Download The ion-association model and the buffer capacity of the carbon

The ion-association model and the buffer capacity of the carbon
dioxide system in seawater at 25°C and 1 atmosphere total pressure
Michael Whitfield
The
Laboratory,
Citadel
Hill,
Plymouth
PLl
2PB,
England
Abstract
The ion-association
model of Berner has been extended to calculate the contributions
of the various ion-pair formation
reactions to the buffer capacity of the carbon dioxide
system in seawater. These reactions are shown to make the major contribution
to the equiof the pH
libriunz buffer capacity at pH values greater’ than 8. However the indifference
to quite large changes in solution composition
arises, not from any pH-statting
effect, but
because the metal-carbonate
ion-pairs form only a small proportion
of the total cation concentration
under normal conditions.
ing the relative merits of the thermodynamic and a,pparent constants ( Wangersky
1972a,h; Pytkowicz 1972) in describing the
carbon dioxide system is not considered
here.
Wangersky (1972a) has suggested that
the buffer capacity of the carbon dioxide
system in seawater is significantly
influenced by the existence of a network of ionic
interactions that can be conveniently
described in terms of an ion-association model
(e.g. Garrels and Thompson 1962). In particular he stated that
Ion-association
The existence of ion pairing in such
proportions suggests that reactions linking the CO:! system with each of the
major ions in seawater must be considered as taking part in the control of
seawater pH. [Wangersky 1972a, p. 21
If control of pH in seawater occurs
through this whole web of equilibria, a
change in the proportions of the major
elements in seawater should lead to a
change in ion pairing and finally to a
change in pH. [Wangersky 1972a, p. 31
MfXeMX.
Here I propose to use an extended ionassociation model to look, in a quantitative
manner, at the buffer capacity of the carbon dioxide system in seawater under equilibrium conditions to test this hypothesis
and to see how far it is possible to explain
Wangersky’s observations in terms of a conventional ion-pairing approach. I am concerned in this instance with a precise analysis of the role of ion-pairing in the buffering
of the carbon dioxide system at equilibrium
and not with the relative importance of
the complementary buffer mechanisms described by Pytkowicz
(1967) and Sill&r
( 1961). The associated discussion concernLIMNOLOGY
AND
OCEANOGRAPIIY
model
The ion-association model takes as its
starting point values of the thermodynamic
formation
constants ( KB) of ion pairs
thought to be formed in the solution. The
free activity coefficients (fx) of the various
components are then calculated on the basis
of some hypothesis (Whitfield
1973a) and
the corresponding stoichiometric constants
are used to describe
( K+ = =‘f~fx/fux)
the individual
equilibria.
The final distribution
of the dissolved
species is calculated by an iterative procedure involving the values of K+ for each
ion-pair and equations defining the total
concentration of each stoichiometric
component. The procedure is described in detail by Garrels and Thompson (1962) who
used the metal chlorides as model unassociated salts and defined the free single-ion
activity coefficients according to the MacInnes’ convention ( MacInnes 1919). Their
model has been updated by Berner ( 1971)
who used more recent values for the activity coefficients of the model salt solutions and for the formation constants (KO) .
His model is extended here to cover a wide
235
MARCH
1974,
V.
19(S)
236
Whitfield
Table 1. Thermodynamic
ion-pair
constants used in the ion-association
pressed as logier).
formation
model (ex-
Table 2. Free single-ion
activity
used in the ion-association
model.
=
H+
OH-
SO 2-
4
HC03-
CO32-
B(OH&-
6.366" 10.329" 9.236*
13.999* l-99"
1.27.1 1.06f -0.25-t
Na+ 0.961
.K+
2.36t 1.16.b
3.4t
Mg2+ 2.1*
H+
ca2+
2.31t
-
1.26t
3.2 t
-
pH range using the assumptions
forr-
= ~2~(NaOII)/fxa+,
(14
(lb)
an d
f B(OIT),-= fur- = ~2*(Imr)/fK+.
Na+
K+
Mg
62:
OH-
so 24
0.95
0.71
0.63
0.29
0.26
0.65
0.17
* Taken as value
+ Taken as value
* Sill&
and Martell (1964).
t Garrels and Thompson (1962).
* Berner (1971).
f11+
= ~2~(IICl)/fC1-,
coefficients
(14
The calculations were carried out with the
computer program HALTAFALL
(Ingri et
al. 1967) using the input data shown in
Tables 1 and 2 and the solution composition
of Garrels and Thompson (1962).
The
analysis is confined to 25°C and 1 atm
pressure.
In their original
paper Garrels and
Thompson effectively fixed their seawater
at pH 8 by defining the ratio
[ HC0,7-] T/ [ COS2-] T = 2.38
x lo-“/2.69 x lo-”
= 8.85.
Calculations using this value in Berner’s
model ( Berner 1971) give results that are
identical with calculations based on the
present variable pH model at a pH of 8
(Table 3, columns B and F), indicating
the compatibility
of the two approaches.
