
235Homogeneous Reactors
that is,
x
e
d
Af
k
=−
−
∫
1
2
2
3
()
θ
θ
θ
θ
(3.372)
Similarly, for a second-order reaction, the fractional conversion x
Ab
(θ) achieved in the
single uid element is obtained by integrating
dd
/
between t = 0 and t = θ.
x
Ab
A
()θ
=
0
(3.373)
Substituting Equations 3.365 and 3.373 in Equation 3.370, we get an expression for con-
version x
Af
in a laminar ow reactor for a second-order reaction:
x
kC
kC
d
Af
A
A
=
+
∫
0
0
2
3
θ
θ
θ
θ
θ
()
(3.374)
which reduces to
x
kC d
kC
Af
A
A
=
+
∫
0
2
2
0
2
21
θ
/
(3.375)
PROBLEM 3.16
A rst-order reaction with rate constant k = 0.15 min
−1
is to be carried out in a tubular ow
reactor. A conversion ...