The solubility of calcite — probably containing magnesium — in seawater

Marine Chemistry, 10 (1980) 9--29 Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands

9

THE SOLUBILITY OF CALCITE --PROBABLY CONTAINING MAGNESIUM IN SEAWATER -

-

DAVID C. PLATH, KENNETH S. JOHNSON and RICARDO M. PYTKOWICZ School of Oceanography, Oregon State University, Corvallis, OR 97331 (U.S.A.)

(Received March 27, 1979 ; revision accepted April 16, 1980 ) ABSTRACT Plath, D.C., Johnson, K.S. and Pytkowicz, R.M., 1980. The solubility of c a l c i t e - probably containing magnesium -- in seawater. Mar. Chem., 10: 9--29. The apparent solubility product of calcite was measured by saturometry as a function of temperature and salinity. Simplified equations for the carbonic-acid dissociation constants of Mehrbach et al., 1973 (Limnol. Oceanogr., 18: 897--907) have been derived t t from their experimental data and used to calculate apparent solubility product, Ksp. Ksp at 25°C and 350/oo salinity, was found to be Ksp ----

4.70 X 10-7(tool 2 kg seawater -2 )

An equation was fitted to the experimental data, resulting in p K s p ~-

6.5795 -- 3.7159 x I o - S ( T S ) + 0.91056(T/S) -- 22.110(1.0/S)

The mean activity coefficients, ~f-+CaCO3,were calculated at various temperatures and salinities, using the thermodynamic solubility product of Jacobson and Langmuir,. 1974 (Geochim. Cosmochim. Acta, 38: 301--318) and the apparent solubility products quoted in their paper. The change in K~'p at each salinity, as a function of temperature, was used to calculate fl~e apparent enthalpy of dissociation for calcite, AH', and the extrapolated value of ~/_/0 was in good agreement with that of Jacobson and Langmuir. Finally, this work was used to calculate saturation profiles for oceanic stations and as a basis for comment of the accuracy of in-situ saturometry, as well as the applicability of in-situ K~p pressure corrections. INTRODUCTION t

T h e d e t e r m i n a t i o n o f the a p p a r e n t solubility p r o d u c t , Ksp , o f c a l c i u m c a r b o n a t e in s e a w a t e r is i m p o r t a n t f o r t h e u n d e r s t a n d i n g a n d p r e d i c t i o n o f t h e b e h a v i o r o f c a r b o n a t e s o n e x p o s u r e t o s e a w a t e r . I t is also crucial f o r t h e d e t e r m i n a t i o n o f t h e origin o f t h e lysocline a n d t h e c a r b o n a t e c o m p e n s a t i o n d e p t h (CCD). T h e l y s o c l i n e is t h e d e p t h a t w h i c h t h e first signs o f d i s s o l u t i o n a p p e a r , w h e r e a s t h e CCD is t h e d e p t h b e l o w w h i c h CaCO3 is essentially absent from the sediments. In this w o r k Kip was d e t e r m i n e d f o r a calcite as a f u n c t i o n o f t e m p e r a t u r e a n d salinity, w h i c h , a l o n g w i t h a revised e q u a t i o n f o r t h e K~ d a t a o f Mehrb a c h et al. ( 1 9 7 3 ) , was a p p l i e d t o d e t e r m i n e t h e degree o f s a t u r a t i o n o f o c e a n i c waters. F u r t h e r m o r e , t h e results w e r e u s e d t o s e e k an u n d e r s t a n d i n g o f t h e n a t u r e o f t h e lysocline a n d o f t h e c a r b o n a t e c o m p e n s a t i o n d e p t h (CCD).

10 !

