The conversion of cyclopropane to propene (Example 14.5) occurs with a first-order rate constant of 2.42 × 10⁻² h⁻¹. How long will it take for the concentration of cyclopropane to decrease from an initial concentration of 0.080 mol/L to
0.020 mol/L?

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. cyclopropane Rate = k[cyclopropane] CH3CH CH₂ 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],