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

The reaction follows first-order kinetics, therefore its rate can be described by the following equation:
ln[N(t)/N0] = -kt
where N(t) is the concentration at time t, N0 is the initial concentration of cyclopropane, k is the rate constant, and t is time. We know that 85% of cyclopropane changes into propene in 79.0 min, therefore the concentration ratio is N(t)/N0 = 0.15. Substituting the values into the equation, we get:
ln(0.15) = -k(79.0 min)
k = -ln(0.15)/79.0 min ≈ 2.40 × 10^-2 min^-1 ≈ 2.40 × 10^10 s^-1. 
Thus, the best choice is E.

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