
180 Green Chemical Engineering
Substituting the Arrhenius equation for k
1
and k
2
into Equation 3.112 and taking deriva-
tives of k
1
and k
2
with respect to T, we get
()
1
10
1
2
20
2
2
−
=
xke
E
RT
xk e
E
RT
A
ERT
A
ERT
(3.113)
Solving the above equation for temperature T, we obtain the expression for optimal tem-
perature T
opt
as
T
RkkEEx x
opt
R
=
⋅⋅−
ln
∆∆
20 10 21
1///
(3.114)
This equation denes the optimal progression of temperature for an exothermic revers-
ible reaction.
3.1.5.2.1 Design of Reactors for Exothermic Reversible Reaction
with Optimal Temperature Progression
In this section, we present the procedures for the design of reactors ...