Page 134 - Materials Chemistry, Second Edition

Mass-Balance Concept and Reactor Design 117

It is a first-order differential equation. It can be integrated with the ini-
tial condition (i.e., C = C at t = 0):
0
C
= e − (/ or C = Ce − (/ (4.8)
Q Vt )
QV t )
0
C 0
Solution:
(a) Methylene chloride concentration in the laboratory before venti-
lation can be found as 2,100 ppmV (see Example 2.4 for detailed
calculations).
(b) The size of the reactor (V) = the size of the laboratory
= (5 m)(6 m)(3.6 m) = 108 m 3
The system flow rate (Q) = ventilation rate
= 200 ft /min = (200 ft /min)
3
3
÷ (35.3 ft /m ) = 5.66 m /min
3
3
3
The initial concentration, C = 2,100 ppmV
0
The final concentration, C = 125 ppmV
125 (2,100)= e − (5.66/108) t

Thus, t = 53.8 min
Discussion:
The actual time required would be longer than 58 min, because the
assumption of completely mixed air inside the room may not be
valid. In addition, if the ambient air contains some methylene chlo-
ride, the cleanup time would be even longer.

4.3 Chemical Kinetics
Chemical kinetics provides information on the rate at which a chemical reac-
tion occurs. This section discusses the rate equation, reaction-rate constant,
and reaction order. Half-life, a term commonly used with regard to the fate of
COCs in the environment, is also described.

4.3.1 Rate Equations

In addition to the mass-balance equation, the reaction-rate equation is
another relationship required for design of a homogeneous reactor. The