The most convenient method for the determination of Ksp is that of Weyl (1961), its advantages being that: (1) A large surface area of solid is introduced into a relatively small volume of seawater, thus reducing the equilibration time and ensuring that equilibrium is reached. (2) A quiescent closed system is employed. Therefore, a saturometer approximates the conditions in the ocean better than any method involving the regulation of pCO2 by gas bubbling. The method avoids excessive dissolution of CaCO3, due to a high pCO2, which could change the relative composition of the major constituents of the seawater. (3) The saturometer can be adapted for use in high-pressure determinations (e.g. Pytkowicz and Fowler, 1967). (4) The pH determinations of this method are consistent with the methods t t used to determine K1, K2 and KB, the apparent dissociation constants of carbonic and boric acids (Mehrbach et al., 1973; Lyman, 1956). (5) The saturometer is adaptable for use with small volumes of solution and solid, a valuable feature for pore-water studies. The chief disadvantage of saturometry determinations, as of any method for solubility determination, is the difficulty of adapting the system to in-situ work. The problem arises because of surface poisoning of the solid by organics, and because of the time involved in reaching equilibrium. The effect of ion-pairs such as NaCO~, CaCO3, on the solubility of calcium carf bonates etc. can also be confusing at times. K~p (Ca2+)T(CO~-)T at equilibrium where (Ca 2+)T (CO~-)T includes free Ca 2+ and COl- as well as their ion-pairs. Pytkowicz and Hawley (1974), among others, have shown that such total quantities as those above are invariant at any given temperature, pressure and salinity, as long as the major ion composition of seawater does not change. The dissolution and precipitation of CaCO3 have been shown to change (Ca 2÷)T in seawater by less than 2%. =

EXPERIMENTAL

All seawater samples were made from 3 2 % north Pacific surface seawater by evaporation or dilution with deionized, distilled water. The seawater, collected in July 1977 aboard the R.V. "Thompson", was poisoned with HgC12. Calcite samples used in the experimental determinations were reagent grade (J.T. Baker) calcium carbonate. Analysis by X-ray diffraction showed this to be synthetic calcite. The temperature in the experiments was controlled to +0.1°C by means of an Amico thermostated water bath. The titration alkalinity was determined by Gran titrations of the seawater samples with HC1 at 25°C. The titration alkalinities of the samples were 2.162, 1.682 and 1.220 meqkgseawater -1 for 34.56, 24.45 and 18.29~/0o salinity, respectively.

11

Small differences in the specific alkalinity of the 34.570/00 sample relative to that of the other salinities could be due to the precipitation of CaCO3 during evaportation of the stock. The average standard deviation for the determination of the titration alkalinity was 0.006 meq seawater -1 . The salinity was calculated from conductivity measurements made with a Bisset--Berman salinometer and substandard seawater. It was also determined to within 0 . 0 1 % using an Auto-Sal salinometer and Copenhagen standard seawater (C1 = 19.376%0). Densities were then calculated from ot values listed in the Handbook of Oceanographic Tables (U.S. Naval Oceanographic Office, 1966). The pH was calculated throughout this work from EMF measurements, using glass pH electrodes (Radiometer, G202C) and saturated calomel reference electrodes (Sargent, S-30080-15C). Prior to each run the slope of the electrode pair response was determined with two NBS buffers, pH 7.415 KH2PO4--Na2HPO4 buffer, and pH 4.004 KHCsH404 buffer. If the slope was found to be within 1% of the theoretical slope (59.16 mV per decade change in hydrogen ion concentration), then the theoretical slope was used in the following equation to calculate pH PHsample = PH7.415 buffer

-

-

(EMFsamp]e -- EMFT.41s buffer)/Slop e

Initial and final pH values were determined for each run since changes in the dissolved CO2 could change the initial degree of saturation. The determinations of initial and final EMF's of the runs in seawater were carried out in a saturometer designed by Elliot Atlas (E.L. Atlas, personal communication, 1977). This cell, shown in Fig. 1, permits the measurement of

'l syricnitge-"' cal e --...

1

seawoter /syringe ~---stopcock

pH electrode

reference electrode

calciteslurr Fig. 1. CaCO3 saturometer (designed by E.L. Atlas).

