[A]. = Assuming pseudo-first-order behavior, the rate at 40% reaction is d[A].0% dt k[R], LALOM The true rate at 40% reaction is k(99.6[A].)(0.60[A].). Therefore, the relative error is 0.004 (or 0.4%) $(100[A].)(0.60 [A].) – ((99.6[A].)(0.60(A)) k(99.6[A].)(0,60[A].)
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