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Chemistry of dissolved inorganic carbon in estuarine and coastal brackish waters
Estuarine
and Coastal Marine
Science (1975) 3, 325-336
Chemistry of Dissolved Inorganic Carbon in Estuarine and Coastal Brackish Waters
W. G. Mook and B. K. S. Koene Environmental Isotqpes Laboratory, the Netherlands Receked 15 July 1974
University
of Groningen,
The rapid increase of the first and second apparent dissociation constants of carbonic acid with salinity results in a remarkable pH distribution in an estuary. On going down-stream, instead of a gradual continuous increase in pH from fresh water values of 7.0 to 7.5 to a marine value of 8.2, the pH shows a certain minimal value at low salinity. With high pH fresh water a sharp decrease at low salinity is observed. Depending on the alkalinity ratio of the fresh river water and the sea water, the carbonate ion concentration in an estuary can remain surprisingly low up to relatively high salinities. This phenomenon might affect the shell growth of certain molluscs. In order to obtain the proper dissociation constants for brackish waters of low chlorinities, a practical adjustment of well known data for pure water and sea water is made: pKi’ (for 0~C1~9%,)=3404~71/T+o~o3z786T-14~8435 -0~089zrCZf pKp’ (for o
ccop CHCOQ cc03 Cl (S) K’ K,’ KS’ CCO, TA CA PH
T
activity of the hydrogen ions, defined by pH = -log a “. molar concentration of dissolved CO* and H,COs. molar concentration of dissolved HCO; ions. molar concentration of dissolved CO:- ions. chlorinity (salinity) of the water. first apparent dissociation constant of carbonic acid. second apparent dissociation constant of carbonic acid. first apparent dissociation constant of boric acid. total dissolved inorganic carbon. titration alkalinity. carbonate alkalinity. values are based on the NBS buffer standards. absolute temperature (at t =o’C: T=273*15 K).
Introduction When fresh and sea water are mixed the individual CO,, HCO, and COs- do not behave conservatively in the dissociation equilibria according to: H,O + CO, 5 H + + HCO, (The concentration
of H&O,
is negligibly
small.) 3%
dissolved inorganic carbon fractions since chemical rearrangement occurs
2 CO;-
+ H+.
326
W. G. Mook & B. K. 5’. Koene
Quantitatively, these shifts are complex, sincethe first and seconddissociationconstants (def. by Lyman, 1957): K;
= a H . c HCO&CO,
Ki
= aH.cC&HCO,=
= Kl~c~21~
HCO,
and K,YHCO,~YCO,
(1)
are functions of the ion activities which strongly depend on the ionic strength (and ionic composition) of the water. Generally, fresh waters can be consideredto be dilute solutions. However, the salt content of seawater affects the activity coefficientsmore than is predicted by the Debye-Htickel theory, due to extensive formation of ion pairs and complexes.The problem of finding the activity coefficients over the entire natural range of chlorinities is consideredin a separatesection. As a consequenceof the large influence of salinity on the activities of, especially, the HCO; and CO:- ions, chemical rearrangement occurs in such a fashion that, when mixing of fresh and sea water occurs, the acidity showsa maximum (pH minimum) at a specific mixing ratio. This effect, and someconsequencesof it, will be discussedin the next sections. In the study of the stable isotopesof carbon in natural waters, the massspectrometrical determination is carried out on the total amount of CO, extracted from the sampleafter acidification. In general however the 813value of the dissolvedbicarbonate, being the largest fraction, is more meaningful from an isotopic point of view (Mook, 1970, 1972). Thus, the al3 of total carbon hasto be corrected for the isotopic concentration of the other two species, having different values, according to: Ps(HC0;)
= #a( X0,)
- s
EEco, (CO& a
- 2s
&o,
(CO:-).
(2)
2
The relevant fractionation values E were given recently by Mook et af. (1974). It will be shown that, apart from the temperature and chlorinity of the sample,it is only necessaryto know the pH, provided that Ki and Ki are known.
The dissolved carbon fractions cannot be determined directly. Relatively easy to measure (by acid titration) is the titration (or total) alkalinity (in mequiv./l) : TA=c
HCOI+
2cC0,
+CH,BO,
+cOH-
cHs
where, in the natural pH range, the last two terms can generally be neglected. The borate concentration is given by Skirrow (1965): CW“‘,
Kf, CB = K;, + aH’
where KB ’ is the apparent constant of the first dissociation of boric acid and the borate content ZB=2*2 x IO-~X CZ(%,). According to Edmond & Gieskes (1970), Kk is represented by pK~=2291~9o/T+o~o1756T-3~385-o~32051Cl~ over the chlorinity range of 4 to 36%,. At lower chlorinities, however, the borate content of the water is so smallthat we use their relation over the entire chlorinity range.
Dissolved carbon in estuarine waters
327
The carbonate alkalinity, defined by: CA=c
I%COs+ 2cco3
(3)
is thus related to the total alkalinity by: K; XB
TA=CA+
(4)
KI, 3-a”’
The carbon fractions can be expressed in terms of CA (from Equations ~~~~=a~.D;cuc~
I
and 3) by:
3 =aHK;.D;cco3=K;K;.D
(5)
where D = CA/(a HK; + 2K;Ki). The molar concentration
of total dissolved inorganic carbon is defined as: xco!2
=
cCO,
+
cHCOa
+
(6)
cC03a
We define two further quantities which we will use in the next sections: Qt = XO,ITA
(7)
and Q = CCO,/CA
= (ai + a,K;
+ K;K,$/(aHK;
Furthermore, we will deal with the fractional concentrations Equation 2), as derived from Equations 5 and 8: cco,/ X0, where E = (1; + a,K;
= a z/E;
cHCO,/
X0,
= a HKJE;
+ zK,K,$.
(*I
of the carbon fractions (cf.