The Garrels and Thompson model has
a number of weak points; the most conspicuous of these being the assumptions
made in assigning activity coefficients to
the ion-pairs and to the free ions (Whitfield 1973a,h). Quite large variations in
HCO 2-
CO3
H2c03
HS04cl-
B(OH)4-
0.68*
0.20
1.13t
0.68
0.63
0.65
-
for singly charged ion-pairs.
for uncharged ion-pairs.
the activity coefficients of the uncharged
ion-pairs (Table 3, column C, cf. Table 2,)
have little effect on the distribution of the
various ion-pairs and will not seriously
alter the conclusions reached here. The
use of a different convention for fixing the
single-ion activity coefficients (Lafon 196!3;
Table 3, column D) produces a significant
change and gives a distribution for the sulfate ion-pairs that is in better agreement
with the experimental measurements of Kestcr and Pytkowicz ( 1969) (see Table ,3,
column G).
The predictions of Lafon’s model and
mine can be compared directly with the
experimental data of Hansson (1973a) by
calculating the total concentrations of the
components of the carbon dioxide system
as a function of pH. The value of [H&03”]
( the total concentration of uncharged species in solution, i.e. [CO,] + [H&03] ) is
obtained directly and the values of [C0s2-:]T
and [HC03-lT1 can be calculated from the
equations
[ COs2-] T = [ C032-]p + [ NaCOs-]
+ [ MgCOs”] + [ CaCOsO]
(2s.)
an d
[ HCOs-] T = [ HCOs-] p + [ NaHCO:iO]
+ [ MgHC03+] + [CaHCOs+],
(2b)
where [Xl, and [X] T indicate the free and
total concentrations of component X.
The predictions of this model are in close
agreement with the experimental findings
Buffer
Table
pairs.
3.
Ion-association
models
capacity
of CO2 in seawater
for seawater*
23rl
1(298”K, 1 atm, 35%, S, pH 8). Distribution
$ anion as ion-pair?
E
C
D
of ion-
Anion
Ion-pair
A+
F
G
so 24
NaSO4MgSOd
CaSO4'
18.3
0:6
22.7
3.2
21.9
o-7
23.5
3-7
19-Y
0.6
29.0
5*1
37.6
0.4
19.6
2.7
24.7
0.8
24.2
3*9
21.9
o-7
23.5
3.7
37.2
0.4
19.4
4-o
Free
55.2
50.2
54*5
39*5
46.4
50.2
39-o
NaC03M&o3'
caco3o
17.5
67.0
6.6
19.1
63.3
7.1
15.1
68.2
8.4
17.8
63.0
8.8
21.4
59.0
7*3
19.1
63.4
7.1
17.3
67.3
6.4
8.9
10.5
8.3
10.4.
12.3
10.5
Y-0
8.3
14.5
3.2
8.4
14.1
3.1
8.0
CaHCO3"
8.6
17.1
3.4
9*5
3.4
8.2
12.4
2.8
8.3
14-5
3.2
8.6
17.8
3.3
Free
70.9
74.0
74.4
79*1,
76.6
74-o
70.3
co 23
KS04-
Free
HC03-
NaHC03'
MgHCOJ+
* Seawater
composition
Na+ (0.4752),
B
(molalities,
K+ (O.OlOO),
Carrels
Mg2+ (0.0540),
and Thompson 1962).
Ca2+ (0.01.04), cl- (0.5543),
so42- (0.0284), COAX- (0.000269), HCO~- (0.00238).
q Recalculated
for
HALTAFALL (Ingri
the composition
shown above using the computer program
parameters from the following
et al. 1967) and the appropriate
references.
F A. Garrels
and Thompson (1962).
the uncharged
ion-pairs
as dipoles
'MgX' P 0.8, (Kester
D. Lafon (1969) using
1969) and
B. Berner
(1971).
C.
Berner
(1971) treating
rather than neutral molecules,
i.e. with
yc,x"
= 0.72 (Yeatts and Marshall 1969).
the supporting
electrolyte
convention for defining
values used to
single-ion
activity
coefficients.
E. As for A but Y
-t@Cl)
calculate
fx were oalculated
from a specific
interaction
model (Whitfield
1973b)
2+
F.
Calculated
from the variable
for the mixture Na+ - K+ - Mg - Ca2+ - Cl-.
composition
is as shown in
pH model described here at pH 8. The solution
except
Pytkowicz
(1969) with experimental
standard
seawater
CT = 2.4
mM and [H~BO~]~ = 0.43
footnote*
values
for
mM.
gulfate
G. Kester and
&n-pair
formation
in a
solution.
of Hansson ( Fig. 1) and with the calculations of Lafon ( 1969), indicating that the
different distributions of the sulfate species
in the two models produce only small
changes in the stoichiometric
equilibrium
constants for the carbon dioxide system.
The equilibration
of the ocean with the
atmosphere ‘may be simulated by allowing
238
Whitfield
‘-‘2C4
-log
HCO,
co,‘-
[Xl,
6
8
4
6
8
10
PH
Fig. 1. Comparison
of the total concentrations
of the components of the carbon dioxide system
(HGOS, HCOs-, CO,“-) in seawater at 25”C, 1 atm
pressure, and 35% S calculated by different
procedures. Experimental
data of Hansson (1973a)
-solid
lines; ion-association
model (this paper)0; ion-association
model ( Lafon 1969)-X.
the model seawater to equilibrate
with
carbon dioxide at a partial pressure of
3.3 X lo-” atm (Fig. 2). If the carbon dioxide solubility data of Murray and Riley
( 1971) in acid solution are used, then the
total concentration
of carbon dioxide in
solution can be calculated as a function of
pH. Typical total concentrations of carbon
dioxide in seawater (0.002 to 0.0027 mol
kg-l) give rise to pII values in the range
8.2 to 8.3, indicating that the behavior of
the open system has been successfully predicted.
