Parametric Estimation - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 298

Chemistry, Reaction Engineering, and Bioprocess Engineering, where reaction kinetic rela-
tionships are obtained by batch experimentation. Further to our discussions, let us use
a real-life example:
Hellin and Jungers (1957) present the data in Table 7.3 on the reaction of sulfuric acid with
diethylsulfate in aqueous solution at 22.9 C:

H SO

4 þð

C H

5 Þ 2

SO

4 % 2

C H HSO (7.30)

2 2 2 5 4

Initial concentrations of H 2 SO 4 (denoted as A) and (C 2 H 5 ) 2 SO 4 (denoted as B) are each
5.5 mol/L ( C B0 ). Find a reaction rate equation for this reaction.

This is a classic problem in physical chemistry. To determine the rate of reaction, we must
first establish the relationship between the data and the rate: the regression model. A simple
mass (mole) balance yields the relationship between the concentration of ethyl hydrosulfate,
C 2 H 5 HSO 4 , and time

¼ C A0 ¼

d C C
d t ¼ 2r ¼ f ðC A ; C B ; C C Þ

(7.31)

TABLE 7.3 Kinetic Data for Aqueous Reaction of Sulfuric Acid with Diethylsulfate

Concentration of
C 2 H 5 HSO 4 , mol/L Measurement number t , min

0 0

1 41 1.18

2 48 1.38

3 55 1.63

4 75 2.24

5 96 2.75

6 127 3.31

7 146 3.76

8 162 3.81

9 180 4.11

10 194 4.31

11 212 4.45

12 267 4.86

13 318 5.15

14 368 5.32

15 379 5.35

16 410 5.42

N 5.80