CC&
X0,
= K;Ki/E
(9)
+ K;K,&
Brackish
water
We prefer to use the chlorinity as indicator of the brackishness related to chlorinity by (Gieskes, 1974):
of the water; the salinity is
S = 1.80655 Cl
(10)
whereas according to Gieskes the formula (Cox, 1965) S = 1.8050 Cl + 0.03%~ is better in the Baltic. In the Figures also S is indicated based on Equation of brackishness, b, is then defined by: CZ= (I-b)Cl,
+ bCI,,,,
IO.
The degree (11)
where f and m denote the fresh and marine values, respectively. If CZr=o the brackishness b = Cl/Cl,,,. In order to be able to calculate the pH distribution in an estuary, the assumption has to be made that we are dealing with a closed system in which we consider the conservation of the total inorganic carbon content and of the titration alkalinity. This implies that no CO, is lost from the water into the atmosphere and that, for instance, no precipitation of calcium carbonate occurs.
328
W. G. Mook & B. K. S. Koene
Then :
and
TA = (I--b)TAf
+ bTA,.
(4
The Q, value for a brackish water sampleas defined by Equation 7 then is:
Q,=(a~+P)(uB+u.K;+K;K~) W fl + (1H)(UHK; + 2J-W;)
(13)
where P = KA( I - ZB/TA). From this a cubic equation for an is deduced,which is essentiallysimilar to the one presented by Gieskes(1974): u;+Au;+Bu”+C=o A = K;(I-QJ
where
+ K;(I-
B = K;K;(I--2&J
(14)
CB/TA)
+ K;K;(I-Q,-
C = K;K;K;I(I--2Qt-
EB/TA)
ZB/TA)
introducing the possibility of calculating the general characteristicsof the pH distribution along the chlorinity gradient of an estuary. A numerical analysisshowsthat for pH calculation to two decimal placesit is justifiable to regard the borate concentration asconservativeduring mixing. If this assumptionis made, CA is alsolinearly related to the degreeof brackishness:
CA = (I --b)CA, + bCA, so that:
QJ~-VQJ+~Qm (14)X
where X = CA,/CA,.
+ b
Equation 14 then reducesto a quadratic form: a; + uHK;(l-Q)
+ K;K;(I--2Q)
= o.
(15)
Before these equations can be solved it is necessaryto obtain values of the dissociation constantsK; and Ki appropriate to the mixed water. The apparent dissociation constants of carbonic acid Following the pioneer work of Buch and co-workers (Buch et al., 1932; Buch, 1951), Lyman prepared a practical set of apparent dissociationconstantsfor seawater (Equation I). The completeand original seriesof determinationswasrevised by Edmond & Gieskes(1970) revealing equations for the temperature- and chlorinity-dependence of the constants (pK = -1ogK): (1957)
pK;
=
3404’7IjT
pK; = 2902*39/T
+O*032786T-IIq.7122-O*ICj178~~"3
+ o~o2379T-6~471o-o~4693~1”~.
(16)
Dissolved carbon in estuarine waters
329
Although theseequationsare the best approximations to marine data, they are not intended for use at low chlorinities and do not extrapolate to the thermodynamic constants at CZ=o (Harned & Davis, 1943; Harned & Scholes,1941), which are representedby the equations: pK, =
3404*71/T
pK, =
2902’39/
0*032786T-14’8435
+ T
+ 0’02379 T-6.4980.
(17)
Redetermination of dissociation constants has also been carried out by Hansson(1973) for the salinity range 20-40%~. In the absenceof accurate measurementsof K; and Kk at low chlorinities we have made smooth adjustmentsbetween the values determined at higher chlorinities and thosefor pure water. The slope of the pK,(C1) relation at CZ=o can be calculated according to the Debye-Hiickel theory for dilute solutions. The apparent and thermodynamic constantsare related by : PK;-PK,
= logy “co,-log YCO,
where y refers to the respective activity coefficients. According to the DH-theory (Garrels & Christ, 1965):
Ad(1-0 log
Y HC03
=
1 +
ti WI+
In aqueoussolutions: A=o*5085 and B=0*3281 x IO*, and for the bicarbonate ion: i N 4.3 x IO-~. According to Lyman & Fleming (1940), the ionic strength of seawater is given by: i.~ =
0~001,.+7
j-
0.03592
Cl + 0~000068 CP.
The activity coefficient for dissolvedcarbon dioxide is defined by: log yco, = log a,-log cr, where a, and a, represent the solubilities of CO, in pure water and seawater, respectively (Buch et al., 1932). The values are given by Gieskes(1974): -1Og a, = -2262*38/T-oao178471T + 15’5873+ -2.77676
cl(0~0117950-
x IO-5T).
The resulting DH-curve is shown in Figure r(a) where the pK; values according to Harned & Davis (1943) and Edmond & Gieskes(1970) are plotted as a function of Cl*. The curve agreeswell with the activity coefficients as computed by Kemp (197Ia, 6). Initially, it seemedto us that a good approximation would be obtained by drawing the tangent from pKr at Cl=0 to the curve of Edmond & Gieskesplotted versusCP, in which presentation Debye-Hiickel predicts a linear behaviour of pK; for low p. Now that the DH theory turns out to give exactly the sameslope at Cl=0 we feel confident that our procedure is justified. The same is true for other temperatures. A similar adjustment procedure is applied to the values of pKi [Figure r(b)]. The resulting pK’ valuesare represented by: PK; = 3404*71/T + o.o32786T-14~8435-0~08921 Cl*
pK; =
2902*39/T+
0*02379T-6.4980-0'7531 cl*
(18)
W. G. Mook & B. K. S. Koene
330
It should be noted that at very low chlorinities severediscrepanciesexist between the pK; values obtained by extrapolation of the Edmond & Gieskesequation and those calculated from the DH theory [Figure a(b)]. Obviously, complex formation contributes appreciably to the lowering of the activity coefficients. In Figure x(a) and (b) the chlorinities below which Equation 18 is valid are indicated by an arrow.
