The isomerization of cyclopropane to form propene is a first-order reaction. At 760 K, 85% of a sample of cyclopropane changes to propene in 79.0 min. Determine the rate constant for this reaction at 760 K.

Question

The isomerization of cyclopropane to form propene is a first-order reaction.  At 760 K, 85% of a sample of cyclopropane changes to propene in 79.0 min. Determine the rate constant for this reaction at 760 K.

Quizplus · Accepted Answer

We can use the first-order rate law equation:

ln([A]t/[A]0) = -kt

where [A]t and [A]0 are the concentrations of cyclopropane at time t and at the start of the reaction, respectively.

We can rearrange this equation to solve for the rate constant k:

k = -ln([A]t/[A]0) / t

Plugging in the given values:

[A]t/[A]0 = 0.15 (since 85% of cyclopropane has changed to propene)
t = 79.0 min

k = -ln(0.15) / 79.0 min ≈ 2.40 x 10^-2 min^-1

Converting minutes to seconds:

k ≈ 2.40 x 10^-2 min^-1 x (1 min / 60 s) ≈ 4.00 x 10^-4 s^-1

Rounding to two significant figures, the correct answer is E: 2.40 x 10^(-4) s^(-1).

The Isomerization of Cyclopropane to Form Propene Is a First-Order