Since the modified ion-association model
gives a reasonable account of the behavior
of the system at equilibrium it can be used
to look at the influence of ion-pair formation
on the buffer capacity of the system. The
discussion will focus on the solution phase
and will not include the precipitation of calcium carbonate at this stage.
Closed systems
I used the ion-association model to construct a logarithmic
distribution
diagram
(Fig. 3) for the free components using pH
as the master variable (Sill& 1967; Stumm
4
6
8
PH
Fig. 2. Calculated
variation of total carbonate
concentration
(CT) with pH for an artificial
seawater in equilibrium
with carbon dioxide at a
partial prcsure of 3.3 x lo-” atm. CT is defined
by the equation
CT = [HzC0~*1 + [HCO,IT
+
[COa2-l
T. The horizontal line indicates a typical
value for CT in the open ocean (~0.0027
mol
liter-‘).
and Morgan 1970). The plots exhibit considerably more curvature than the corresponding plots showing the total concentrations ( e.g. Fig. 1) so that the diagram
cannot be constructed on the basis of simple rules ( Sill&n 1959; Butler 1964) but
must be derived from detailed calculations.
IIowever, once constructed, the diagram
presents a simple pattern.
The curves for the carbonate and bicarbonate complexes lie parallel to the lines
representing the free ligands ( Fig. 3). Their
displacement from the line of the free component can be deduced from
log
~hcOs
= log [MIICO;,]
- log [Ml&T -- log [ IICOs-] [?,
so that
log [ MHCOR] - log [ HCO&l
log
Khl~O,
+ log
=
CMl p;
( 3a >
similarly
log [ MCOJ
log
- log [ co32-.] =
K*iwco,
+ log
UN,.
(W
Buffer
capacity
of CO, in seawater
rI80
PX
60
O.
/
cT
40
8
8
6
4
10
PH
Fig. 3. Logarithmic
distribution
diagram
for
the components of the carbon dioxide system in
seawater at constant CT. pX = -log [Xl,. The letters identify
equations in Table 4 that describe
the formation
of the various
components.
For
the distribution
of
example
curve e describes
MgCOe” as a function of pH.
The medium ions exert their greatest influcncc on the carbon dioxide system at high
pH values (pH > 9) where the metalcarbonate complexes become the predominant species in solution (Fig. 4).
Calculation
of the buffer
capacity
As Pytkowicz (1972) has pointed out,
the buffer capacity of the carbon dioxide
sys tern in seawater can be accurately described in terms of the total concentrations
of the solution components. On this basis
the buffer capacity of the carbon dioxide
system in seawater can be defined by the
equation (Stumm and Morgan 1970; Butler 1964)
/3r/ln 10 =
c&K,” [ I-I’]
( [H+12-I- 4&*[H+]
+ &*K2*)
( [Hk12 -l- KI”[H+]
+ KI*K2*)2
= [H’] + [OH-] +
w2co3*l[I-IcoL+
+ [HCO&
D32CQ3*3
[HCO&[C032-]T
+ [ I-ICo/J~
+ [C032-]/
(4)
6
8
6
10
PH
Fig. 4. Distribution
of the components of the
carbon dioxide system cxprcssed as a percentage
of CT. The letters identify
equations
in Table
4 that describe the formation
of the various components ( cf. Fjg. 3 ) .
where Kz* = [HC03-].[H+]/[H2C03*]
and
K2* = [C032-.]T[H~]/[HCO~-]~.
The values
of pT calculated from the ion-association
model and from the experimental dissociation constants ( Hansson 1973a) using
equation 4 will be virtually identical (see
Fig. I ) . The buffer capacity curve (Fig.
5) shows maxima at pH values where
[H&03’k] = [IIC03-]T
and [HC03-lT =
[ COs2-]1r. From equation 4 the value of
these maxima is given by
(PT)mnx = CT In 10/4,
(5)
where CYl represents the total concentration
of all carbon dioxide species (Fig. 2). The
buffer capacity associated wjth the selfionization of water is predominant at pH
values <4 and >lO (Fig. 5). Although
it is possible to ascribe differences between
Fig. 5 and the corresponding picture for
carbon dioxide in freshwater ( Stumm and
Morgan 1970) to ion-pair formation, it is
inaccurate to assume that the buffer capacity of the system is extended in any way
240
Whitfield
Table 4. Reactions
considered
the buffer capacity of the carbon
in seawatm.
in calculating
dioxide system
Ionization fractions (al and cxo) can be
defined so that for reaction A
al(A)
Reaction
a
b
c
d
e
Ca*+
Mg*+
H,c03
Nat
Mg*+
f
Ca*+
Na+
HCOf
H20
g
h
i
-log, ,K
+ H2CO3 4CaHCOf
-I- H2CO3 eMgHC03+
s
H2CO3 C-l
HC03- e
HC03- *
I-Ico3-6
-I+
-i+
e
e
+ II+
+ H'
t H+
mo3NaHC03+ t H+
W03’
caco3o
NaC03Zco3
OH-
= [MX]/Cx
(94
ao ( A ) = [ HX] p/G,
5.450
5.502
6.124
and for reaction
w
B
f%(B) = PWG
6.745
(lo4
a0 ( B ) = [ HX] zP/C,Y.