6.0;
’
I I
2 Cl ‘a
3
4
Figure I. (a) pK,’ for the first dissociation of carbonic acid. The arrow indicates the chlorinity, below which the pKr’ relation presented in this paper is valid. At higher chlorinities the equation of Edmond & Gieskes (1970) applies. (b) p& for the second dissociation of carbonic acid. The arrow indicates the chlorinity, below which the pK,’ relation presented in this paper is valid. At higher chlorinities the equation of Edmond & Gieskes (1970) applies. (0) Hamed & Davis, 1943 ; (0) Buch, 1951; (0) Lyman; (- - -) Edmond & Gieskes, 1970; (- - - -) Debye-Hiickel; -, this paper.
The rapid increaseof K; and K; with increasing chlorinity (Figure 2) is of importance when studying fresh water carbon chemistry, including stablecarbon isotopic work. The use of the thermodynamic constants or those of Edmond & Gieskes,in order to calculate the CO, percentagein river waters containing IOO mg/l of chloride, causeserrors of about 15%.
The pH diatribudon
in an estuary
Using the proper setsof dissociationconstantswe are able to calculate the pH distribution in an estuary for which the characteristicsof the fresh and seawater componentsare known.
Dissolved carbon in estuarine waters
331
Figure 3(a), (b) and (c) shows the dependenceof the distribution on pHr, pH,, TAfITA,, Cl,,, and temperature. The most striking feature is the pH minimum which is observed for those curves having lower initial pHr values. As will be pointed out later, this might have certain implications for the formation of shell carbonate by molfuscsin an estuary.
r OO
. . . . 5
IO
I5 Cl (Xc.)
! 20
25
Figure 2. (a) The first apparent dissociation constant (Kr’) according to the values of pK,’ presented in Figure :(a) as a function of chlorinity and temperature. The dashed lines indicate the deviations of the equations from Edmond & Gieskes and those from these authors in the chlorinity ranges where they do not apply. (b) The second apparent dissociation constant (Ks’) according to the values of pKa’ presented in Figure r(b) as a function of chlorinity and temperature. The discrepancy between the actual values and those calculated according to the Debye-Htickel theory (dashed line) is obvious.
At the high fresh water pH the pH sharply decreaseswith increasing chlorinity. An example of this is to be found at the outlet of the Dutch IJsselLake into the Wadden Sea. Due to atmospheric exchangeduring the large residencetime of the river water in the lake, pH values as high as 9.5 are observed (Mook, 1970).
W. G. Mook & B. K. S. Koene
332
We originally met with the peculiar effect of chlorinity on pH in the estuary of the Western Scheldt where we needed the chemical composition of the water for correcting the carbon isotopic abundances (Mook, ‘970). In Figure 4 two series of measurements made on board the B’h~~ra [Netherlands Institute of Sea Research (Texel)] are given. The calculated curves
9.5
,
9-e
1
I
I
1
I--
(b)
(a)
J
7.5
,’ ,I
7.0
I 0
l--J
!
9.5
5 I
IO I
15
5
IO
I
I
15
20
I
20
I
___--0
__--I
,
0
5
_/-
.’
/
,’
I
IO c/ ( %.I
,’
/
I
15
20
(cl
I 0
Cl (%*I
Figure 3. (a) Calculated pH as a function of chlorinity by mixing fresh and sea water: dependence on pH fresh and the alkalinity ratio. t= 15 “C; . . . . . ., T/l,/ TA,=o.s; - - - -, TAIlTAm= 1.0; -, TAr/TA,=a.o. (b) Calculated pH as a function of chlorinity by mixing fresh and sea water: dependence on temperature. TA,/TA,=I.o; - - - -, t=5 “C; t=25 “C. (c) Calculated pH as a function of chlorinity by mixing fresh and ‘sea water: dependence on the pH and chlorinity of sea water. t= 15 “C; TA,/TA,=x.o.
Dissolved carbon in estuarine waters
333
(drawn lines) are seento show a reasonableagreementwith our measurements.The hiatus at the chlorinity of 9x0 is causedby the fact that during the samplingthe actual streamchannel was left by short-cutting a curve of the estuary. During both cruises the total alkalinity turned out to be linearly related to the chlorinity and thus conserved.
Laboratory
experiments
To further establishthe Cl effect on pH we ‘titrated’ fresh water with seawater and observed the pH change. In Figure 5 the results are given of two seriesof measurements.Fresh water
Cl (%.) Figure 4. pH distribution in the estuary of the Western Scheldt. Two series of measurements were carried out on board the Eph~~a (N.I.O.Z., Texel). The curves are calculated using measured fresh and sea water data. - - - -, 0, Western Scheldt 7 May 1969; --, 0, Western Scheldt 5 November 1969.
Figure 5. Laboratory determination fresh water with sea water. The and sea water data.
of pH as a function curves are calculated
of chlorinity by titrating using the measured fresh
334
W. G. Mook
& B. K. S. Koene
of high pH wasobtained by adding a drop of NaOH solution to tapwater. The generaltrend of both curves is fairly well in agreementwith theory. As an alternative approach an attempt was made to calculate K; from an experimentally determinedpH distribution curve. This turned out to be impossibleto us, sincethe calculated pK; very strongly dependson pH, which hasto be determined to within *o*oor. The carbon distribution In Figure 6 the fractional concentrations of the inorganic carbon speciesCO,, HCO; are COP- are given asa function of pH, for two temperatures and two chlorinities. The extension of the ‘sea water curves’ at c~=19-3& to non-realistic pH values has been given to show the dependenceof the distribution on high ionic strength, asmay be observed in the thermal waters.
20
4.5
5.0
5.5
6.0
6.5
7.0
7.5
0.0
0.5
9.0
9.5
IO.0
PH
Figure 6. Calculated concentration distribution species (C02, HCO, and CO:-) as a function water and average sea water of Cl= 19.35%~; -,
of the dissolved inorganic carbon of pH and temperature for pure 5 “C; - - -, 2s “C.
