Biomedical Engineering Reference
In-Depth Information
Solution: The ratio of the rate of this reaction at 310 K to that at 300 K,
E
R
T
15000
1:9872
1
e
E=RT
1
e
E=RT
2
¼ exp
k
2
T
300
1
310
300
¼
¼ exp
¼ 2:252
k
310
1
Between 300 and 400 K, this ratio is very large,
E
R
T
15000
1:9872
1
e
E=RT
1
e
E=RT
2
¼ exp
k
2
T
300
1
400
300
¼
¼ exp
¼ 539:29
k
400
1
This shows that for this activation energy an increase in temperature of 10 K approxi-
mately doubles the rate and an increase of 100 K increases it by a factor of more than 500.
Example 3-2 shows why temperature is so important in chemical reactions. For many non-
reacting situations, a 10 K increase in T is insignificant, but for our example it would decrease
by a factor of two the size of the reactor required for a given conversion. A decrease in
temperature of 100 K would change the rate so much that it would appear to be zero, and
an increase of this amount would make the rate so high that the process would be difficult
or impossible to handle.
Let us consider finally the units of k. We choose units to make the rate (in moles/liter/
time) dimensionally correct. For r
k
C
O
RA
A
, k has units of liter
O
RA
1
$
mole
l-O
RA
$
time
1
, which
¼
gives k units of time
1
for O
RA
¼
1 and k of liters/mole time for O
RA
¼
2.
3.6. STOICHIOMETRY
When a chemical reaction is written (for a given set of stoichiometric coefficients), we need
to balance the number of each atom species (if nuclear reaction is absent).
Molecules are lost and formed by reaction, and mass conservation requires that amounts
of species be related. In a closed (batch) system, the change in the numbers of moles of all
molecular species n
j
is related by reaction stoichiometry.
For our NO decomposition example,
/
2
N
2
þ
2
2
;
from an O atom balance, we see that the total number of moles of the oxygen atoms in the
system is
NO
O
n
NO
þ 2
n
O
2
¼
constant
(3.54)
1
while an N atom balance gives
n
NO
þ 2
n
N
2
¼
(3.55)
constant
2
Subtracting these, we obtain
n
N
2
n
O
2
¼
constant
(3.56)
3
in a closed system. The stoichiometry of the molecules requires that the moles of these species
be related by these relations.
Search WWH ::
Custom Search