8.1 F. Salvador, J. L. Gonzalez, and M. A. Herraez [Int. J. Chem. Kinet., 14, 875 (1982)] studied the kinetics of the isomeriza- tion of cholest-5-en-3-one in cyclohexane in the presence of trichloroacetic acid as a catalyst. The stoichiometry of this reaction is A → B, where A refers to cholest-5-en-3-one and B to cholest-4-en-one. Species A and B both form association complexes with trichloroacetic acid. In the presence of excess acid, the kinetics of the isomerization reaction are described by a rate expression that is pseudo first-order in A: r = kobserved (A) At 25.4°C the observed rate constant is 1.087 × 10-³ s-¹ for the concentration of trichloroacetic acid employed (7.37 x 10-³M). Consider this reaction as it takes place in a semibatch reactor operating at 25.4°C. Initially, this reactor contains 20 L of a cyclohexane solution that contains the desired amount of trichloroacetic acid, but no A. The reactor is fed with a cyclohexane solution containing species A (2 x 10-3 M) and trichloroacetic acid (7.37 x 10-3 M). The feed stream enters at 25.4°C at a constant rate of 5 L/min for a total time of 30 min. Subsequently, the reactor functions as a batch reactor. The reactor is well stirred during both phases of the reaction. Prepare plots of the concentrations of species A and B as functions of time for a total elapsed time of 100 min. At what time does the concentration of species A pass through a maximum? How much total time is necessary to convert 98% of the A fed to the reactor into B?

Fig: 1