As a consequenceof the anomalouspH distribution in estuaries,each fractional carbon concentration deviates significantly from what would follow from a conservative (linear) mixing of only this compound. Actually, the CO%- ion concentration in normal cases (PH, N 7.0-7.5) turns out to have an almost constant low value up to high chlorinities (Figure 7). In contrast, for high fresh water pH and high TAJTA, (or X) a maximum cCOQ is observed. Although shell carbonate formation by molluscs cannot be considered to be a simple inorganic precipitation, the above observationsshould have somebearing on this process. The saturation concentration of CO:- in estuaries of different CAJCA, is plotted in Figure 7. A few simplifications are made. The fresh water is considered to contain only Caa+ as cations: cCaf N 4 CA, = gX . CA,,,
Dissolved carbon in estuarine waters
335
where in Figure 7 CA,.,, is taken equal to 25 mequiv/l. The Ca2+ concentrations at intermediate chlorinities are calculated according to linear mixing: cca = (1--bhr
+ b ccam
(20)
where for ccamwe took a value of 10.5 mmole/l (Culkin, 1965). The saturation concentration of the CO:- ions is then calculated using the solubility products as given by Edmond & Gieskes(1970): K&,(&cite) = (0*x614 + 0.02892CL0~0063t) x
IO-~
K:,(aragonite) = (0.5115 + 0-02892 CLoeoo63t) x
IO-~
(21)
TA,/TA, .x. i 4 0 ....
Arogonite
Figure 7. Calculated absolute and fractional concentration of carbonate ions as a function of chlorinity by mixing sea water and fresh water of different pH. The saturation concentrations with respect to precipitation of aragonite and calcite are given for comparison. t=xs “C; pH,=%z; .-.-a, pH,=7.0; ---, pHr=8.0; ,....., pHr=9.0; -, cw.p (I &op).
where t denotesthe temperature in “C. Figure 7 showsthat supersaturationoccurs (depending on pH, and CA,/CA,), at relatively high chlorinities, at leastwith most rivers. Possibly this phenomenon is related to the fact that the shell growth of mussels(Myrilus edulis) in the Dutch Western Scheldt becomessignificant in an explosive manner at chlorinity values exceeding II%,, (at Kruiningen).
W.
336
G. Mook
&
B. K.
S. Koene
Acknowledgements The authors gratefully acknowledge the valuable comments of Dr J. M. T. M. Gieskes made on an earlier version of this paper. The co-operation of the Netherlands Institute of Sea Research at Texel in disposing facilities for the field and laboratory measurements made this work possible. Mr G. Steen assisted in carrying out the laboratory experiments. References Buch,
K., Harvey, H. W., Wattenberg, H. & Gripenberg, S. 19x2 Uber das Kohlensluresystem im Meerwasser. Rapport Conseil Exploration de la Mer 79, 1-70. Buch, K. 1951 Das Kohlens-ure Gleichgewichtssystem im Meerwasser. Hawsforskning Institutets Skrift Helsingfors No. 151, 18 pp. Cox, R. A. 1965 The physical properties of sea water. In Chemical Oceanography pp. 73-120, Vol. I (Riley, J. P. & Skirrow, G., eds) Academic Press, London. Culkin, F. 1965 The major constituents of sea water. In Chemical Oceanography Vol. I, pp. 121-162. (Riley, J. P. & Skirrow, G., eds). Academic Press, London. Edmond, J. M. & Gieskes, J. M. T. M. 1970 On the calculation of the degree of saturation of sea water with respect to calcium carbonate under in situ conditions. Geochimica et Cosmochimica Acta 28,
1261-1291.
Garrels, R. M. & Christ, C. L. 1965 Solutions, Minerals and Equilibria. Harper & Row, New York, London. Gieskes, J. M. T. M. 1975 The alkalinity-total carbon dioxide system in seawater. In: The Sea (Maxwell A. E., ed.), Wiley-Interscience, New York, London. In press. Hansson, I. 1973 The determination of dissociation constants of carbonic acid in synthetic sea water in the salinity range of 20-40%,, and temperature range 5-30 “C. Acta Chemica Scandinavica 27, 93 r-44. Harned, H. S. & Davis, R. Jr 1943 The ionization constant of carbonic acidin waterand thesolubility of carbon dioxide in water and aqueous salt solutions from o to 50 “C. Journal of the American Chemical Society 65, 2030-2037. Harned, H. S. & Scholes, S. R. 1941. The ionization constant of HCO; from o to 50 “C. Journal of the American Chemical Society 63, 1706-1709. Kemp, P. H. r97ra Chemistry of natural waters. I. Fundamental Relationships. Water Research 5, 297-311.
Kemp,P. H. rg7Ib Chemistry ofnaturalwaters. III. Carbonic Acid. Water Research 5,611~619. Lyman, J. 1957 Buffer mechanism of sea water. Ph.D. Thesis, U.C.L.A., 196 pp. Lyman, J. & Fleming, R. H. 1940 Composition of sea water.gournaZ of Marine Research 3, 134-146. Mook, W. G. 1970 Stable carbon and oxygen isotopes of natural waters in The Netherlands. Proc. I.A.E.A. Conf. on the Use of Isotopes in Hydrology, Vienna (1970), 163-190. Mook, W. G. 1972 On the reconstruction of the initial “‘C content of groundwater from the chemical and isotopic composition. Proc. 8th Int. Conf. on Radiocarbon Dating, Wellington, New Zealand, D31-41. Mook, W. G., Bommerson, J. C. & Staverman, W. H. 1974 Carbon isotope fractionation between dissolved bicarbonate and gaseous carbon dioxide. Earth and Planetary Science Letters 22, 169-176. Skirrow G. 1965 The dissolved gases-carbon dioxide. In Chemical Oceanography, pp. 227-322, Vol. I. (Riley, J. P., & Skirrow, G., eds). Academic Press, London.
