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278 Chapter 14 Chemical Kinetics (c) Given: part (a) Find: write a rate law and estimate k Conceptual Plan: Using the result from part (a), the slope of the plot is the rate constant. Solution: Slope = = 0.0 0.00 M = 0.010 Rate = or Rate = k[A] or Rate = 0.010 [A] Check: The units (s⁻¹) are correct. The magnitude of the answer makes physical sense because of the rate and concentration data. Remember that concentration is in units of M; so plugging the rate constant into the equation has the units of the rate as M s⁻¹, which is correct. 14.37 Given: reaction order: (a) first-order, (b) second-order, and (c) zero-order Find: units of k Conceptual Plan: Using rate law, rearrange to solve for k. Rate = k[A]", where n = reaction order Solution: For all cases, rate has units of M and [A] has units of M. M (a) Rate = = so = Rate [A] = M S = M (b) Rate = = Rate = S = (c) Rate = = k = Check: The units and are correct. The units for k change with the reaction order so that the units on the rate remain as M s⁻¹. 14.39 Given: A, B, and C react to form products. Reaction is first-order in A, second-order in B, and zero-order in C. Find: (a) rate law; (b) overall order of reaction; (c) factor change in rate if [A] doubled; (d) factor change in rate if [B] doubled; (e) factor change in rate if [C] doubled; and (f) factor change in rate if [A], [B], and [C] doubled Conceptual Plan: (a) Using general rate law form, substitute values for orders. Rate = where m, n, and = reaction orders (b) Using rate law in part (a), add up all reaction orders. overall reaction order =m+n+p (c) Through (f), using rate law from part (a), substitute concentration changes. Rate 2 = Rate 1 Solution: (a) m = = and p = 0 so Rate = or Rate = (b) overall reaction order = m + n + p = 1 + 2 + 0 = 3, so it is a third-order reaction overall (c) Rate Rate 2 1 = and = = = so Rate Rate 2 1 = = 2 so the reaction rate doubles (factor of 2) (d) Rate Rate 2 1 = and = = = Rate Rate 2 1 = = = 4 so the reaction rate quadruples (factor of 4) (e) Rate Rate 2 1 = and [A]₂ = [B]₂ = 1, = 2 Rate Rate 2 1 = = 1 so the reaction rate is unchanged (factor of 1) Copyright © 2017 Pearson Education, Inc.