A NEW METHOD FOR DETERMINING
THE TOTAL
CARBONATE
ION CONCENTRATION
IN SALINE WATERS
H. James Simpson and Wallace S. Broecker
Lamont-Doherty
Geological
Palisades,
Observatory
New York
of Columbia
10964
University,
AEEXRACI’
A new method of determining
total carbonate ion content of saline waters requires
measurement of the partial pressure of carbon dioxide gas ( Pco2) in equilibrium
with an
initial solution, plus two more PCO, measurements made after adding a known amount of
strong base and after further adding boric acid. These three PCO, measurements, plus the
total inorganic carbon concentration
(X0,)
are used to compute the total carbonate ion
concentration
of the original solution, without the use of any system of apparent dissociation constants. Experimental
data for seawater samples using this method yield total carbonate ion concentrations
in agreement with those calculated
using Lyman’s apparent
dissociation constants for carbonic and boric acids. The method can be equally well applied
to other saline natural waters.
Carbon is present in natural water systems in a great variety of chemical forms,
resulting from a complicated interplay of
chemical
weathering,
ocean-atmosphere
gas exchange, biological activity, mineral
formation
and dissolution,
and internal
mixing. Most of the dissolved carbon in
seawater is present as dissociation products of carbonic acid or as dissolved CO2
gas, all of which are generally charactcrized as the “total dissolved inorganic carbon,” i.e. 2,C02. The detailed solution
chemistry of the dissociation products of
carbonic acid is complicated by the presence of major ion complexes formed by
HC03- and COs2- with the alkali and alkaline earth metals abundant in all saline
waters. It is common to discuss the chcmistry of the dissociation products of carbonic acid in saline waters in terms of
total bicarbonate ion and total carbonate
ion, where “total” is understood to include
the free ions plus those ions combined
with the alkali and alkaline earth metals
as complex species.
Current methods for determining
total
1 Financial
support for this study and support
of H.J.S. was provided
by U.S. Atomic Energy
Commission
Grant AT( 30-l )2493 and AT( 30-l )
2663.
Lamont-Doherty
Geological
Observatory
Contribution
No. 1930.
LIMNOLOGY
AND
OCEANOGRAPHY
carbonate ion content in saline waters are
all dependent on emf measurements made
with the glass electrode. In general, it is
necessary to measure two complete potentiometric titration curves (including
one
in which all carbon dioxide species are
excluded by prior acidification)
to determine the carbonate ion content of a natural saline solution. For seawater, assuming
a constant alkali plus alkaline earth to
chloride matrix and a constant boron-chloride ratio and the validity
of a set of
laboratory determined “apparent” dissociation constants, the usual practice is to
measure only two diagnostic properties of
the inorganic
carbon system. Methods
based on pH or alkalinity determinations
electrode
measurements,
while
involve
those based on the determination
of Ptro,
and XC02 involve measurements that can
both be made with an infrared gas analyzer. Park (1969) has reviewed the advantages of the various combinations of
two mcasurcd parameters of the inorganic
carbon system in seawater, all of which
require knowledge of a system of apparent
dissociation constants.
A method is presented here by which
one can obtain the total carbonate ion concentration of a solution, using only measurements made with an infrared analyzer
426
MAY
1973,
V. 18(3)
DETERMINING
TOTAL
calibrated by means of volumetric measurements of COa gas. One purpose of this
approach is to provide a method of total
carbonate ion determination
independent
of electrode measurements, as an internal
check on the current understanding
of
seawater carbonate chemistry.
Secondly,
since this method is independent of a system of apparent dissociation constants, it
should provide a method for investigating
the carbonate chemistry of saline waters
other than seawater, where such constants
are normally not available.
Except for
making two complete potentiometric
titration curves, the only available method for
calculating total carbonate ion concentrations in saline solutions other than seawater is one based on model calculations
similar to those made for seawater by
Garrels and Thompson ( 1962)) requiring
knowledge of a large number of complexing constants and activity coefficients as
well as a chemical analysis of all the major
ionic species.
The method described here involves
making three Pcoz measurements and one
8C02 measurement, using techniques for
Pcez and ZCOz determination as described
by Broecker and Takahashi (1966) and Li
et al. (1969). Briefly, by measuring the
CO2 content of air equilibrated
with a
large water sample (for seawater N 20 liters ) , and the CO2 content of nitrogen
swept through an acidified small aliquot
of the same sample (for seawater 25-50
ml), the carbon dioxide gas partial pressure (Pee,) and the total dissolved inorganic carbon content ( Y&‘02) of the sample are obtained.
A known amount of
strong base (KOH) is added to the 20-liter
sample and the consequent decrease in
Pco2 is determined by a second equilibration using air as a carrier gas. Finally, a
known amount of boric acid is added to
the same sample and the consequent rise
in ho2 is determined by a third equilibration using air as a carrier gas, Four
measurements are required, while in the
method of Li et al. (1969) only one Pco2
and one ~$02 measurement are used in
conjunction with three apparent dissocia-
CARBONATE
427
ION
tion constants (two carbonic acid constants
and one boric acid constant).