and Coastal Marine
Science (1975) 3, 325-336
Chemistry of Dissolved Inorganic Carbon in Estuarine and Coastal Brackish Waters
W. G. Mook and B. K. S. Koene Environmental Isotqpes Laboratory, the Netherlands Receked 15 July 1974
University
of Groningen,
The rapid increase of the first and second apparent dissociation constants of carbonic acid with salinity results in a remarkable pH distribution in an estuary. On going down-stream, instead of a gradual continuous increase in pH from fresh water values of 7.0 to 7.5 to a marine value of 8.2, the pH shows a certain minimal value at low salinity. With high pH fresh water a sharp decrease at low salinity is observed. Depending on the alkalinity ratio of the fresh river water and the sea water, the carbonate ion concentration in an estuary can remain surprisingly low up to relatively high salinities. This phenomenon might affect the shell growth of certain molluscs. In order to obtain the proper dissociation constants for brackish waters of low chlorinities, a practical adjustment of well known data for pure water and sea water is made: pKi’ (for 0~C1~9%,)=3404~71/T+o~o3z786T-14~8435 -0~089zrCZf pKp’ (for o
ccop CHCOQ cc03 Cl (S) K’ K,’ KS’ CCO, TA CA PH
T
activity of the hydrogen ions, defined by pH = -log a “. molar concentration of dissolved CO* and H,COs. molar concentration of dissolved HCO; ions. molar concentration of dissolved CO:- ions. chlorinity (salinity) of the water. first apparent dissociation constant of carbonic acid. second apparent dissociation constant of carbonic acid. first apparent dissociation constant of boric acid. total dissolved inorganic carbon. titration alkalinity. carbonate alkalinity. values are based on the NBS buffer standards. absolute temperature (at t =o’C: T=273*15 K).
Introduction When fresh and sea water are mixed the individual CO,, HCO, and COs- do not behave conservatively in the dissociation equilibria according to: H,O + CO, 5 H + + HCO, (The concentration
of H&O,
is negligibly
small.) 3%
dissolved inorganic carbon fractions since chemical rearrangement occurs
2 CO;-
+ H+.
326
W. G. Mook & B. K. 5’. Koene
Quantitatively, these shifts are complex, sincethe first and seconddissociationconstants (def. by Lyman, 1957): K;
= a H . c HCO&CO,
Ki
= aH.cC&HCO,=
= Kl~c~21~
HCO,
and K,YHCO,~YCO,
(1)
are functions of the ion activities which strongly depend on the ionic strength (and ionic composition) of the water. Generally, fresh waters can be consideredto be dilute solutions. However, the salt content of seawater affects the activity coefficientsmore than is predicted by the Debye-Htickel theory, due to extensive formation of ion pairs and complexes.The problem of finding the activity coefficients over the entire natural range of chlorinities is consideredin a separatesection. As a consequenceof the large influence of salinity on the activities of, especially, the HCO; and CO:- ions, chemical rearrangement occurs in such a fashion that, when mixing of fresh and sea water occurs, the acidity showsa maximum (pH minimum) at a specific mixing ratio. This effect, and someconsequencesof it, will be discussedin the next sections. In the study of the stable isotopesof carbon in natural waters, the massspectrometrical determination is carried out on the total amount of CO, extracted from the sampleafter acidification. In general however the 813value of the dissolvedbicarbonate, being the largest fraction, is more meaningful from an isotopic point of view (Mook, 1970, 1972). Thus, the al3 of total carbon hasto be corrected for the isotopic concentration of the other two species, having different values, according to: Ps(HC0;)
= #a( X0,)
- s
EEco, (CO& a
- 2s
&o,
(CO:-).
(2)
2
The relevant fractionation values E were given recently by Mook et af. (1974). It will be shown that, apart from the temperature and chlorinity of the sample,it is only necessaryto know the pH, provided that Ki and Ki are known.
The dissolved carbon fractions cannot be determined directly. Relatively easy to measure (by acid titration) is the titration (or total) alkalinity (in mequiv./l) : TA=c
HCOI+
2cC0,
+CH,BO,
+cOH-
cHs
where, in the natural pH range, the last two terms can generally be neglected. The borate concentration is given by Skirrow (1965): CW“‘,
Kf, CB = K;, + aH’
where KB ’ is the apparent constant of the first dissociation of boric acid and the borate content ZB=2*2 x IO-~X CZ(%,). According to Edmond & Gieskes (1970), Kk is represented by pK~=2291~9o/T+o~o1756T-3~385-o~32051Cl~ over the chlorinity range of 4 to 36%,. At lower chlorinities, however, the borate content of the water is so smallthat we use their relation over the entire chlorinity range.
Dissolved carbon in estuarine waters
327
The carbonate alkalinity, defined by: CA=c
I%COs+ 2cco3
(3)
is thus related to the total alkalinity by: K; XB
TA=CA+
(4)
KI, 3-a”’
The carbon fractions can be expressed in terms of CA (from Equations ~~~~=a~.D;cuc~
I
and 3) by:
3 =aHK;.D;cco3=K;K;.D
(5)
where D = CA/(a HK; + 2K;Ki). The molar concentration
of total dissolved inorganic carbon is defined as: xco!2
=
cCO,
+
cHCOa
+
(6)
cC03a
We define two further quantities which we will use in the next sections: Qt = XO,ITA
(7)
and Q = CCO,/CA
= (ai + a,K;
+ K;K,$/(aHK;
Furthermore, we will deal with the fractional concentrations Equation 2), as derived from Equations 5 and 8: cco,/ X0, where E = (1; + a,K;
= a z/E;
cHCO,/
X0,
= a HKJE;
+ zK,K,$.
(*I
of the carbon fractions (cf.
