When heated, cyclopropane is converted to propene (Example 14.5). Rate constants for this reaction at 470°C and 510°C are k =1.10 × 10⁻⁴ s⁻¹ and k = 1.02 × 10⁻³ s⁻¹, respectively. Determine the activation energy, E_a, from these data.

Data given in Example 14.5

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EXAMPLE 14.5 The First-Order Rate Equation Problem in the past, cyclopropane, C3H₁, was used in a mixture with oxygen as an anesthetic. (This practice has almost ceased today because the compound is flammable.) When heated, cyclopropane rearranges to propene in a first-order process. HICH H HICIH cyclopropane ->> CH₂CH=CH₂ Rate = k[cyclopropane] propene k = 2.42 h¹ at 500 °C If the initial concentration of cyclopropane is 0.050 mol/L, how much time (in hours) must elapse for its concentration to drop to 0.010 mol/L? What Do You Know? The reaction is first-order in cyclopropane. You know the rate constant, k, and the initial and final concentrations of this reactant, [R], and [R]t.