Only two
extra measurements are required here instead of three to define the total carbonate
ion concentration because only the ratios
of these dissociation constants are needed.
The development of the theoretical justification of this method is done stepwise,
beginning
with a hypothetical
seawater
sample in which carbonic acid is the only
weak acid present [i.e. B ( OH) 3, H3POd,
and H&SiOd are absent].
C. Garver
performed
a substantial
amount of the experimental work during
the latter stages of this investigation
and
greatly facilitated its completion. K. Wolgemuth collected the deep Pacific sample
that provided so much entertainment.
DERIVATION
OF EQUATIONS
For any aqueous solution the dissolved
CO2 gas, bicarbonate ion and carbonate
ion can be related by the following chemical reaction:
I-120 + co2 + co32- = 2HCOg.
Letting
cIT1,O= 1
=
y2mo,-. [ HCOs-] 2
a&o, *YC03”[ co32-]
=
y2~-~co,-. x2
aPc0,
[ HC03-]
l
2tot
* YC03” * y * [ co32-]
tot *
Where a is the solubility constant of CO2,
the ys are the activity coefficients, and x
and y are, respectively, the fractions of the
bicarbonate and carbonate ions not combined in major ion complexes. Defining k2
to include all the constant factors and substituting into the above expression,
k2 = kl a
yyco?x2 Y211C0,-
CIICO3-I
=
~coz
l
[
2tot
co32-]
tot
*
Since
[IICO3-I
tot = [X021
- aho,
- [co32-l
tot,
428
H.
the following
JAMES
SIMPSON
AND
expression results :
k _ ( wo212-
aho,
contains
two
unknowns,
]C032-]‘tot.
To obtain a
second independent equation necessary for
solution, charge balance is invoked. The
change in carbonate ion concentration,
ACOs2-, will be related to the amount of
base added, A, in a manner consistent with
the conservation of charge, i.e.
[co32-l
tot
The CO2 partial pressure is then,
P co, =
( [8CO21-
S. BROECKER
Equation
- [CO32-] tot)2
pcoz * [co32-]
WALLACE
~Pco, - [C032-ltot)2
k2 rCOs2-] tot
’
Now if a small amount of strong base
(less than the bicarbonate ion concentration) is added to a carbonic acid solution
the following reactions will take place:
OH- + CO2 * HC03-
1
tot and
ACOs2- = A + AC0, - AOII-,
where
droxide
( [OH-]
content,
an d
AOH- equals the change in hyion concentration of the solution
’ - [OH] ) . The change in CO2 gas
ACO,, is given by
AC0, = a ( P’co2 - PCo,) .
OH- + HCOs- + C03”-,
I Ience
thus shifting the distribution
of inorganic
carbon species to increase the carbonate
ion content and decrease the Pco2. The
new CO2 partial pressure, P’co2, and the
new carbonate ion concentration [ COs2-] tot
+ aCOs2- can be related as follows:
([SC021
- aP’co,-
[ cos2-] tot - ACOs2-) 2
P’coz =
k’2 ( [COs2-] tot + AC032-) ’
[ m32-] ‘tot= [ co32-] tot + AC03’and dividing the expression for PICOQby
that for Pco,, the following expression is
derived:
P’coz kz [ SOa]
k’2
- a P’co, - [ COs2-] ‘tot
[ 8CO2] - d’co,
[ co32-]
x [coB2-]
tot
‘tot *
In the presence of the buffer system provided by the inorganic carbon species, the
AOH- contribution
to this expression is
very small. For simplicity it will be neglected at this point. Thus
[ cos2-]
Substituting
-=Pco!2
AC032- = A + a ( PICoz- PCo2)- AOH-.
2
- [ COs2-] tot
(1
If, as is the case for seawater, the concentrations of [ HC03-] tot and ]C032-] tot arc
small compared to those of the cations
with which they complex, the complexing
factors x and y will not change (nor will
the activity coefficients).
In such a case
k2 = k’,; thus the two total carbonate ion
concentrations
are expressed as an implicit function of only the two CO2 pressures, the total dissolved inorganic carbon
content, and the CO2 solubility constant.
‘tot - [ co32-] tot =
A + dp’co,
- pco,) -
(2)
Equations 1 and 2 can now be solved
for ]:C032-] ltot and [C032-] tot, provided a
value for a is known and the change in
OH- content of the solution is neglected.
If the amount of base added is comparable
to [C032-] tot (i.e. l-3 x lo-” M in seawater) the change in OH- is about 0.5%
of the change in carbonate ion. A value
for a can be obtained for any water sample in question by using an infrared analyzer ( Li and Tsui 1971). If carbonic
acid were the only weak acid present in
natural solutions, the discussion would be
complctc.
However attention must now be directed to correction for the influence of
additional weak bases. The most important of these, in seawater, is boric acid.
The predominant
boric acid species between pH 5 and 12.5 at concentrations
GO.025 M are B(OH), and B(OII)‘i- (Ingri
1963). Since boron in seawater is less than
2% of the value where anions containing
several boron atoms become important (i.e.
DETERMINING
Table
1.