CC&
X0,
= K;Ki/E
(9)
+ K;K,&
Brackish
water
We prefer to use the chlorinity as indicator of the brackishness related to chlorinity by (Gieskes, 1974):
of the water; the salinity is
S = 1.80655 Cl
(10)
whereas according to Gieskes the formula (Cox, 1965) S = 1.8050 Cl + 0.03%~ is better in the Baltic. In the Figures also S is indicated based on Equation of brackishness, b, is then defined by: CZ= (I-b)Cl,
+ bCI,,,,
IO.
The degree (11)
where f and m denote the fresh and marine values, respectively. If CZr=o the brackishness b = Cl/Cl,,,. In order to be able to calculate the pH distribution in an estuary, the assumption has to be made that we are dealing with a closed system in which we consider the conservation of the total inorganic carbon content and of the titration alkalinity. This implies that no CO, is lost from the water into the atmosphere and that, for instance, no precipitation of calcium carbonate occurs.
328
W. G. Mook & B. K. S. Koene
Then :
and
TA = (I--b)TAf
+ bTA,.
(4
The Q, value for a brackish water sampleas defined by Equation 7 then is:
Q,=(a~+P)(uB+u.K;+K;K~) W fl + (1H)(UHK; + 2J-W;)
(13)
where P = KA( I - ZB/TA). From this a cubic equation for an is deduced,which is essentiallysimilar to the one presented by Gieskes(1974): u;+Au;+Bu”+C=o A = K;(I-QJ
where
+ K;(I-
B = K;K;(I--2&J
(14)
CB/TA)
+ K;K;(I-Q,-
C = K;K;K;I(I--2Qt-
EB/TA)
ZB/TA)
introducing the possibility of calculating the general characteristicsof the pH distribution along the chlorinity gradient of an estuary. A numerical analysisshowsthat for pH calculation to two decimal placesit is justifiable to regard the borate concentration asconservativeduring mixing. If this assumptionis made, CA is alsolinearly related to the degreeof brackishness:
CA = (I --b)CA, + bCA, so that:
QJ~-VQJ+~Qm (14)X
where X = CA,/CA,.
+ b
Equation 14 then reducesto a quadratic form: a; + uHK;(l-Q)
+ K;K;(I--2Q)
= o.
(15)
Before these equations can be solved it is necessaryto obtain values of the dissociation constantsK; and Ki appropriate to the mixed water. The apparent dissociation constants of carbonic acid Following the pioneer work of Buch and co-workers (Buch et al., 1932; Buch, 1951), Lyman prepared a practical set of apparent dissociationconstantsfor seawater (Equation I). The completeand original seriesof determinationswasrevised by Edmond & Gieskes(1970) revealing equations for the temperature- and chlorinity-dependence of the constants (pK = -1ogK): (1957)
pK;
=
3404’7IjT
pK; = 2902*39/T
+O*032786T-IIq.7122-O*ICj178~~"3
+ o~o2379T-6~471o-o~4693~1”~.
(16)
Dissolved carbon in estuarine waters
329
Although theseequationsare the best approximations to marine data, they are not intended for use at low chlorinities and do not extrapolate to the thermodynamic constants at CZ=o (Harned & Davis, 1943; Harned & Scholes,1941), which are representedby the equations: pK, =
3404*71/T
pK, =
2902’39/
0*032786T-14’8435
+ T
+ 0’02379 T-6.4980.
(17)
Redetermination of dissociation constants has also been carried out by Hansson(1973) for the salinity range 20-40%~. In the absenceof accurate measurementsof K; and Kk at low chlorinities we have made smooth adjustmentsbetween the values determined at higher chlorinities and thosefor pure water. The slope of the pK,(C1) relation at CZ=o can be calculated according to the Debye-Hiickel theory for dilute solutions. The apparent and thermodynamic constantsare related by : PK;-PK,
= logy “co,-log YCO,
where y refers to the respective activity coefficients. According to the DH-theory (Garrels & Christ, 1965):
Ad(1-0 log
Y HC03
=
1 +
ti WI+
In aqueoussolutions: A=o*5085 and B=0*3281 x IO*, and for the bicarbonate ion: i N 4.3 x IO-~. According to Lyman & Fleming (1940), the ionic strength of seawater is given by: i.~ =
0~001,.+7
j-
0.03592
Cl + 0~000068 CP.
The activity coefficient for dissolvedcarbon dioxide is defined by: log yco, = log a,-log cr, where a, and a, represent the solubilities of CO, in pure water and seawater, respectively (Buch et al., 1932). The values are given by Gieskes(1974): -1Og a, = -2262*38/T-oao178471T + 15’5873+ -2.77676
cl(0~0117950-
x IO-5T).
The resulting DH-curve is shown in Figure r(a) where the pK; values according to Harned & Davis (1943) and Edmond & Gieskes(1970) are plotted as a function of Cl*. The curve agreeswell with the activity coefficients as computed by Kemp (197Ia, 6). Initially, it seemedto us that a good approximation would be obtained by drawing the tangent from pKr at Cl=0 to the curve of Edmond & Gieskesplotted versusCP, in which presentation Debye-Hiickel predicts a linear behaviour of pK; for low p. Now that the DH theory turns out to give exactly the sameslope at Cl=0 we feel confident that our procedure is justified. The same is true for other temperatures. A similar adjustment procedure is applied to the values of pKi [Figure r(b)]. The resulting pK’ valuesare represented by: PK; = 3404*71/T + o.o32786T-14~8435-0~08921 Cl*
pK; =
2902*39/T+
0*02379T-6.4980-0'7531 cl*
(18)
W. G. Mook & B. K. S. Koene
330
It should be noted that at very low chlorinities severediscrepanciesexist between the pK; values obtained by extrapolation of the Edmond & Gieskesequation and those calculated from the DH theory [Figure a(b)]. Obviously, complex formation contributes appreciably to the lowering of the activity coefficients. In Figure x(a) and (b) the chlorinities below which Equation 18 is valid are indicated by an arrow.
