Chemistry
Chemistry
Problem
For the gas-phase isomerization of cyclopropane to propene, the concentration of cyclopropane, , obeys the empirical expression where concentration is in and time is in seconds, for . Answer the following questions based on this relation. a. Part 1: (a) Determine the instantaneous rate of disappearance of cyclopropane at . b. Part 2: (b) Calculate the average rate of disappearance of cyclopropane over the interval . c. Part 3: (c) Explain why the two rates obtained in parts (a) and (b) are not identical, relating your explanation to the shape of the concentration-versus-time curve implied by the given expression.Intuitive explanation
This problem gives you the concentration as an explicit function of time—a rare gift! Rather than measuring rates from a graph or using integrated rate laws, you can directly extract the reaction order and rate constant by recognizing what mathematical form this equation takes. The key is to compare the given expression to the standard integrated rate law forms: zero-order (linear), first-order (exponential), and second-order (reciprocal). Once you identify which one matches, the rate constant and initial concentration fall out immediately.
Intuitive explanation
This problem gives you the concentration as an explicit function of time—a rare gift! Rather than measuring rates from a graph or using integrated rate laws, you can directly extract the reaction order and rate constant by recognizing what mathematical form this equation takes. The key is to compare the given expression to the standard integrated rate law forms: zero-order (linear), first-order (exponential), and second-order (reciprocal). Once you identify which one matches, the rate constant and initial concentration fall out immediately.