TOTAL
CARBONATE
429
ION
of charge balance expression for base addition
Derivation
with
borate
included
B(OH)4- + HC09- = B(OH)3 + COT2- + H20
Letting
aH20
= 1 (since
x "co 2-
aB(OH)
ky. =
is not important)
yB(OH)3CB(OH)31YCo 2- x YCCOT2-ltot
=
!3 = aB(0H)4- x aHCOg-
Defining
the exact value
aH20 is constant,
x zCB(OH)~-I totYHC(&- x x~Hco, 1
’ tot
/
yB(OH),
yB(OH)4- x yHCOqyB(OH)? x yCOT2-
xz
x-xk
'
3
and making the following
CB(OH)4-I
substitutions,
end CHC03-I
= CB - CB(OH),I
tot
,' tot
tot
the following
expression
Fr
K032-1
CC03d-lebot
- aPco2 - [CO3 '-Ito~[B(OH)4-I
(cco2
“%02
results:
(CB - CB(OH)Jltot)
k4 =
= cco2
'
tot
om the above expression,
CB( OH)4-I
tot
CB
cco2 - %02
=
k4
and after
tot
cco$-1
f AB(OH),
-1
+1
>
tot
of base, the borate
the addition
CB( OH14-I
(
ion concentration
becomes
CB
=
- '-do2
k4
-b ACOz2-
and the change in borate
XB
cco2 - %02
AB(OH)4- =
k4
( cco32-1 tot f lico3*The charge balance equation becomes
ACOT2- =A + dp~o
2 - pco2)
Combining the above charge balance
following
results:
rcq-1
-1
-t-l
1
- AoH- -
expression
CB
cco2 - %02
k4
(
cco32-l
t 0-t;
-1
+1
)
AB(OH)4- .
and that
for AB(OH)4-, the
- pco2) - AOH- =
tot
m?
tot
430
II.
Table 2.
Derivation
JAMES
of equations
SIMPSON
relating
Pt!02
cc o2 - aP;o2
P&O2
cco2
AND
total carbonate
-
[CO3
-=
Equation
tration,
WALLACE
and borate
species
for addition
of boric acid
2
2-y
2-y
S. BROECKER
tot
1
'
tot
11
Eo32-l
- "P602 - lco3
tot
4 is analogous to equation 1.
[
cco32-l
x
(4)
tot
The change in borate
AB(OH)4-, can be obtained. as follows.
After
ion concen-
the ad.dition
of boric
acid.
CB(OH)4-l
tot
CB + AB
11
cco2 - apco2
+ AB(OH)4- =
k4
where AB = boric
(
[co,2-1
,
-1
”
tot
4-l
>
acid added.
Hence
AB(OH)4- =
CB + AB
Using the charge balance condition
and the expression
[C 032-1 '
tot
above for the boric
for AB(OH)4-, the following
- [co32-l"
-tot
+ 'y.(P;o
0.025 M), only the two major species, boric
acid and borate need be considered. Assuming the possibility of complex borate
analogous to the complex ion species for
carbonic acid, the fraction of uncomplexed
borate is defined as x. A reaction relating
boric acid and carbonic acid species is
given in Table 1, followed by a derivation
of an expression relating the change in
total carbonate ion to the total boron concentration and the ratio of two apparent
constants. No solution for [COS2-] tot and
[COS2-] ltot can be extracted from equations
equation
acid addition,
is obtained:
' > - AtOH- =
2 - Pco2
1 ( which is still valid) and 3 ( Table 1)
without assigning a value for kd, which is
equivalent to the ratio of the second “apparent” dissociation constant of carbonic
acid to the first “apparent” dissociation
constant of boric acid (K’z : KIB). Our present knowledge of these constants is based
on pH measurements. Thus k4 must be
redetermined by a method independent of
electrode measurements.
This can be done by adding a known
quantity of boric acid to seawater and remeasuring its CO2 partial pressure. The
DETERMINING
addition of boric
to the reactions:
TOTAL
acid to seawater leads
B(OHh +
COs2- + H20 + B (OH)d- + IICOR-;
B(OH)3 + OH-+ B(OH)d-;
B(OH)3 + HC03- + I-I20 * B(OII)d- +
CO2 + HZO.
CARBONATE
431
ION
Table 3. Concentrations
(in. M) of weak acids
and their various species in typical water from the
deep Pacific (pH = 7.9)
cc 02
245 x lo-+*
3 x 10-T
co2
HC03-
232 x 10-5
-GO+3
If charge is to be conserved
Acos2- = -AB (OH) 4- - AOH- +
a (P”Co2 - ~‘co,) ’
Two equations can now be written analogous to equations 1 and 3, which describe
the effect on the Poe, of the system when
boric acid is added. Since the operations
of base and boric acid additions were
performed in sequence, with a Pecz measuremcnt made after each step, the conditions after base addition are denoted
with “primed” variables, and those after
boric acid addition with “double-primed”
or “seconded” variables. The derivation of
these two equations is given in Table 2.
A set of equations (1, 3, 4, 5) is now
derived, which can be solved for [ C032-]tot,
[COs2-]‘tot, [C032-]“tot, and 7~4.The A’OHappearing in equation 5 is very small, as
was the case for AOH- in equation 3 and
can be neglected. Again, a must be obtained from a separate measurement (see
Li and Tsui 1971).