-I- H+
7.665
+ Ii+ 7.913
+ H+ 9.186
+ H+ . g.776
(lob)
It can be shown (Stumm and Morgan 1970)
that the total buffer capacity of reactions
A and 13 in water can be calculated from
+ H+ 13.791
beyond the capacities calculated from equation 4. Calculations of the buffer capacity
from the ion-pair model represent a redistribution of the contributions to pT but do
not result in the introduction of any additional terms.
According to the ion-association model
the metal ions contribute to the buffering
capacity of the carbon dioxide system via
the reactions (Table 4)
+ I-I+ (6a)
M”’ + II&O:1 e ALU-ICO~@-~)-+
+ d[OH-]
P-P-.
dpI1
d[H+]
dpH
P->
Considering
the first term, al(A)
and
a0 (A) can be expanded to give ( combining 7, 9a, 9b, and the appropriate version
of 8 for each complex)
al(A)
= K$,JM]P(
K&s + ~K?ux[M]i.-t- [II:; )-I
so(A) = [H+](K&s+
and
~K*,,~ey[M]p+
Al
( 12)
[I-I+])-‘.
( 13)
M”- + I-IC03- = AJEO:,‘“-~)+ + II+.
(6b)
The buffer capacity of such a system of
reactions can be approximated by considering the general buffer reaction
M + 11X = MX + I-I-’
(B)
The total concentration of ligand X( =C032or IIC0,7-) is given by
Cx = [Xl,
+ [HXIF + x[MX]
Al
(7)
for a system containing
M cations (M
= Na-+, Ca2+, Mg2+) forming ion-pairs with
X.
The stoichiometric constant for reaction
A is given by
K?KS = [MX][H+]/[M]~[IIX]p.
(8)
equations
12 and 13 for reac-
(K:$,, + ~KLJ,,y[M].
AI
= CsdaL/dpH.
(4
where 11X may also dissociate according to
the equation
HX = I-I’ + x.
Combining
tion A,
+ [I-r-+])-”
(14)
Therefore from the definitions of al(A)
and cyo( A) ( equations 9a and 9b),
c d49
-
x dpH
= 2.3[MX] [E[X]p,‘Cx;
(15)
= 2.3[X]1,JHX]p,‘C,s.
(16)
similarly
c
d%(B)
~
x dpH
When these values are combined with the
corresponding derivatives for [OH-] and
[H+] (Stumm and Morgan 1970) the total
buffer capacity becomes
Buffer
capacity
Table
5.
Feature
B/;“lO
x104
Condition
a
Approx buffer
capacity
[:H+]
First
maximum
Second
minimum
Second
('H*COJ = rMfy1
[H2C03] + bfC031'
[:H,C03] = [MCOJ]
[H2C03] + @CO31
Third
minimm
10
fea-
First
minimum
maximum PJ1q
6
of predominant
capacity curues.
Identification
tures on the buffer
4
241
of CO, in seawater
= ~-ICO~]~’
= CMCOJ
[:mco31 = [OH-I
[MHCOs + [H+]
[MCOJ] + [OH-]
[MHCO~] + [OH-]
PH
Fig. 5. The buffer
capacity
of the carbon
dioxide system in seawater as a function
of ~1-1.
The solid line follows ,& calculated from the experimental
data of Hansson ( 1973a) using equation 4. The results of calculations
from the ionpair model using equation 17 are shown as open
circles. The individual
contributions
of the magnesium complexes
(equations
b and e: Table
4) and the free ligands (equations c and 32: Table
4) are shown as broken lines.
Prl,/ln 10 = [I-I+] + [OH-]
+ ~[HX]~~~[Xl./CX
(17)
This solution is approximate in that the
individual
reactions have been treated independently.
The buffer reactions (Table
4) can be treated in this way provided
that their equilibrium
constants are adequately separated. The error will not be
more than 5% provided that the ratio of
successive constants is not greater than 100
( Stumm and Morgan 1970). Clearly reactions a to CZcan be treated independently
from reactions e to h with little error, but
the ‘reactions within each group will not
bc mutually i.ndependent so that the resulting value of prP will be in error, particularly
in the region of maximum buffering. However, the calculated curve follows the experimental curve quite closely (Fig. 5).
The maximum error observed in pIP using
equation 17 is about 15% in the region of the
second buffer maximulll (Fig. 5). The profile of the first buffer maximum is accurately reproduced.
Much greater errors
of
* M E Na, Mg or Ca. For the contribution
the free components substitute
[HCOJ-&, for
2[MHC03]
and [CO3 ], for [MC03].
