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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