
185Homogeneous Reactors
The rate equation is
AA
where k = k
0
e
−ΔE/RT
and C
A
= C
A0
(1 − x
A
)
Substituting appropriate terms into the heat balance Equation 3.221, we have
{}
+
{}
+− −
QHVrxT
MC T
RA
()()((,))[]∆
(3.222)
where
M: mass hold of the reactor (kg)
mean specic heat (kJ/kg°C)
Rearranging Equation 3.222, we get
dT
dt
H
C
rx T
Q
MC
R
P
AA
P
=
−∆
−
+
()
(,)
ρ
(3.223)
The molal balance equation (or the design equation) for the batch reactor is
−=−
rx T
A
AA
(,)
which is written in terms of conversion x
A
as
−=
−
dx
dt
rx T
C
A
AA
A
(,)
0
(3.224)
Solving the rst-order differential Equations 3.223 and 3.224 simultaneously, we obtai ...