The corresponding pH values and buffer
capacities
can be read off from Fig. 3.
arc introduced if plr/‘ln 10 is calculated
from the logarithmic distribution
diagram
( Fig. 3) by summing the concentrations of
all components rcprcscnted by lines with
slope SL oi -1 (Stumm and Morgan 1970)
since the lines in the present diagram show
marked curvature, particularly in the region
of maximum buffering.
A more exact but
far more complex solution can be obtained
by following through the derivation given
by Stumm and Morgan ( 1970) for a multicomponent system. It is sufficient, for the
present purposes, to use equation 17 to calculate the relative contributions
of the
various reactions (Table 4) to the total
buffer capacity. Since equations 4 and 17
are two alternative
descriptions
of the
same system pY1=pII, if both descriptions
are valid. The predominant features of the
buffer capacity curves associated with the
various postulated reactions (Table 4; see
aZso Fig. 5) can be estimated quite simply
from the logarithmic distribution
diagram
(Fig. 3, Table 5).
From the relative contributions
of the
various reactions to the total buffer capacity it is clear (Fig. 6) that, if the ionassociation model is to be espoused, the
reactions resulting in the formation
of
metal-carbonate ion-pairs (reactions e to g :
242
Whitfield
3
80
0
/B0
a
60
1
2
IP
40
PH
6
20
io
PH
1
4
Fig. 6. Percentage
contributions
of the various reactions listed in Table 4 to the buffer capacity of the carbon dioxide system in seawater as
calculated
from the ion-association
model.
The
letters on the curves refer to the reactions listed in
Table 4.
The positions of the maxima and minima shown
in Fig. 5 are indicated
by arrows.
Table 4) make major contributions to the
buffer capacity of the system in seawater
above pH 7.5. The formation of MgCO:,O
contributes more than 50% of the total at
pH 8.5.
Influence of seawater composition
the buffer capacity
on
The effect of solution composition on the
buffer capacity can be illustrated by the
simulation of acid-base titration curves for
seawater of different compositions and by
studying the effect of variations in composition on the pH of a standard seawater
solution.
The concentration
of free magnesium
ions in solution can be altered either by
changing the total magnesium concentration (maintaining
the charge balance by
the addition or subtraction of sodium ions)
or by changing the total sulfate concentration (maintaining
the charge balance by
the addition or subtraction
of chloride
ions) so as to alter the proportion of magnesium complexed by sulfate ions. Both
procedures
were used by Wangersky
(1972a).
Titration curves simulating the addition
of strong acid or strong base to seawater
(Fig. 7) were calculated from the ionassociation model. The value of CT (see
equation 5) was held constant in all titra-
‘\\r
4
I
a
I
24
meq
strong
acid
I
L
1
40-
56
x 10
Fig. 7. Calculated curves corresponding
to the
titration
of seawater with strong acid. The acid
used in the calculations
was sufficiently
concen
trated ( 20 M ) to make concentration
corrections
negligible.
Crr was kept constant throughout
the
titration.
The system was out of contact with the
atmosphere and initially
contained only 10-l” MII’.
Solution compositions were as follows (with charge
balance maintained
as described
in the text)
l-artificial
seawater (see F in Table 3); 2-artiIicial seawater with [Mg”+]T x 2; 3-artificial
seawater with [Mg”‘] T x 0.5; 4-artificial
seawater
with
[SO~~‘-IT x 0.5; S-artificial
seawater
with
[SO:,“-IZ~ X 2. A solution with [Mg*+]T x 0.5 und
[SO.,%]T X 2 would follow
curve 3 initially
and
then curve 5 at low pII.
tions so that the maximum buffer capacity
of the system will be unaffected by change:<
in solution composition.
However the titration curves will be displaced from one
another since changes in sohrtion composition are likely to influence the stoichiometric cons tan ts ( K1 *, Kz*) and the details
of the buffering process (Fig. 6). Although
the [Mg”+], : [SOd2-lT ratio was altered
from 0.48 to 7.61 (cf. 1.90 for normal seawater) as suggested by Wangersky (1972aI1,
the titration curves show very little alteration in the buffer capacity of the system
(Fig. 7). Alterations in [ S042-]21 show the
greatest influence at low pH values where
the reaction S0.12- + H+ * HSO,- will play
a significant role in the buffering process.
Variations in [Mg2+]T have most effect at
high pH values where, according to the ionassociation hypothesis, the formation
of
Buffer
capacity
of CO, in seawater
PH
I
I
o-04
0.08
ml
‘ti tranf’
Fig. 8. The influence
of changes in solution
composition
on the pH of standard seawater.
I.
Starting solution contains 0.0054 M [Mg”]T
and
Each 10 ~1 of titrant increases
0.5724 M [ Na’]r.
[M~“]T by 0.02 M and decreases [Na+]T by 0.04 M.
II. Starting solution contains 0.00284 M [SO.?.]T
Each 10 ~1 of titrant inand OX054 M [Cl-IT.
creases [SO,‘-]T by 0.01 M and decreases [Cl-IT
by 0.02 M. III.
Starting solution as defined in
Table 3 (see F), Each 10 ~1 of titrant increases
[SO?-IT by 0.005 M and [Na+]T by 0.01 M and
decreases [Cl-IT by 0.01 M and [Mg2’lT by 0.005 M.