Boric and carbonic are not the only
weak acids present in saline waters. The
influence of silicic and phosphoric acids
must be considered; their effects are considered for deep Pacific water (where
they arc most abundant in seawater). The
forms and concentrations of the species of
Si and P are compared with those of C
and B in Table 3. Since the phosphorus
content of deep Pacific water is only 0.3 x
10ms M it is clear that uptake of 011 ion
by this clement is unimportant
(relative
to [COs2-] changes ) . Although the silicon
concentration is a third that of boron, if
the presently accepted value for the first
dissociation constant of silicic acid in seawater (~3 X lo-lo) is correct, then changes
in the H3Si04- concentration as a result
of the addition of small amounts of strong
co3*-
10 x 10-T
tot
CB
B(OHj3
B(OH14-
5 x lo->
ESi
IL.3 x 10-5
H4SiO4
12,5 x 10-5
HgSi04-
0,5 x 10-T
0.30 x lo-yp
H2P04-
0.00 x 10-T
HPo42-
0.26 x lO-5
POLL'
0.04 x 10-5
*Li et al. (1969).
Bverdrup et al.
(1942).
base and boric acid will be negligible.
If
a water were encountered where either of
these weak acids proved important, their
contribution
could be directly evaluated
by adding phosphoric acid, silicic acid, or
both, as was done for boric acid.
It is clear that provided the borate,
phosphate, and silicate contents of a saline
water sample are known and that a rough
estimate of its OH ion content can be
made, it should be possible to determine
its total carbonate ion content by the
method outlined here. Since major ion
complexing makes the prediction of dissociation constants of these weak acids quite
uncertain in saline natural waters, this
method provides a means to circumvent
understanding in detail all the complexing
that takes place.
EXPERIMENTAL
RESULTS
Several large volume seawater samples
have been used to test the method of total
432
H.
JAMES
SIMPSON
AND
Table 4. Pcoz of Bermuda surface water at various stages in the titration
sequence (22.4”C)
WALLACE
S. BROECKER
ide was added (standardized against acid
phthalate)
to the 19-liter sample and
stirred
with
a glass rod. The PcoZ of the
CO2 in
A OH
A Boric acid.
perturbed seawater sample was again deppm I lo6 (0.2197 N)
(0.2806 N)
termined in triplicate, using equilibration
periods of about 50 min. Finally, 40 ml
Initial
of 0.28 N boric acid was added to the
la
0
0
397kl
same water sample, and the PceZ once more
lb
0
0
determined in triplicate.
A summary of
399"l
the experimental
results is presented in
lc
39621
0
0
Table 4. The experiment was conducted
After base addition
over a period of about 8 hr, at a temperature of 22.4”C. The experimental results
*a
lgofl
20 ml
0
are listed as concentrations of carbon di2b
1g15
0
0
oxide in the equilibrated gas sample (after
2c
192fl
0
0
I&O vapor removal).
The value of Pea,
in units of 10d6 atm is numerically about
After base end,boric acid additions
5% less than the COz, concentration
in
3a
30221
0
40 ml
parts per million; it is slightly lower be303kl
0
0
cause the CO2 measurement is made after
3-b
removal
of water vapor. The Pea, must
304fl
0
0
3c
thus be corrected back to the “predried”
conditions. The initial Pco, of the sample
cc o2 = 213.3 x 10mT M
of about 400 x 10dF atm was decreased to
Precision
of
CC02
214.3 x lo+ M
about half that value by addition of 23 X
measurement
213.7 x low5 M
lo-” moles of KOH per liter of sample.
The ho2 of the sample after addition of
'Total volume = lg.03 laters
strong base was then increased to about
Gas g 2 liters
300 x lo-” atm by addition of 59 X lo-”
Salinity
= 36.6%,
moles of boric acid per liter of sample.
The error limits of about 0.3% shown in
Table 4 indicate the precision of the analysis of the CO2 content of a single flask
carbonate ion determination
developed
sample. The variation of about 1% behere. Experimental techniques and calcutween
replicate equilibrations probably relation procedures for seawater samples collected from the deep Pacific Ocean, as sults from temperature inhomogeneities in
well as the surface Atlantic Ocean, have the 19-liter sample, as well as temperature
been described in detail (Simpson 1970).
drift in the sample-bath system.
The results of one base-borate addition
Calculation of total carbonate ion
experiment are detailed here.
concentration by base-borate
A 19-liter sample of surface seawater,
addition method
collected off Bermuda, was placed in a
glass carboy and immersed in a constant
The experimental results summarized in
temperature bath. Aliquots of 50 ml were
Table 4 can be used to solve the four
used to measure ZC02, and about 2 liters
independent equations derived earlier for
of air were circulated through the 19-liter
the total carbonate ion concentration pressample, with two dispersers, to obtain a
ent during each of the three steps of the
l-liter flask sample for Pco, measurement.
experiment, plus the ratio of the second
The initial Pco, of the water was deterdissociation of carbonic acid to the first
mined from three separate equilibrations.
dissociation constant of boric acid.