6.0;
’
I I
2 Cl ‘a
3
4
Figure I. (a) pK,’ for the first dissociation of carbonic acid. The arrow indicates the chlorinity, below which the pKr’ relation presented in this paper is valid. At higher chlorinities the equation of Edmond & Gieskes (1970) applies. (b) p& for the second dissociation of carbonic acid. The arrow indicates the chlorinity, below which the pK,’ relation presented in this paper is valid. At higher chlorinities the equation of Edmond & Gieskes (1970) applies. (0) Hamed & Davis, 1943 ; (0) Buch, 1951; (0) Lyman; (- - -) Edmond & Gieskes, 1970; (- - - -) Debye-Hiickel; -, this paper.
The rapid increaseof K; and K; with increasing chlorinity (Figure 2) is of importance when studying fresh water carbon chemistry, including stablecarbon isotopic work. The use of the thermodynamic constants or those of Edmond & Gieskes,in order to calculate the CO, percentagein river waters containing IOO mg/l of chloride, causeserrors of about 15%.
The pH diatribudon
in an estuary
Using the proper setsof dissociationconstantswe are able to calculate the pH distribution in an estuary for which the characteristicsof the fresh and seawater componentsare known.
Dissolved carbon in estuarine waters
331
Figure 3(a), (b) and (c) shows the dependenceof the distribution on pHr, pH,, TAfITA,, Cl,,, and temperature. The most striking feature is the pH minimum which is observed for those curves having lower initial pHr values. As will be pointed out later, this might have certain implications for the formation of shell carbonate by molfuscsin an estuary.
r OO
. . . . 5
IO
I5 Cl (Xc.)
! 20
25
Figure 2. (a) The first apparent dissociation constant (Kr’) according to the values of pK,’ presented in Figure :(a) as a function of chlorinity and temperature. The dashed lines indicate the deviations of the equations from Edmond & Gieskes and those from these authors in the chlorinity ranges where they do not apply. (b) The second apparent dissociation constant (Ks’) according to the values of pKa’ presented in Figure r(b) as a function of chlorinity and temperature. The discrepancy between the actual values and those calculated according to the Debye-Htickel theory (dashed line) is obvious.
At the high fresh water pH the pH sharply decreaseswith increasing chlorinity. An example of this is to be found at the outlet of the Dutch IJsselLake into the Wadden Sea. Due to atmospheric exchangeduring the large residencetime of the river water in the lake, pH values as high as 9.5 are observed (Mook, 1970).
W. G. Mook & B. K. S. Koene
332
We originally met with the peculiar effect of chlorinity on pH in the estuary of the Western Scheldt where we needed the chemical composition of the water for correcting the carbon isotopic abundances (Mook, ‘970). In Figure 4 two series of measurements made on board the B’h~~ra [Netherlands Institute of Sea Research (Texel)] are given. The calculated curves
9.5
,
9-e
1
I
I
1
I--
(b)
(a)
J
7.5
,’ ,I
7.0
I 0
l--J
!
9.5
5 I
IO I
15
5
IO
I
I
15
20
I
20
I
___--0
__--I
,
0
5
_/-
.’
/
,’
I
IO c/ ( %.I
,’
/
I
15
20
(cl
I 0
Cl (%*I
Figure 3. (a) Calculated pH as a function of chlorinity by mixing fresh and sea water: dependence on pH fresh and the alkalinity ratio. t= 15 “C; . . . . . ., T/l,/ TA,=o.s; - - - -, TAIlTAm= 1.0; -, TAr/TA,=a.o. (b) Calculated pH as a function of chlorinity by mixing fresh and sea water: dependence on temperature. TA,/TA,=I.o; - - - -, t=5 “C; t=25 “C. (c) Calculated pH as a function of chlorinity by mixing fresh and ‘sea water: dependence on the pH and chlorinity of sea water. t= 15 “C; TA,/TA,=x.o.
Dissolved carbon in estuarine waters
333
(drawn lines) are seento show a reasonableagreementwith our measurements.The hiatus at the chlorinity of 9x0 is causedby the fact that during the samplingthe actual streamchannel was left by short-cutting a curve of the estuary. During both cruises the total alkalinity turned out to be linearly related to the chlorinity and thus conserved.
Laboratory
experiments
To further establishthe Cl effect on pH we ‘titrated’ fresh water with seawater and observed the pH change. In Figure 5 the results are given of two seriesof measurements.Fresh water
Cl (%.) Figure 4. pH distribution in the estuary of the Western Scheldt. Two series of measurements were carried out on board the Eph~~a (N.I.O.Z., Texel). The curves are calculated using measured fresh and sea water data. - - - -, 0, Western Scheldt 7 May 1969; --, 0, Western Scheldt 5 November 1969.
Figure 5. Laboratory determination fresh water with sea water. The and sea water data.
of pH as a function curves are calculated
of chlorinity by titrating using the measured fresh
334
W. G. Mook
& B. K. S. Koene
of high pH wasobtained by adding a drop of NaOH solution to tapwater. The generaltrend of both curves is fairly well in agreementwith theory. As an alternative approach an attempt was made to calculate K; from an experimentally determinedpH distribution curve. This turned out to be impossibleto us, sincethe calculated pK; very strongly dependson pH, which hasto be determined to within *o*oor. The carbon distribution In Figure 6 the fractional concentrations of the inorganic carbon speciesCO,, HCO; are COP- are given asa function of pH, for two temperatures and two chlorinities. The extension of the ‘sea water curves’ at c~=19-3& to non-realistic pH values has been given to show the dependenceof the distribution on high ionic strength, asmay be observed in the thermal waters.
20
4.5
5.0
5.5
6.0
6.5
7.0
7.5
0.0
0.5
9.0
9.5
IO.0
PH
Figure 6. Calculated concentration distribution species (C02, HCO, and CO:-) as a function water and average sea water of Cl= 19.35%~; -,
of the dissolved inorganic carbon of pH and temperature for pure 5 “C; - - -, 2s “C.