0 ther components have the concentrations
listed
in Table 3 and these arc maintained
constant
throughout
the titration.
MgC0,70 ion-pairs dominates the buffering
process (Fig. 6). The overall effect is
small and would appear at first to support
his proposal (Wangersky 1972a, p. 5) :
The effects of fairly large variations in
composition are in fact fairly small.
This is only to be expected if the entire mass of inorganic solutes in seawater is involved in the equilibria.
However the differences between the
various titration curves are small simply
because magnesium is always present in
large excess over carbonate so that the actual concentration of the MgCOsO complex
is not greatly affected by the changes in
solution composition shown in Fig. 7. Since
[ Mg2+],, does not appear in the buffer capacity equation, changes in its value are
only indirectly felt.
243
This point is more clearly made if much
larger excursions in the [Mg2’] r : [ SO4”-]21
ratio are considered. From the acid-base
titration curves (Fig. 7) it was observed
that, using the present model, 2.55 mM of
strong acid are required to adjust the seawater to pH 8 in a closed system. To study
the effect of changes in [Mg”+], on the pH
of seawater this amount of acid was added
to a seawater with the usual composition
(Table 3) but with only a tenth the normal magnesium concentration
(i.e. 5.4
mM ) and with the sodium concentration
adjusted accordingly to maintain the charge
balance. The pH of the resulting solution
was then calculated together with the distribution of species in the carbon dioxide
sys tern ( represcntcd in Fig. 3). The solution composition was then altered by adding magnesium ions and removing sodium
ions to maintain the charge balance and
the same parameters were calculated. The
results are shown as a titration ( curve I:
Fig. 8) for clarity. Each 0.01 ml of the
hypothetical titrant changes the magnesium
concentration by an increment of 0.02 M
and decreases the sodium concentration by
a step of 0.04 M. Therefore the normal
seawater co:mposition is attained after the
addition of about 0.025 ml giving a pH
of 8. The titration was continued until the
Vahe
Of [ Mg2-I-1, was more than five
times
the normal seawater concentration
(i.c.
0.2854) and the sodium was almost totally
depleted
( [ Na] T = 0.0124). The
ionic
strength varies from 0.659 to 0.939 M during the course of the titration.
The effect
of this variation on the free ion activity
coefficients
(Table 2) is small and has
been neglected. The pI1 of the system is
remarkably resistant to changes in [ Mg2-c]T
(Fig. 8: curve I). A shift of [Mg2-b]II from
a tenth to five times the normal seawater
concentrations results in a decrease in pH
(reaction e: Table 4) of only 0.55 pI1 units.
It is instructive to look at the influence of
this change in composition on the distribution of species in the carbon dioxide system. From the buffering point of view the
most important parameters at this pH are
244
Whitfield
h
[MCO,l
B
0.10 -
0*05 c
I
0.05
I
0.10
W41 T
Fig. 9. Variation
in concentration
of metalcarbonate
ion-pairs
accompanying
the titrations
shown in Fig. 8. The solid lines show the variation
of [MCOJ
during the titration.
The vertical line
indicates
norm‘al seawater composition.
A. Corresponds to curve I, Fig. 8. The dashed
lines show the variation
that would be expected
over the corresponding
pH range if [ M]~~ were
held constant.
The curve marked z corresponds
to the sum [NaCO;]
+ [MgC030].
B. Corresponds
to curve II, Fig. 8.
the concentrations
of the MgC030 and
NaCOs- ion-pairs ( Fig. 9A, cf. Fig. 6).
In the natural situation, magnesium removal is likely to be compensated for by
an increase in the sodium concentration so
that the total buffer capacity resulting from
the formation of metal-carbonate ion-pairs
will only be slightly affected, even by the
total depletion of magnesium (Fig. 9A).
Large increases in the magnesium concentration will also have a small effect on
the buffer capacity, not because of any
compensation from the concomitant
decrease in sodium ion concentration, but bccause the concentration
of MgC030 iortpairs is limited not by the value of [ Mg2+]21
but by the availability
of carbonate ion:;.
If it were postulated that some other species (e.g. K+) that did not form ion-pails
with carbonate were introduced to maintain the charge balance, the buffer capacity
would not be markedly affected unless the
magnesium concentration was depleted to
such an extent that [ Mg2+lT became the
limiting factor in the formation of MgC030
ion-pairs (i.e. about a tenfold depletion of
[ Mg2+] Ip would be required).
The ovcral!l
effect agrees, in a qualitative manner, with
Wangersky’s postulates, but the introduc:tion of the concept of an interlinked pHstatting system would appear to be superfluous. This is clearly illustrated in Fig. 6
where the minimum in the buffering capacity is shown to coincide with the situation
where most of the reactions listed in Table
4 play a significant role in the bufferin::
process. Where the buffer capacity is at
a maximum the buffering process is dominated by a single reaction.
Wangcrsky (1972a, p, 5) suggested that
since three-fourths of the sulfate present in normal seawater is tied up in
ion pairs-in
competition with carbonate and bicarbonate
for cations-a
change in sulfate concentration should
be directly and strongly reflected in
pH change.
procedure has also bee::1
A “titration”
used to study the effects of alteration in
the sulfate concentration on the pH of sea.water. In this instance the starting point
was a seawater containing 0.00284 M sullfate and 0.6054 M chloride. Each O.Ol+J
increment
of titrant
increases [ S0,2-] T
by 0.01 M and decreases [Cl-] by 0.02 M.