Then 20 ml of 0.22 N potassium hydrox-
DETERMINING
Table
5.
Summary
TOTAL
CARBONATE
of base-borate
addition
1.
--
Pco2
2.
kr-K’z : Kn
4.
2
cco2
A - (CCOT2-1'
tot
-( ~co32-1”
tot
2
- cco32-l
ccq-1
tot
tot
- aPh02 - cco3
cc o2 - aP;02
(
AOH--change
A’OII--change
27'
cc o2 - a4yJ
GO,
-=
Go,
3.
(
and variables
[co32-l
zCOa-total
inorganic carbon
A-base
addecl
AB-borate
added
ZB-total
borate in original solution
a-solubility
of carbon dioxide
cc o2
equations
Unknown
to f-original
total carbonate
total carbonate after base added
[CO.?-l’tot[cO,a-l”i 0t- total carbonate after borate added
Known
PCO,
Pco2-original
P’co2-Pco2 after base added
P”Coz-Pco2 after borate added
P&o2 _
433
ION
x
2
2-y
- [CO3
tot
2-31
'x
tot J
- cco32-1
1 + a(p(4o
> + cl(P;o
tot
Table 5 summarizes the four equations which must be solved simultaneously,
as well as the 14 variables present in
these equations. Listed under the heading
“known” are four measured variables, plus
quantities.
two “added’
The last two
known variables, XB and a, require knowledge of the salinity of the water sample.
Under the heading “unknown” are the four
variables to be calculated, plus two hydroxide ion terms, which represent the
cco32-]
[co32-l"
- OLpAo2 - cco3
- cco32-l’
tot
cco32-l ’
)
tot
in [OH-]
with base addition
in [OH-] with borate addition
2 - pco2)
2
-
P&)
2
tot
'
tot
tot
- *OR'- =
> _ &)H-
=
change in hydroxide ion resulting from
addition of strong base and boric acid. As
shown above these terms can be safely
neglected (or a correction can be applied
after the COs2- concentration calculation
is carried out).
The equations in Table 5 cannot be
manipulated to provide cxplici t rcprcscntation of any of the unknown variables nor
can they be rcarrangcd to form a linear
set of equations.
Simultaneous solution
434
H.
JAMES
SIMPSON
AND
Table 6. Comparison
of results from base-borate
addition with those using Lyman’s constants
Step
in
exp
Bermud.a surface water - 22.4%
*
*
Base-borate
LpWl’S
addition method. constants method
1
22.8
2
39.6
28.3
3
k4
0.43
23.0
40.0
28.6
c.40
*CCo~*-ltot x lo5 M.
was obtained by a successive approximation method with a digital
computer,
Each equation was solved for only one
variable, holding the others constant, by
use of the derivative of each expression,
The computed value for one equation was
used as a fixed input to the next function.
For a solution criterion of less than 0.1%
change in any variable in a complete cycle
through the four equations, the computation requires between 10 and 50 cycles to
converge (for details see Simpson 1970).
The solution of the equations in Table
3, using the experimental data shown in
Table 4, is shown in Table 6. The total
carbonate ion concentration of the original
sample was calculated to be 22.8 x lo-” M
by the base-borate addition method.
Calculation of total carbonate ion
concentration using apparent
dissociation constants
To provide a framework for comparison,
the same Pcoz and 8C02 data will be used
to calculate the distribution
of carbonic
acid and boric acid species at each step
during the addition experiment, using a set
of apparent dissociation constants. Two
sets of such constants are in gcncral usage
for treatment of the carbonate chemistry
of seawater at 1 atm pressure, one determined by Buch (1951) and one determined
by Lyman ( 1956). There are significant
differences between these sets of constants,
primarily concerning the second dissocia-
WALLACE
S. l3ROECKER
tion constant of carbonic acid. Li et al.
(1969) stated that the constants determined
by Lyman (1956) were the most consistent
with other observations, while Takahashi
et al. (1970) supported the validity
of
Buch’s
( 1951) constants, concluding that
the KIB values of Lyman should bc increased by 30%. In this paper, Lyman’s
constants, as expressed by Li et al. (1969)
will be used as a basis of comparison. The
following expressions are used to calculate
the distribution of carbonic and boric acid
species.
aJT+=
KI
k+
Where the constants a, K1, and K2 are defined as follows:
a0 = (770 - 29.5T + 0.685T2 - 0.0075
T”) X lo-” moles atm-l;
a = cuo/explo (0.0806 - 600074T)
( Cl”/,0/20) ;
-log K1 = 6.34 - 0.01 Cl%,
0.00008 T) T;
-
(0.008
X
-
-log K2 = 9.78 - 0.02 Cl%0 - 0.012T;
-log Kn = 9.26 - 0.016 Cl%, - 0.01 T;
and T is temperature in “C.
Table 7 shows the results of calculations
using the above constants with the experimental data given in Table 4. The total
carbonate values arc also shown in Table
6 for comparison with the results of the
base-borate addition
calculations.
From
Table 7, it is clear that the CX(P’coz - Pco,),
a( P”Coz - P’oo2), and AOII terms in the
equations derived here are small compared
to the ACOs2- terms.
