What is the rearrangement of cyclopropane to propene and how does the concentration affect the reaction?

The rearrangement of cyclopropane (cyclopropyl) to propene is a chemical reaction that involves the conversion of cyclopropane into propene under certain conditions. At a temperature of 500 °C, this reaction follows first-order kinetics with respect to cyclopropane (denoted as CH₂CH₃ or CH₂CH₂CH₃ in some texts), meaning that the rate of the reaction depends only on the concentration of cyclopropane.

Given that the rate constant (k) for this reaction at 500 °C is 6.70 x 10^-4 s^-1 and the initial concentration of cyclopropane (CH₂CH₃) is 0.167 M, we can analyze how the concentration will change over time. For first-order reactions, the concentration at any time can be determined using the following first-order rate equation:

C_t = C₀ e^-kt

Where:

• C_t = concentration at time t
• C₀ = initial concentration (0.167 M in this case)
• k = rate constant (6.70 x 10^-4 s^-1)
• t = time in seconds

By substituting the values, we can calculate the concentration of cyclopropane at any given time, which will help us understand how much cyclopropane remains as it converts into propene.