
294 Green Chemical Engineering
The fractional conversion of B in the solid particle x
B
(θ) at any time θ is
x
n
B
B
B
()θ= −1
0
(4.13)
where n
B0
is the initial number of moles of B in the solid particle at the time of start of the
reaction
BO B
=
4
3
3
(4.14)
From Equations 4.10, 4.13 and 4.14, we get
x
r
R
r
R
x
B
CC
B
=−
=−
3
or
/
(4.15)
Equation 4.15 relates the fractional conversion x
B
to the radius r
c
of the unreacted core. We
will derive the equation for calculating fractional conversion x
b
(θ) for each one of the rate-
controlling steps.
1. Gas lm resistance is rate controlling
Combining Equations 4.12, 4.1 and 4.6, we get
r
r
dr
kC R
A