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Chapter 14 Chemical Kinetics 279 Rate 2 (f) Rate 1 = and [B]₂ = = 2 Rate 1 Rate 2 = = = 8 so the reaction rate goes up by a factor of 8 Check: The units (none) are correct. The rate law is consistent with the orders given, and the overall order is larger than any of the individual orders. The factors are consistent with the reaction orders. The larger the order, the larger the factor. When all concentrations are changed, the rate changes the most. If a reactant is not in the rate law, then changing its concentration has no effect on the reaction rate. 14.41 Given: table of [A] versus initial rate Find: rate law and k Conceptual Plan: Using general rate law form, compare rate ratios to determine reaction order. Rate 2 = Rate 1 Then use one of the concentration/initial rate pairs to determine k. Rate = k[A]" Solution: Rate Rate 2 1 = Comparing the first two sets of data, 0.053 0.210 M/s M/s = and 3.9623 = 0.473 M/s If we compare the first and the last data sets, = and 8.9245 = 3" n = 2 0.053 M/s This second comparison is not necessary, but it increases our confidence in the reaction order. So Rate = Selecting the second data set and rearranging the rate equation, k = Rate = (0.200 = 5.25 so Rate = 5.25 Check: The units (none and M⁻¹ are correct. The rate law is a common form. The rate is changing more rapidly than the concentration, so second order is consistent. The rate constant is consistent with the units necessary to get the rate as M/s, and the magnitude is reasonable because we have a second-order reaction. 14.43 Given: table of [A] versus initial rate Find: rate law and k Conceptual Plan: Using general rate law form, compare rate ratios to determine reaction order. Rate 2 k Rate 1 = k Then use one of the rate pairs to determine k. Solution: Rate Rate 2 1 = Comparing the first two sets of data: 0.12 0.16 M/s = (0.0104 (0.0078 and 1.3333 = so n = 1. If we compare the first and the last data sets: 0.12 0.20 = (0.0078 (0.0130 and 1.6667 = n = 1. This second comparison is not necessary, but it increases our confidence in the reaction order. So Rate = k [A]. Selecting the second data set and rearranging the rate equation k = Rate [A] = 0.16M S = 0.065 so Rate = 0.065 [A] Check: The units (none and s⁻¹) are correct. The rate law is a common form. The rate is changing proportionately to the concentration, so first-order is consistent. The rate constant is consistent with the units necessary to get rate as M/s and the magnitude is reasonable since we have a first-order reaction. 14.45 Given: table of [NO₂] and [F₂] versus initial rate Find: rate law, k, and overall order Conceptual Plan: Using general rate law form, compare rate ratios to determine reaction order of each reactant. Be sure to choose data that changes only one concentration at a time. Rate 2 = Rate 1 Copyright © 2017 Pearson Education, Inc.