DETERMINING
Table
Step in
exp
7. Bermuda
CC02*
surface
t
PC02
water
TOTAL
CARBONATE
calculations
using Lyman’s
ccq-I
tot
PH
*
435
ION
constants
*
(22.4’C)
*
*.
OH-
C alk
-co2
246.1
1.2
0.2
269.5
0.6
0.3
0.9
0.2
Initial
214
384
214
214
185
After
293
23.0
8.19
After
base addition
8.47
base and. boric
8.30
40.0
acid. addition
28.6
270.2
*M x 105.
-I-Atm x 106.
fEq liter-l
x 105.
and evaluation of
base-borate addition method
Sensitivity
Calculation of total carbonate ion concentrations in seawater by either of the
methods outlined here involves complicated functional relationships.
The sensitivity of the calculated value of the species
of interest-the
total carbonate ion concentration-to
errors in the measured parameters is difficult
to predict from the
form of the equations. Several calculations
were performed by varying each measured
parameter by a certain percentage and
determining the effect on the calculated
carbonate ion concentration.
Table 8 shows the effect of changes in
various measured parameters on the carbonate ion concentrations calculated from
the equations shown above, using K1, &,
and KI$ values obtained by Lyman ( 1956).
The effect of a change in the value of K2
is also shown, The resulting percentage
error in carbonate ion is smaller than the
percentage error in the Pee, measurement.
The resulting percentage error is nearly
twice as large in the total carbonate ion
concentration as in the SCOz measurement.
Table 9 shows a set of sensitivity calculations for the base-borate acid addition
method of carbonate ion determination,
for the same data used in Table 8. The
value for total carbonate ion is quite sen-
sitive to the first two Pco, measurements.
Errors in the measured values of Pccz and
P’C02 result in errors four times as great
in the total carbonate ion concentration.
Errors in P” eo, or SC02 cause only minor
errors in the carbonate ion concentrations.
Thus the values of carbonate ion determined by Lyman’s constants are insensitive
to Pcoz errors and quite sensitive to ZCO2
errors, while the addition method values
are insensitive to ZCO2 errors and very
sensitive to Pcoz errors for the first two
measurements.
The effect of each increment of added
KOII on the distribution
of the carbonic
acid and boric acid species can be seen
by examining Table 7. A total of 23.1 M
of alkalinity
was added to decrease the
Pcoz from 384 to 185 x lO-G atm. The total
alkalinity
increase indicated by Lyman’s
constant calculations is 23.4 x lo-” M plus
0.1 x lo-‘) M increase of hydroxide ion. Of
the total increase of 23.4 x 1O-5 M, 17.0
goes into increasing the total carbonate
ion, 5.9 goes into increasing B ( OH ) 4-, and
0.5 goes into increasing the total bicarbonate ion from some of the dissolved COa.
Thus, about 73% of the base goes into increasing the carbonate ion, 25% into increasing the concentration of B (OH) 4-, 2%
into decreasing the CO2 concentration, and
only a fraction of a percent into increasing
the hydroxide ion concentration.
436
I-1. JAMES
SIMPSON
Table 8. Sensitivity
of Lyman’s
constant
culations to errors in measured parameters
apparent constants
AND
caland
WALLACE
Table
S. BROECKER
9. Sensitivity
of adclition
tions to errors in measured
% change
Perturbed.
variable
pc o2
Input
'Variable
perturbed.
* % change
in
variable
403
22.2
384
%O,
%O,
cz
cc o2
A borate
PK $
-3
23.0
36.5
-5
24.0
+4
194
185
+5
38.7
-3
176
-5
41.4
+4
308
+5
27.5
-3
40.0
28.6
293
278
-5
29.7
2251'
+5
25.2
+10
203:f
-5
20.9
-9
62'f'
"5
28.6
0
56-b
-5
28.6
0
+20
26.7
i-16
-20
J-9.3
9.03
9.11
+4
23.0
9.21
Measured. values:
-16
CC02 = 214 x 10 -5
A borate
=
59 x 10d5
*Atm X 106.
tM x 105.
Some indication of accumulated unccrtainty comes from comparing the computed increase of alkalinity and hydroxide
ion concentration of 23.5 X lo-‘) M (calculated using Lyman’s constants) with the
measured increase of 23.1 ( a discrepancy
of boric acid
of about 2%). Addition
should cause no incrcasc in alkalinity. The
increase of calculated alkalinity in Table
7, minus the decrease in OH and increase
in dissolved Cog, is about 0.3 X 1O-s M.
The computed value of 22.8 x lOA” M of
total carbonate by the base-borate addition method agrees remarkably well with
the value of 23.0 determined from Lyman’s
constants.
.
% change
'
cco32-1
variable
22.8
None
+.5
method calculaparameters
0
+5
19.8
-13
PCo2
-5
-1-18
Go,
1-5
26.9
27.6
Go2
-5
18.9
-17
*ao,
-r-5
21.9
-4
GO,
cc o2
-5
23.9
+5
- 3
-b 4
%02
+.5
-r-21
cc o2
-5
23.6
ali
-+5
-I- 2
AB
-5
23.2
22.4
25.2
20.6
4-11
“5
-5
t- 2
-10
*M x 1050
Additional
experimental
data
During an early stage of this investigation, some additional data were obtained
under much less well controlled experimental conditions. In one case the temperature control was poor, while in another
a very large amount of additional inorganic carbon was present in the sample
used for the addition experiment.
