Biomedical Engineering Reference
In-Depth Information
E
a
5
activation energy (kJ/mol), R
5
universal gas constant
(kJ/mol K),
T
5
temperature
(K), W
0
5
initial weight of
calcium carbonate
(g),
W
t
5
weight of calcium carbonate after time t (g).
The equilibrium partial pressure given by (Stanmore and Gilot, 2005):
10
7
e
2
ð
20474
=
T
Þ
:
P
eq
5
4
137
3
Using QWM, we can continuously monitor the change in weight
with time. So using this data we can calculate dX/dt as well as the conver-
sion X.
Example 16.1
While calcination is done in presence of CO
2
at 900
C for 1590 s, the conver-
sion obtained was 20%. So dX/dt
0.000126 s
2
1
.
For the same condition, the partial pressure of CO
2
5
1.010 atm while the
equilibrium pressure for calcination reaction at 900
C is 1.087 atm.
Step 1: Substituting the values of X,dX/dt, P
CO
2
, and P
eq
in
Eq. (13.1)
, one
can calculate the value of k.
5
002212 s
2
1
Step 2: Now k is the function of temperature so to find the reaction rate con-
stant and activation energy, the above step has to be repeated at different tem-
peratures and calculate k for each temperature.
k
0
:
5
Temperature (
C)
900
950
1000
k (s
2
1
)
0.00221
0.00310
0.00958
Step 3: Arrhenius plot and identifying the reaction rate constant (k
0
) and the
activation energy (E
a
).
The Arrhenius plot is the plot of ln k
0
versus 1/T. It is plotted from the data
above. (
Figure 13.6
). So the intercept on y-axis of the plot will give the value of
ln k
0
and the slope will give
2
E
a
/R. Thus from this one can calculate the value
of k
0
and
E
a
.
From the above graph: E
a
/R
2
5
21,717
E
a
21
;
717
0
:
008314
180
:
56 kJ
=
mol
5
3
5
And ln k
0
12.265
5
64 s
2
1
k
0
212
;
139
:
5
So the final kinetic equation becomes:
P
eq
P
CO
2
P
eq
dX
dt
5
2
10
6
180
56
RT
:
e
2
0
:
21
3
3
3
ð
1
2
X
Þ
3
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