The titration was continued until [ S042-]yl
Rufjer capacity
245
of CO, in seaumter
reached five times the normal value (0.143
M ) . The change in ionic strength throughout the titration (0.682-0.819 M ) was small
and its influence on the activity coefficients
was neglected. The overall shift in pII
( -I- 0.11 units curve II : Fig. 8) is only a
fifth of the value observed for corresponding alterations in [Mg”-‘] T.
There is evidence (Berner 1972) that
the sulfate budget of the ocean is in a state
of imbalance and that the present value of
[ SOh2-lT may be doubled in 14 million
years. My calculations indicate that much
larger excursions in sulfate concentrations
will result in only a small change in the pH
of seawater due to shifts in the ion-associCalculations of the conation equilibria.
centrations of MgCO,?O and NaCO:$- (Fig.
9B) indicate that a decrease in the concentration of MgCOso (because of competition
with the formation of MgSOdO) is almost
compensated by a simultaneous increase in
the concentration of NaC03- resulting from
the release of carbonate ions from the
magnesium ion-pairs. Depletion of magnesium and increase of sulfate concentration both tend to increase pH (Fig. 8),
and the largest effects are expected at low
magnesium concentrations
(Figs. 8 and
9A). However, a tenfold depletion of magnesium accompanied by a threefold increase in sulfate only results in a pH shift
of 0.25 units ( curve III: Fig. 8). The pH
of seawater is therefore particularly
resistant to changes in the composition of the
major electrolytes.
Wangersky ( 1972a) supported his arguments by presenting experimental data on
the influence of variations in the partial
pressure of carbon dioxide on the pH of
various artificial seawaters. These conditions will now be simulated with the aid of
the ion-association model,
Open systems
The procedures used to analyze the carbon dioxide equilibria
in closed systems
can also be applied to open systems (e.g.
Fig. 2) provided that care is taken to treat
the gaseous and aqueous phase components
on the same concentration scale.
From the measurements of Murray atid
Riley ( 1971) the concentration of I-I&OS*
is related to the partial pressure of carbon
dioxide ( PcO,) by the equation,
as
=
[II2C~O:I”l/~co,
= 289 x 10-d mol liter-l
atm-l
(18)
at 25°C and 1 atm total pressure. For the
purpose of my calculations the concentration of carbon dioxide in the gaseous phase
[ COJg was expressed in units of mol liter-l
using the expression,
[CO&
= Pco, x V/RT
= 0.0409 PcoZ mol liter-l.
(19)
The master variable diagram at constant
P
analogous with Fig. 3 for closed systc?ZZ, indicates that over most of the pH
range the concentrations of the bicarbonate and carbonate species may bc represented by two systems of parallel lines with
slopes +l and +2 (Fig. 10). The cquations of these lines can be simply calculated. For carbonic acid ( equation c:
Table 4)
log [ IICOn-] JY=
(log [H&Ioi7*] + log K&o,)
+ pH.
(20)
The term in brackets is constant. Similarly
for the formation of the metal-bicarbonate
ion-pairs
log [MHCOs]
(log
[M]F
=
+ log
~%mco,
+ log
[H2C03*])
+ PI-I,
(21)
where the formation constant refers to the
relevant equilibria a, 79,or d (Table 4).
For the carbonate complexes
log [ co,2-]Io =
(log [H2C03*]
an d
log [MCOJ =
(log [H2C03*]
+ log K:~oo,) + 2 pH
(22)
+ log ZU,,o, -I- log [Ml,)
+ 2 pH. (23)
The equilibrium constants used in equations
22 and 23 refer to reactions derived by
summing equation c (Table 4) with equations h and e to g respectively.
At high pH vahies the carbonate complexes represent significant proportions of
246
Whitfield
t
seawgter
-.-.~
PX
6
8
4
6
8
PH
Fig. 10. Logarithmic
distribution
diagram for
the components of the carbon dioxide system in
seawater at constant Pco,. The letters identify
the equations in Table 4 that describe the formation of the various components.
For example
curve f represents the distribution
of CaC,Ono as
a function
of pH. pX =-log
[Xl,.
The curve
marked CT corresponds
to Fig. 2 and the horizontal line marked “seawater”
indicates the typical open ocean situation.
the total metal concentration so that the
free metal concentrations in equations 21
and 23 are no longer constant and the plots
deviate from linearity ( Fig. 10). The curvature becomes noticeable above pI1 8.5.
Comparison of equations 3a and 3b with
equations 20 to 23 indicates that below this
pH the relative contributions of the various
equilibria to the total buffer capacity will
be the same in both open and closed systems. The deductions drawn from Fig. 6
may therefore be used in the discussion of
open systems.
