Biomedical Engineering Reference
In-Depth Information
Consider next the reaction system
N
2
þ
O
2
/ 2
NO
(3.15)
2
NO
þ
O
2
/ 2
NO
2
(3.16)
In NO
x
smog formation (NO
x
is a mixture of NO, N
2
O, NO
2
,N
2
O
4
, and N
2
O
5
), the NO is
produced by the reaction of N
2
and O
2
at the high temperatures of combustion in automo-
biles and fossil fuel power plants, and NO
2
and the other NO
x
species are produced by subse-
quent low-temperature oxidation of NO in air. NO is colorless, but NO
2
absorbs visible
radiation and produces brown haze. We write these reactions as a set of two reactions among
four species,
A
l
A
2
þ 2A
3
¼ 0
(3.17)
2A
3
A
2
þ 2A
4
¼ 0
(3.18)
where A
l
is N
2
,A
2
is O
2
, etc. This is a simplification of all the possible reactions involving
N and O atoms, since we have not included stable molecules such as N
2
O, N
2
O
2
,NO
3
,
and N
2
O
5
.
We can generalize this notation to any set of reactions as
X
N
S
n
ij
A
j
¼ 0;
i
¼ 1; 2;.;
N
R
(3.19)
j
¼1
or
2
4
3
5
2
4
3
5
2
4
3
5
n
11
n
12
/ n
1j
/ n
1N
S
A
1
A
2
«
A
j
«
A
N
S
0
0
«
0
«
0
n
21
n
22
/ n
2j
/ n
2N
S
«
« 1 « 1
«
¼
n
i1
n
i2
/ n
ij
/ n
iN
S
«
« 1 « 1
«
n
N
R
1
n
N
R
2
/ n
N
R
j
/ n
N
R
N
S
as a set of N
R
reactions among N
S
species, with j (
¼
1toN
S
) the index of chemical species and
i (
1toN
R
) the index of the reaction. Thus, we call v
ij
the stoichiometric coefficient of species
j in reaction i. We will use this standard notation throughout this topic, and we suggest that
you always give the i's and j's these meanings and never reverse them.
¼
3.3. REACTION RATES
Reaction kinetics and reactor design are at the heart of producing almost all industrial
chemicals and biologics. It is primarily a knowledge of reaction kinetics and reactor design
that distinguishes the bioprocess (or chemical) engineer from other engineers. The selection
of the reaction system that operates in the safest and most efficient manner can be the key to
the economic success or failure of a chemical plant or biological facility. For example, if a reac-
tion system produced a large amount of undesirable by-product, subsequent purification and
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