You have been charged with the task of converting an environmentally unfriendly plant liquid purge stream of component A at a concentration of CAf
in part to a benign liquid product D according to EPA regulations. This conversion can be completed with the simple reaction
Ultimately, you must use these data to characterize the kinetics describing the reaction.
a. Level I analysis: First, derive a mathematical model describing the batch system pictured here and the time-dependent concentrations of species A [CA
(g-mol/L)] and D [CD
(g-mol/L)] for the general reaction rate r [(g-mol/L s)], and system volume V (L).
b. Level II analysis: Explain why a Level II analysis is not needed for this system.
c. Level III analysis:
i. Propose a constitutive equation to describe the relation between the reaction rate (r) and the measured concentration of A in the system (i.e., a reaction-rate expression in which r = k . . .).
ii. Use this constitutive equation to solve the mathematical model for the batch reactor for the time-dependent concentration of A(CA).
iii. Examine the functional form of the solution. Which preceding plot (a, b, or c) would you use to validate the proposed constitutive relation? Why? Determine the value of k describing the reaction using data from the appropriate plot.
What assumptions are made in the kinetic model and its solution? How could you check to see if these assumptions are met in practice?