These
data, although less reliable, add support to
the conclusions drawn for the experiment
outlined above.
An addition experiment at 25.2”C was
performed on a 20-liter sample of Bermuda
surface water collected at the same time
as the sample used for the experiment at
22.4”C. Strong base and boric acid were
added in two steps instead of one as in
the 22.4”C experiment. Problems with the
infrared analyzer caused an uncertainty
of about 5% in the Pco, of the water sample after the first aliquot of strong base.
The results of this “five-step” experiment
are summarized in Table 10. The total
DETERMINING
Table
10.
Sunamary
TOTAL
of results
CARBONATE
for Bermuda
437
ION
surface
water
at 252°C
Addition method.
computation
constants
computation
Lyman’s
*
Step in
em
Pco*
PH
C alk+
cco32-1
tot
cco32-I
+
tot
*
Initial
421
8.17
After
277
246.7
addition
After
200
ad.d.ition
8.45
After
After
316
8.28
of second. aliquot
of first
271.4
ad.d.ition
aliquo-t
aliquot
271.8
ti
39
of boric
acid:
34
29.6
of boric
acid.
29
0.44
M
214.0 x 10"
M
213.5 x lO-5
M
*Atm x lo6
-I
of base
34.5
0.41
tEq liter
33
41.2
of second. aliquot
k4
CC02 = 211.8 x lO-5
of base
32.7
270.9
addition
8.36
257
of firs-t
259.4
8.33
22
23.6
x 105
x lo5
carbonate ion concentrations computed by
the addition method were usually a few
percent lower than those computed with
Lyman’s constants.
The final experiment described here was
the first one performed and is the most
puzzling. A 45-liter sample of deep Pacific
water (2,000 m), which had been stored
about 1 year in several polyethylene bottles was transferred to a glass carboy for
the addition experiment. Over a period of
monitored
days the Pco, was periodically
and appeared to be gradually increasing,
although there was no comparable monotonic temperature increase in the water
sample. The Pco, increase was enhanced
by more frequent equilibrations,
Before
the addition experiment, several aliquots
of base were added to decrease the PcTo,
to about 1,200 x 1O-6 atm, and then three
more aliquots of base and two aliquots of
boric acid were added with a Pet, measurement made following
each addition.
Two 8CO2 measurements made after completion of the Pcop measurements averaged
312 x lo-” M, more than 25% higher than
published ZCOa values for deep Pacific
water ( Li et al. 1969) .
The data obtained for the deep Pacific
water equilibrations
are summarized in
Table 11. The agreement between the two
sets of total carbonate ion computations
is better than lo%, despite the large excess
of inorganic carbon present in the water
sample.
that heterotrophic
It appears likely
microbial
activity, possibly oxidation of
organic material from the polyethylene
438
H.
Table
JAMES
11.
SIMPSON
Summary
AND
WALLACE
S. BROECKER
of results for deep Pacific
water
at 17.5”C
Lyman's constants
computation
Step in
pco2*
em
cco12-1
C alki
-@H
Addition method.
computation
+
*
cco32-1
tot
-tot
Initial
7.88
1,151
After
326.9
addition
8.08
708
After
After
ad'dition
addition
After
431
8.28
After
490
8.23
24.3
of second aliquot
of base
30.4
of third
of first
36Oa7
ad.d.ition
of base
22.4
.360.6
ad.d.ition
14.8
aliquot
349.8
8.34
369
of first
338.9
8.22
496
14.4
aliquot
of base
41.1
38.6
aliquot
of boric
acid.
34.1
of second aliquot
361.2
33.3
30.7
36.3
of boric
acid
32.9
0.42
cc o2 = 311 x lO-5
313 x 10"
*Atm x lob.
+Eq liter-1
w
M
M
X 105.
x 105.
bottles, was responsible for the unusual nature of the inorganic carbon system in this
large sample of deep Pacific water. Significant container contamination
of samples stored in large polyethylene
bottles
has also been observed in radiocarbon studies (J, C. Vogel, personal communication).
EXPERIMENTAL
NOTES
Several possible difficulties
in the experimental procedure for the base-borate
addition
technique
should be clarified.
KOH is added as a concentrated solution;
during initial pipetting into a large seaforms and
water sample, a precipitate
then redissolves. Presumably this precipitate is magnesium hydroxide, calcium hy-
droxide, or both. It is essential that the
precipitate redissolve before a Pee, measurement is taken. Borate was added as a
boric acid solution.
Since boric acid is
relatively insoluble, it is necessary to make
a solution close to saturation so that small
volumes can be used for the actual addition
Boric acid powder can be added
directly, but requires thorough mixing to
dissolve. Most commercial boric acid powder is quite difficult to “wet” and tends
to float on the surface.
