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290 Chapter 14 Chemical Kinetics -4 = 89.5 mol kJ -5 and intercept = 26.769 = In A then A = = = 4.22 X 10¹¹ -6 Check: The units (kJ/mol and s⁻¹) are cor- k -7 rect. The plot was extremely linear, confirming -8 Arrhenius behavior. The activation energy and y = 10759x + 26.769 -9 frequency factor are typical for many reactions. -10 (b) Given: part (a) results Find: k at 15 °C 0.0029 0.003 0.0031 0.0032 0.0033 0.0034 Conceptual Plan: °C K then T, Eₐ, A k 1/Temperature (1/K) °C + 273.15 = K In = R + In A Solution: 15 °C + 273.15 = 288 K then 1000 In k = R + = -89.5 + n(4.22 X s⁻¹) = -10.610 k = = 2.5 X Check: The units (M⁻¹ s⁻¹) are correct. The value of the rate constant is less than the value at 25 °C. (c) Given: part (a) results, 0.155 M C₂H₅Br and 0.250 M OH⁻ at 75 °C Find: initial reaction rate Conceptual Plan: °C K then k then k, [OH⁻] initial reaction rate °C + 273.15 = K In +A Rate = Solution: 75 °C + 273.15 = 348 K then 1000 J k = R + In = -89.5 J + 10¹¹ = -4.1656 k = = 1.5521 X 10⁻² Rate = k = (1.5521 X 10⁻² = 6.0 X 10⁻⁴ M Check: The units are correct. The value of the rate is reasonable considering the value of the rate con- stant (larger than in the table) and the fact that the concentrations are less than 1 M. 14.101 (a) No, because the activation energy is zero. This means that the rate constant (k = will be independent of temperature. (b) No bond is broken, and the two radicals (CH₃) attract each other. (c) Formation of diatomic gases from atomic gases 14.103 Given: for radioactive decay of C-14 = 5730 years; bone has 19.5% C-14 in living bone. Find: age of bone Conceptual Plan: Radioactive decay implies first-order kinetics, k then 19.5% of [C-14]₀, k t = -kt + Solution: = 0.693 k Rearrange to solve for k.k = 0.693 = 5730 0.693 yr = 1.20942 X 10⁻⁴ yr⁻¹ then [C-14], = 0.195 [C-14]₀ Because [C-14], = -kt + In rearrange to solve for t. t = k 1 [C-14]₀ [C-14], = 1.20942 X 1 10⁻⁴ yr⁻¹ In = 1.35 X 10⁴ yr Check: The units (yr) are correct. The time to 19.5% decay is consistent with the time being between two and three half-lives. Copyright © 2017 Pearson Education, Inc.