Page 145 - Materials Chemistry, Second Edition

128 Practical Design Calculations for Groundwater and Soil Remediation

Discussion:
Using the obtained rate constant and the initial concentration to cal-
culate the concentration at some other time t can serve as a check
on the value. For example, the concentration, at t = 2 hours, can be
determined using Equation (4.16) as:

C f = 350 × e − (0.606)(2) = 104 mg/kg

The calculated concentration, 104 mg/kg, is reasonably close to the
reported experimental value, 100 mg/kg.

Example 4.10: Batch Reactor with Second-Order Kinetics

A batch reactor is to be designed to treat soil that contains 200 mg/kg of
PCBs. The required reduction of PCBs is 90%. The rate constant is 0.5[(mg/
kg)(h)] . What is the required residence time for the batch reactor?
−1
Strategy:
Although the order of the reaction is not mentioned in the problem
statement, it is a second-order reaction because the units of k are
[(mg/kg)(h)] .
−1
Solution:
(a) For a 90% reduction (η = 90%)

C = 200 (1 − 90%) = 20 mg/kg
f

(b) Insert the known values into Equation (4.18) (see Table 4.1):

200
20 =
1(0.5 )200+ τ

τ = 0.09 h

Discussion:
The only difference between the reactors in Examples 4.7 and 4.10 is
the reaction kinetics. With the same numerical value of the reac-
tion-rate constants, the required residence time to achieve the same
conversion rate is much shorter in the reactor with second-order
kinetics.