Biomedical Engineering Reference
In-Depth Information
Propylene will not significantly transform back to cyclopropane, and we call this reaction
irreversible. The irreversible first-order reaction
A
(3.7)
is the most used example in chemical kinetics, and we will use it throughout this topic as the
prototype of a “simple” reaction. However, the ring opening of cyclopropane to form
propylene (which has absolutely no industrial significance) is one of only a handful of irre-
versible isomerization reactions of the type A
/
B
B.
Next consider the formation of nitric oxide from air:
/
N
2
þ
O
2
/ 2
NO
(3.8)
This extremely important reaction is the source of air pollution from automobiles. It is
responsible for all NO
x
formation in the atmosphere (the brown color of the air over large
cities) as well as nitric acid and acid rain. This reaction only occurs in high-temperature
combustion processes and in lightning bolts, and it occurs in automobile engines by free
radical chain reaction steps. It is removed from the automobile exhaust in the automotive
catalytic converter. The above reaction can also be written as
1
2
N
2
þ
2
O
2
/
NO
(3.9)
We could generalize these reactions as
1
2
A þ
2
B / C
(3.10)
or
A þ B / 2C
(3.11)
with A
NO. The coefficients of the chemical symbols in a reaction are
termed stoichiometric coefficients and can be multiplied by a constant factor and still preserving
mass conservation.
We need to generalize stoichiometric coefficients both of reactants and products. For this
we move all terms to the left with appropriate signs, so that the preceding reaction becomes
¼
N
2
,B
¼
O
2
, and C
¼
A B þ 2C ¼ 0 (3.12)
Note that convention negates the sign of coefficients for reactants. Further, since the alphabet
is limited, we will increase our capacity for naming chemicals by naming a species j as A
j
,so
that this reaction is
A
1
A
2
þ 2A
3
¼ 0
(3.13)
with A
l
¼
N
2
,A
2
¼
O
2
, and A
3
¼
NO. In this notation, the generalized single reaction becomes
X
N
S
n
j
A
j
¼ 0
(3.14)
j
¼1
where N
S
denotes the total number of species involved in the system. Most chemical
process of practical interest forms several products (some undesired) and involves multiple
reactions.
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