Page 162 - Elements of Chemical Reaction Engineering 3rd Edition

134 Isothermal Reactor Design Chap. 4

C2. Variables
Dependent: concentrations
Independent: time
C3. Knowns and unknowns
Knowns: concentratlon of ethylene glycol as a function of time
Unknowns:
1. Concentration of ethylene oxide as a function of time
2. Specific reaction rate
3. Reactor volume
C4. Inputs and outputs: reactant fed all at once to a batch reactor
C5. Missing information: None; does not appear that other sources need to be
sought.
D. Assumptions and approximations:
Assumptions
1. Well mixed
2. All reactants enter at the same time
3. No side reactions
4. Negligible filling and emptying time
5. Isothermal operation I .*""
Approximations
1. Water in excess so that its concentration is essentially constant.
E. Spec$cation. The problem is neither overspecified nor underspecified.
F. Related material. This problem uses the mole balances developed in Chapter
t 1 for a batch reactor and the stoichiomeq and rate laws
developed in Chapter 3.
G. Use an algorithm. For an isothermal reaction, use the chemical reaction engi-
neering algorithm shown in Figure 4-2.
Following the
algorithm Solution

1. A mole balance on a batch reactor that is well mixed is
1 dNA -
----rA (E4- 1.1)
V dt

2. The rate law is
-rA = kC, (E4- 1.2)

Since water is present in such excess, the coccentration of water at any time t
is virtually the same as the initial concentration and the rate law is indepen-
dent of the concentration of H20. (CB E CBO.)
Rate Law 3. Stoichiometry. Liquid phase, no volume change, V = Vo (Table E4-1.2):