Li (1967) and Takahashi et al. (1970)
discussed the importance
of correcting
co,
data
for
the
loss
of
XC02
from the
P
water sample to the gas used for infrared
analysis, This correction has not been ap-
DETERMINING
TOTAL
plied to our data. Air with a concentration
of about 320-350 ppm CO2 was used as
the initial carrier gas to reduce the loss of
CO2 from the water sample. In the two
addition experiments involving
Bermuda
surface water, the transfer of COa between
sample and carrier gas was quite small and
opposite in sign during the base addition
and boric acid addition steps. Although
the corrections amount to changes of about
1% in Pcozand P’~o~,the cumulative effect
on the total carbonate ion concentration
calculated for the original water sample
is a decrease of almost 5%.
DISCUSSION
CARBONATE
ION
439
values of K’2 yield values about
30% higher than with Lyman’s and those
determined here.
Our method can best be used in saline
natural water with pH values approximately those of seawater or higher. Low
ionic strength solutions or saline solutions of pH substantially lower than seawater cannot be examined directly by this
method for determination of ]COs2-] r.
Because of its lack of dependence on
apparent dissociation constants, the baseborate addition method can be applied to
the study of the carbonate system in saline
natural waters other than seawater. Such
a study has been carried out for several
high alkalinity lakes in the western Great
Basin of the United States and, combined
with that of seawater, indicates some possible revisions of the currently accepted
major ion complexing constants (Simpson
and Takahashi 1973). For saline waters
other than seawater, it is necessary to measure the total boron concentration and to
estimate the value of a on the basis of the
salinity in order to compute the total carbonate ion concentration.
I3ucB’s
Our method was developed to study the
carbonate chemistry in saline waters. As
it is important that ambiguities regarding
the carbonate ion concentration
of seawater be resolved by several independent
approaches, this method was first applied
to scawatcr. The agreement of our results
with the apparent dissociation constants
determined for seawater by Lyman ( 1956)
suggests that the ratio of the constants
determined by him cannot be in error by
more than 10%. It also suggests that the
REFERENCES
ratio of the first dissociation constant for
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1966.
Calcium carbonate precipitation
on lthe Bastant for carbonic acid as determined by
hama Banks.
J. Gcophys. Res. 71: 1575Lyman is correct to within 15%. With
1602.
careful experimental technique, an uncerBUCH, K. 1951. Das Kohlensare Glcichgewichtstainty of 5% ( i.e. 23 * 1 X 10~” M) in total
system im Mecrwasser.
Havsforskningsinst.
Skr. Helsingfors
151. 18 p,
carbonate ion concentration includes the
results of both a base-borate addition ex- GARRELS, R. M., AND M. E. THOMPSON. 1962.
A chemical model for sea water at 25°C and
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Amer. J. Sci.
man’s apparent dissociation constants.
360: 57-66.
The experiments described here were INGRI, N. 1963. Equilibrium
studies of polyanions containing
B-III,
Si-IV, Ge-IV, V-V.
conducted at 20-25°C. Additional experiSven. Kern.. Tidskr. 75( 4) : 199-230.
ments were conducted at about 10°C.
LI, T.-H.
1967.
The dcgrec of saturation
of
There is no limitation on the experimenCaCOx in the oceans.
Ph.D. thesis, Columtal temperature other than convenience.
bia Univ.
176 p.
Many measurements have been made in -,
T. TAKAI-IASHI, AND W. S. BROECKER.
1969. Degree of saturation of CaCOa in the
the field at in situ temperatures.
The
oceans.
J. Gcophys. Rcs. 74: 5507-5525.
pressure dependence of [COs2-] 11is about
-,
AND T.-F. Tsu~.
19871. The solubility
5% for 50@-atm pressure ( Li et al. 1969).
of CO, in water and sea water.
J. Geophys.
Using in situ temperature and a simple
Rcs. 76: 4203-4207.
LYMAN,
J. 1956. Buffer mechanisms of sea waapproximate
correction for the pressure
tcr. Ph.D. thesis, Univ. Calif., Los Angeles.
effect, [ COs2-] T measurements can be
196 p.
made to better than 5%. Calculations with
PARK, P. K.
1969.
Oceanic CO, system:
An
440
H.
JAMES
SIMPSON
AND
evaluation
of ten methods of investigation.
Limnol. Oceanogr. 14: 179-186.
SIMPSON, I-1. J. 1970.
Closed basin lakes as a
tool in geochemistry.
Ph.D. thesis, Columbia
Univ.
325 p.
-,
AND T. TAKAIIASIII.
1973. Interstitial
water studies, leg 15-chemical
model of
seawater and saline waters.
Deep-Sea Drilling Proj. Rep. 15: In press.
WALLACE
S. BROECKER
SVERDRUP, H. U., M. W. JOHNSON, AND R. H.
FLEMING.
1942. The oceans. Prentice-Hall.
TAKAHASHI, T,, AND OTIIERS. 1970. A carbonate chemistry profile at the 1969 GEOSECS
intercalibration
station in the eastern Pacific
Ocean.
J. Geophys. Res. 75: 7648-7666.
Submitted: 3 March 1972
Accepted: 2 February 1973