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Chapter 14 Chemical Kinetics 291 14.105 (a) For each, check that all steps sum to overall reaction and that the predicted rate law is consistent with experi- mental data (Rate = For the first mechanism, the single step is the overall reaction. The rate law is determined by the stoichiometry; so Rate = and the mechanism is valid. For the second mechanism, the overall reaction is the sum of the steps in the mechanism: + 2HI(g) So the sum matches the overall reaction. + 2HI(g) Because the second step is the rate-determining step, Rate = Because I is an intermediate, its concentration cannot appear in the rate law. Using the fast equilibrium in the first step, we see that = k₂ [I] or Substituting this into the first rate expression, we get Rate = k₁ H₂ and the mechanism is valid. (b) To distinguish between mechanisms, you could look for the buildup of I(g), the intermediate in the second mechanism, or for the buildup of I(g) and the intermediates in the third mechanism. 14.107 The steps in the mechanism are as follows: + H(g) H(g) + HBr(g) Br(g) Because the second step is the rate-determining step, Rate = k₂[H₂][Br]. Because Br is an intermediate, its concen- tration cannot appear in the rate law. Using the fast equilibrium in the first step, we see that [Br₂] = or [Br] = Br₂ Substituting this into the first rate expression, we get Rate = k₂ k₁ The rate law is 3/2 order overall. 14.109 (a) For a zero-order reaction, the rate is independent of the concentration. If the first half goes in the first 100 minutes, the second half will go in the second 100 minutes. This means that none, or 0%, will be left at 200 minutes. (b) For a first-order reaction, the half-life is independent of concentration. This means that if half of the reac- tant decomposes in the first 100 minutes, half of this (or another 25% of the original amount) will decom- pose in the second 100 minutes. This means that at 200 minutes, 50% + 25% = 75% has decomposed or 25% remains. (c) For a second-order reaction, = k[A]₀ 1 = 100 min and the integrated rate expression is 1 + 1 We can rearrange the first expression to solve for k as k = 100 min [A]₀ Substituting this and 200 minutes into or 33% the remains. integrated rate expression, we get [A], 1 = 100 200 min min + 1 [A], 1 = [A]₀ 3 = 3 Copyright © 2017 Pearson Education, Inc.