Wangersky (1972a) considered the influence of solution composition on the pH
of open systems equilibrated with various
partial pressures of carbon dioxide. I have
reconstructed his experimental conditions
here on the assumption that the system
reached equilibration
in the course of his
experiments. The calculated curve for a.rtificial seawater ( curve 2: Fig. 11A) runs
parallel to that obtained experimentally by
Wangersky (curve 1: Fig. 1lA) but is djsplaced into the more alkaline region by one
pII unit. The calculated curve would a:ppear to be in better agreement with the accepted properties of seawater, in that tyI)ical atmospheric values for pcoe give a PI-I
of 8.2 to 8.3 whereas Wangersky’s data give
a pH of 7.2 to 7.3. The reason for this djscrepancy is unclear as Wangersky giv#es
few experimental details.
Th,e influence
of varying
[ Mg2 ‘1Il :
[SOL~2-]~~ratios on the curves (Figs. 11A
and 11B) is in accord with the deductions
drawn from calculations on closed systems.
As Wangersky suggests the effects are small,
but my calculations failed to reproduce in
detail the behavior that he observed. A
decrease in [Mg2+], should produce a shift
to high pH and an increase a shift to low
pH (Fig. 1lA: curves 4 and 3; cf. Fig. 8).
Wangcrsky observed this behavior only at
low values of PcO,; in all other cases the
curves were shifted to higher pH values by
an alteration in [ Mg2+lT. This behavior is
not readily explained.
Both the model system and the experimental system show similar shifts in pH
when [ S042-] T is altered ( Fig. 11B ) , although the marked shift observed by Wangersky to lower pH when the sulfate concentration is decreased is unexpected.
The calculation and the experiments are
in close agreement when the effects of simultaneous
variations
in [ Mg2+lIT and
[SOd2-] T are considered ( curves 4 and 15:
Fig. 11B).
Conclusions
There can be no doubt that the composition of the ionic medium influences the
buffer capacity of the carbon dioxide system since the experimental
equilibrium
constants ( apparent or stoichiometric j are
observed to alter when the medium changes
( Ben-Yaakov and Goldhaber 1973; Hansson 1973a).
Stoichiometric
constants of high preci-
Buffer
capacity
of
CO, in seawater
247
seawaters with various compoFig. 11. The influence
of variations
in PCO~ on the pH of artificial
sitions. Changes in the magnesilrm concentration
are accompanied
by complementary
changes in the
Similarly
changes in the sulfate concentration
sodiun concentration
to maintain the charge balance.
are balanced by changes in the chloride concentration
(see text).
A. l-Artificial
seawater ( Wangersky
1972a); 2-artificial
seawater
(this paper);
3-[Mgz’],
X
2; 4-[Mg2+]T
X 0.5. The h orizontal lines mark the normal range of pcoa in the atmosphere.
B. l-Artificial
seawater (this naner):
2-rSOi”-]~
X 0.5; 3-[S0.?-]~
X 2; 4-[SO42-]r
X 0.5, [Mg”],
x 2; 5-[SO4’-]T
x 2, [Mg’+& x 0.5. - ’ ’
-
sion are now available (Hansson 1973a)
together with a pH scale for seawater as
an ionic medium (Hansson 19731>). Ruffcr
capacities calculated from these stoichiometric constants can be accurately reproduced, at 25°C and 1 atm pressure, by a
modified ion-association model,
If for geochemical or physicochemical
reasons we wish to break down the total
buffer capacity of the system into its component parts, the ion-association model provides us with a convenient summary of the
various interactions in solution. Using this
model we can show that, at normal pH
values, the formation of MgCOn” makes the
major contribution
to the buffer capacity
of the system in seawater.
Quite large variations in [Mg2+lT cause
only slight alterations in the pH and the
buffer capacity because the concentration
of the magnesium carbonate ion-pair represents only a small proportion of [Mg2+lTT.
Only at very low magnesium concentrations is the effect significant and, in the
natural situation, it is liable to be compensated for by complementary changes in the
concentration of NaC03- as the charge balance is maintained.
Indirect changes in the free magnesium
concentration brought about by alterations
in the sulfate concentration have a very
small effect, partly because of the influcnces noted. above and partly because the
carbonate ions, relcascd as magnesium sulfate ion-pairs are formed, are taken up by
the sodium ions.
All of thcsc effects can be treated quite
effectively in closed or open systems by
the ion-association
model and no new
mechanisms are required. In fact, unless
the cation concentrations become severely
depleted, the indiffercncc of the seawater
pH to changes in solution composition
arises because the major cations are only
slightly complexed rather than from their
involvement in the whole network of equilibria.
Pytkowicz (1972) agrees that the formation of ion-pairs influences the effective
concentrations of the carbonate and bicarbonate ions in seawater and therefore in
turn affects the apparent constants, the pH,
and indirectly the buffer capacity. He emphasizes, however, that the ion-pairs do
not buffer seawater and that this is still
248
Whitfield
done by the classic reaction,
2IICO3-, total * H&OS*
+ COS2-, total.
This contention is stated quantitatively
in
equation 4. However, if the ion-association
model is to help us understand the reason
why the buffer capacity of the carbon dioxide system is different in seawater from
that in distilled water, then it is valid to
express the total buffer capacity in terms
of the relative contributions of the various
ion-pair formation reactions (equation 17,
Figs. 5 and 6). The difference between this
view and that of Pytkowicz is purely one
of semantics.
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Submitted:
Accepted:
1 August 1973
5 December 1973