Part B | 9.2
264 Part B Tools and Methods in Marine Biotechnology
carbonate (CO
2
3 )
CO 2 .g/ $ CO 2 .aq/ ;
CO 2 .aq/ C H 2 O $ HCO
3 C H
C
;
HCO
3 $ CO
2
3 C H
C
;
or
CO 2 .aq/ C OH
$ HCO
3 :
(9.5a)
It must be emphasized that the speciation of CO 2 is
a gas–liquid equilibrium process. The equilibrium absorption of CO 2 from the gas phase to the liquid phase
is described by Henry’s law
P A D HŒCO 2 aq
(9.5b)
where P A is the partial pressure of CO 2 in the gas in
contact with the liquid, [CO 2 ] is the concentration of
CO 2 dissolved in the liquid medium that is in equilibrium with the CO 2 partial pressure in the aeration gas,
and H is the Henry’s law constant. The subsequent mass
action expressions for dissolved CO 2 speciation in a liquid medium are
K 1 D
ŒH
C
ŒHCO
3
ŒCO 2 aq
;
K 2 D
ŒCO
2
3 ŒH
C
ŒHCO
3
:
(9.6)
From the mass action expressions and Henry’s law for
absorption of CO 2 , it can be shown that the predicted
equilibrium concentrations of bicarbonate [HCO
3 ] and
carbonate [CO
2
3 ] ions are
ŒHCO
3 D 10
.CpKa;1pH/ P A
H
ŒCO
2
3
D 10
.CpKa;2pH/
ŒHCO
3 :
(9.7)
The total dissolved carbon concentration (C A;T ) is the
sum of all specie concentrations
C A;T D ŒCO 2 aq C ŒHCO
3 C ŒCO
2
3 :
(9.8)
The pK a values for dissociation of HCO
3 and CO
2
3
are 6:05 and 9:23, respectively, in seawater of 35 ppt
salinity at 15
ı C. The Henry’s law constant (H) for
dissolution of CO 2 is 0:026 L atm mmol
1 at the same
conditions. Selected equilibrium properties of CO 2 and
O 2 in fresh water and seawater are presented in Table 9.3.
Representative plots of equilibrium species concentration versus pH are shown in Fig. 9.3. The dissolved
concentration of CO 2 in seawater is a function of temperature and CO 2 partial pressure but is not a function
of pH, whereas the ionic bicarbonate and carbonate
species concentrations are also a function of pH. For
example, if ambient air containing 350 ppm CO 2 (CO 2
partial pressure P A of 0:00035 atm CO 2 ) is bubbled into
a seawater medium at 15
ı C, then at pH 8:0 the equilibrium dissolved CO 2 , HCO
3 and CO
2
3 concentrations
are 0:014 mM, 1:2 mM, and 0:071 mM respectively.
However, at pH 7:0 the equilibrium concentrations of
CO 2 , HCO
3 and CO
2
3
are 0:014 mM, 0:12 mM and
0:00071 mM, respectively. At high pH, this bicarbonate
reservoir can serve as ballast for dissolved CO 2 .
9.2.2 Specific Growth Rate
The specific growth rate is a convenient tool for characterizing the intrinsic biomass production rate in the
exponential phase of growth. It is defined as the derivative of the cell density (C x , g cells/L
1 culture) versus
cultivation time (t) curve divided by the cell density
D
1
C x
dC x
dt
:
(9.9)
The specific growth rate () is a normalized parameter with units of reciprocal time, e.g., h
1 , similar to
a first-order rate constant associated with a first-order
chemical reaction.