As a consequenceof the anomalouspH distribution in estuaries,each fractional carbon concentration deviates significantly from what would follow from a conservative (linear) mixing of only this compound. Actually, the CO%- ion concentration in normal cases (PH, N 7.0-7.5) turns out to have an almost constant low value up to high chlorinities (Figure 7). In contrast, for high fresh water pH and high TAJTA, (or X) a maximum cCOQ is observed. Although shell carbonate formation by molluscs cannot be considered to be a simple inorganic precipitation, the above observationsshould have somebearing on this process. The saturation concentration of CO:- in estuaries of different CAJCA, is plotted in Figure 7. A few simplifications are made. The fresh water is considered to contain only Caa+ as cations: cCaf N 4 CA, = gX . CA,,,
Dissolved carbon in estuarine waters
335
where in Figure 7 CA,.,, is taken equal to 25 mequiv/l. The Ca2+ concentrations at intermediate chlorinities are calculated according to linear mixing: cca = (1--bhr
+ b ccam
(20)
where for ccamwe took a value of 10.5 mmole/l (Culkin, 1965). The saturation concentration of the CO:- ions is then calculated using the solubility products as given by Edmond & Gieskes(1970): K&,(&cite) = (0*x614 + 0.02892CL0~0063t) x
IO-~
K:,(aragonite) = (0.5115 + 0-02892 CLoeoo63t) x
IO-~
(21)
TA,/TA, .x. i 4 0 ....
Arogonite
Figure 7. Calculated absolute and fractional concentration of carbonate ions as a function of chlorinity by mixing sea water and fresh water of different pH. The saturation concentrations with respect to precipitation of aragonite and calcite are given for comparison. t=xs “C; pH,=%z; .-.-a, pH,=7.0; ---, pHr=8.0; ,....., pHr=9.0; -, cw.p (I &op).
where t denotesthe temperature in “C. Figure 7 showsthat supersaturationoccurs (depending on pH, and CA,/CA,), at relatively high chlorinities, at leastwith most rivers. Possibly this phenomenon is related to the fact that the shell growth of mussels(Myrilus edulis) in the Dutch Western Scheldt becomessignificant in an explosive manner at chlorinity values exceeding II%,, (at Kruiningen).
W.
336
G. Mook
&
B. K.
S. Koene
Acknowledgements The authors gratefully acknowledge the valuable comments of Dr J. M. T. M. Gieskes made on an earlier version of this paper. The co-operation of the Netherlands Institute of Sea Research at Texel in disposing facilities for the field and laboratory measurements made this work possible. Mr G. Steen assisted in carrying out the laboratory experiments. References Buch,
K., Harvey, H. W., Wattenberg, H. & Gripenberg, S. 19x2 Uber das Kohlensluresystem im Meerwasser. Rapport Conseil Exploration de la Mer 79, 1-70. Buch, K. 1951 Das Kohlens-ure Gleichgewichtssystem im Meerwasser. Hawsforskning Institutets Skrift Helsingfors No. 151, 18 pp. Cox, R. A. 1965 The physical properties of sea water. In Chemical Oceanography pp. 73-120, Vol. I (Riley, J. P. & Skirrow, G., eds) Academic Press, London. Culkin, F. 1965 The major constituents of sea water. In Chemical Oceanography Vol. I, pp. 121-162. (Riley, J. P. & Skirrow, G., eds). Academic Press, London. Edmond, J. M. & Gieskes, J. M. T. M. 1970 On the calculation of the degree of saturation of sea water with respect to calcium carbonate under in situ conditions. Geochimica et Cosmochimica Acta 28,
1261-1291.
Garrels, R. M. & Christ, C. L. 1965 Solutions, Minerals and Equilibria. Harper & Row, New York, London. Gieskes, J. M. T. M. 1975 The alkalinity-total carbon dioxide system in seawater. In: The Sea (Maxwell A. E., ed.), Wiley-Interscience, New York, London. In press. Hansson, I. 1973 The determination of dissociation constants of carbonic acid in synthetic sea water in the salinity range of 20-40%,, and temperature range 5-30 “C. Acta Chemica Scandinavica 27, 93 r-44. Harned, H. S. & Davis, R. Jr 1943 The ionization constant of carbonic acidin waterand thesolubility of carbon dioxide in water and aqueous salt solutions from o to 50 “C. Journal of the American Chemical Society 65, 2030-2037. Harned, H. S. & Scholes, S. R. 1941. The ionization constant of HCO; from o to 50 “C. Journal of the American Chemical Society 63, 1706-1709. Kemp, P. H. r97ra Chemistry of natural waters. I. Fundamental Relationships. Water Research 5, 297-311.
Kemp,P. H. rg7Ib Chemistry ofnaturalwaters. III. Carbonic Acid. Water Research 5,611~619. Lyman, J. 1957 Buffer mechanism of sea water. Ph.D. Thesis, U.C.L.A., 196 pp. Lyman, J. & Fleming, R. H. 1940 Composition of sea water.gournaZ of Marine Research 3, 134-146. Mook, W. G. 1970 Stable carbon and oxygen isotopes of natural waters in The Netherlands. Proc. I.A.E.A. Conf. on the Use of Isotopes in Hydrology, Vienna (1970), 163-190. Mook, W. G. 1972 On the reconstruction of the initial “‘C content of groundwater from the chemical and isotopic composition. Proc. 8th Int. Conf. on Radiocarbon Dating, Wellington, New Zealand, D31-41. Mook, W. G., Bommerson, J. C. & Staverman, W. H. 1974 Carbon isotope fractionation between dissolved bicarbonate and gaseous carbon dioxide. Earth and Planetary Science Letters 22, 169-176. Skirrow G. 1965 The dissolved gases-carbon dioxide. In Chemical Oceanography, pp. 227-322, Vol. I. (Riley, J. P., & Skirrow, G., eds). Academic Press, London.