Question. The photocatalytic degradation of a model aromatic compound (AC) was measured in a batch-reactor experiment conducted at UNO. It was determined that the concentration of AC, measured as COD, decreased exponentially with irradiation time, and that COD plateaued due to saturation of the catalyst without reaching complete elimination.
The rate law equation for the elimination of COD in this photocatalytic system is of the form:
r = -k(Xt - XL)
where k is the reaction rate constant, Xt = CODt⁄CODinitial is the fraction of COD remaining at time t, and XL = CODplateau⁄CODinitial is the limiting fraction or fraction of COD remaining at plateau.
a) If X0 corresponds to the fraction of COD remaining at time zero, write a mass balance on X for a batch reactor and derive a model equation for Xt as a function of X0, XL, k and t.
b) Fit the experimental data given below to the equation model derived in Part a, and obtain the values of XL and k (Assume X0 = 1). Perform a nonlinear regression of the data through the least squares method using Excel Solver.
|
Time
(min)
|
COD
(mg/L)
|
|
0
|
234
|
|
30
|
194
|
|
60
|
174
|
|
90
|
156
|
|
120
|
144
|
|
240
|
101
|
|
360
|
70.1
|
|
480
|
52.4
|
c) Plot Xt vs t in minutes (0 min < t < 800 min) and report the COD concentration (in mg/L) at 600 min.
Scan any handwritten work and submit it along an Excel file showing the data regression and Solver analysis, and the graph chart of Part c.