The specific growth rate of a particular phototrophic
marine organism in a liquid suspension culture is affected by both intrinsic environmental conditions (pH,
temperature, salinity, light intensity) and the available
nutrient composition. At optimal pH, temperature, and
salinity, the specific growth rate is principally affected
by three variables: 1) the dissolved carbon dioxide
concentration in the liquid medium; 2) the dissolved
limiting nutrient concentration in the liquid medium;
and 3) the incident light intensity to the cell surface for
photosynthesis. Like most living organisms, the specific
growth rate of phototrophic cells exhibits saturation
with respect to each of these variables. The Monod
model is most commonly used to describe saturation
growth kinetics. By the Monod approach, the combined
effect of these three variables on the specific growth rate
is given by
D
C A
K A C C A
C N
K N C C N
I
I k C I
max ;
(9.10)
264 Part B Tools and Methods in Marine Biotechnology
carbonate (CO
2
3 )
CO 2 .g/ $ CO 2 .aq/ ;
CO 2 .aq/ C H 2 O $ HCO
3 C H
C
;
HCO
3 $ CO
2
3 C H
C
;
or
CO 2 .aq/ C OH
$ HCO
3 :
(9.5a)
It must be emphasized that the speciation of CO 2 is
a gas–liquid equilibrium process. The equilibrium absorption of CO 2 from the gas phase to the liquid phase
is described by Henry’s law
P A D HŒCO 2 aq
(9.5b)
where P A is the partial pressure of CO 2 in the gas in
contact with the liquid, [CO 2 ] is the concentration of
CO 2 dissolved in the liquid medium that is in equilibrium with the CO 2 partial pressure in the aeration gas,
and H is the Henry’s law constant. The subsequent mass
action expressions for dissolved CO 2 speciation in a liquid medium are
K 1 D
ŒH
C
ŒHCO
3
ŒCO 2 aq
;
K 2 D
ŒCO
2
3 ŒH
C
ŒHCO
3
:
(9.6)
From the mass action expressions and Henry’s law for
absorption of CO 2 , it can be shown that the predicted
equilibrium concentrations of bicarbonate [HCO
3 ] and
carbonate [CO
2
3 ] ions are
ŒHCO
3 D 10
.CpKa;1pH/ P A
H
ŒCO
2
3
D 10
.CpKa;2pH/
ŒHCO
3 :
(9.7)
The total dissolved carbon concentration (C A;T ) is the
sum of all specie concentrations
C A;T D ŒCO 2 aq C ŒHCO
3 C ŒCO
2
3 :
(9.8)
The pK a values for dissociation of HCO
3 and CO
2
3
are 6:05 and 9:23, respectively, in seawater of 35 ppt
salinity at 15
ı C. The Henry’s law constant (H) for
dissolution of CO 2 is 0:026 L atm mmol
1 at the same
conditions. Selected equilibrium properties of CO 2 and
O 2 in fresh water and seawater are presented in Table 9.3.
Representative plots of equilibrium species concentration versus pH are shown in Fig. 9.3. The dissolved
concentration of CO 2 in seawater is a function of temperature and CO 2 partial pressure but is not a function
of pH, whereas the ionic bicarbonate and carbonate
species concentrations are also a function of pH. For
example, if ambient air containing 350 ppm CO 2 (CO 2
partial pressure P A of 0:00035 atm CO 2 ) is bubbled into
a seawater medium at 15
ı C, then at pH 8:0 the equilibrium dissolved CO 2 , HCO
3 and CO
2
3 concentrations
are 0:014 mM, 1:2 mM, and 0:071 mM respectively.
However, at pH 7:0 the equilibrium concentrations of
CO 2 , HCO
3 and CO
2
3
are 0:014 mM, 0:12 mM and
0:00071 mM, respectively. At high pH, this bicarbonate
reservoir can serve as ballast for dissolved CO 2 .
9.2.2 Specific Growth Rate
The specific growth rate is a convenient tool for characterizing the intrinsic biomass production rate in the
exponential phase of growth. It is defined as the derivative of the cell density (C x , g cells/L
1 culture) versus
cultivation time (t) curve divided by the cell density
D
1
C x
dC x
dt
:
(9.9)
The specific growth rate () is a normalized parameter with units of reciprocal time, e.g., h
1 , similar to
a first-order rate constant associated with a first-order
chemical reaction.
The specific growth rate of a particular phototrophic
marine organism in a liquid suspension culture is affected by both intrinsic environmental conditions (pH,
temperature, salinity, light intensity) and the available
nutrient composition. At optimal pH, temperature, and
salinity, the specific growth rate is principally affected
by three variables: 1) the dissolved carbon dioxide
concentration in the liquid medium; 2) the dissolved
limiting nutrient concentration in the liquid medium;
and 3) the incident light intensity to the cell surface for
photosynthesis. Like most living organisms, the specific
growth rate of phototrophic cells exhibits saturation
with respect to each of these variables. The Monod
model is most commonly used to describe saturation
growth kinetics. By the Monod approach, the combined
effect of these three variables on the specific growth rate
is given by
D
C A
K A C C A
C N
K N C C N
I
I k C I
max ;
(9.10)