12 EMF and the equilibrium of pore waters with a mineral in a totally closed system. Firstly, the cell was filled with seawater, and its initial pH was determined. Subsequently, the carbonate species under study (calcite) was placed in a glass syringe and 'washed' with CO2-free N 2. The syringe with the calcite was then placed on the pH electrode side of the saturometer and a matching syringe was filled with seawater and placed on the reference electrode side. The piston of the seawater syringe was depressed forcing seawater from the cell into the CaCO3 and forming a slurry which was then injected carefully into the pH-electrode side of the saturometer. The slurry was injected until the active surface of the pH electrode was completely covered by at least one centimeter of slurry. Since only the pore water reached equilibrium with the calcite, the additional slurry injected limits the diffusion of non-equilibrated seawater to the electrode surface. Equilibration of the pore water with CaCO3 was accomplished in 8--12 h, depending on the initial degree of saturation and the temperature. The criterion used for equilibrium conditions was a change in EMF of less than 0.1 mV h -~ ; runs of durations greater than 24 h yielded the same end potential as those of 8--12 h. The seawater samples were not stirred prior to, or during the measurement of the initial pH as it was observed that a stirring potential was associated with a moving magnetic field. Stirring the sample was n o t possible after the calcite was added as it was essential that the pore water remain undisturbed. CALCULATIONS K~p was calculated from the experimental results using a modified version of the m e t h o d of Ingle et al. (1973}. This modification included the effects r of the borate system. Ksp is defined as the product of the calcium ion and carbonate ion concentrations at equilibrium with CaCO3. Due to the dependence of the carbonate system on pH, precipitation or dissolution of CaCO3 will result in a characteristic pH change. Precipitation (or dissolution in the case of undersaturated waters) changes both the total CO2 (TCO2) and the carbonate alkalinity (CA). The carbonate alkalinity is the difference between the titration alkalinity and the borate alkalinity (BA). It is therefore possible to represent the equilibrium conditions by [(TCO2) I + A]/[(TAi--BAr) + 2A] = [(aH)~ + (aH}fK'l + g'tg~]/

[(aH )tK~ + 2K~ g~ ]

(1)

where A is the a m o u n t of CaCO3 precipitated or dissolved and K~ and K~ are the dissociation constants of the carbonate system. The subscripts i and f refer to the initial and final (equilibrium) conditions of the experiment. The equilibrium constants of Mehrbach et al. (1973) were used in this work after simplification as shown in the next section. Lyman's (1956) first dissociation constant for the boric acid system was used in our calculations since it was defined on the same pH scale used in both this work and that of Mehrbach et al. (1973).

13 From eq. 1, A can be calculated, as can the Ks'p, from ?

gsp

= [(Ca/) + A)] (CO]-)f

(2)

where (CO]-)f = [(TAi -- BAf) + 25] g~/[(aH)f + 2K~ ]

(3)

RESULTS

Apparent equilibrium constants When the apparent equilibrium constants of Mehrbach et al. (1973) were ? used in the calculation of K~p, the resultant values showed a reversal in temperature dependence at salinities below 2 5 % relative to that at higher salinities. The amounts of calcite used were not determined. This could lead to problems according to the theory of Wollast and Reinhard-Derie (1977) (see also Pytkowicz and Cole, 1980). However, when the constants of Lyman (1956) as expressed by Takahashi et al. (1976) were substituted, the expected inverse dependence on temperature was seen for K~ at all the salinities used. Upon critically examining the equations of Mehrbach et al., the source of the error was discovered. Mehrbach et al. (1973) used a multivariable linear regression to fit their experimental data to empirical equations, involving a five-parameter equation for pK~ and an eight-parameter equation for pKg. The authors believe this to be an overdetermination of the system presented and that it is unwarranted by the experimental data. These equations were simplified by using Mehrbach's experimental data and the same regression program (OSU--SIPS), but reducing the number of terms. This resulted in the following equations pK~ = 17.788-- 0.073104(T) -- 0.0051087(S) + 0.00011463(T) ~

(4)

pK~ = 20.919-- 0.064209(T) -- 0.011887(S) + 0.000087313(T):

(5)

where T is the temperature in kelvins and S is the salinity in parts per thousand. The standard deviations of the data from the regression curves are 7.64 × 10 -3 and 1.11 × 10-: for pK~ and pK~, respectively. Interestingly, the criterion for a minimum number of terms which could satisfactorily reproduce the data yielded equations similar in form to those presented by Takahashi et al. (1976) based upon the data o f Lyman (1956). The expression used here for pK~ differs only in the presence of the T 2 term not found in the equation used by Takahshi et al. Equations 4 and 5 were then t used to calculate Ksp in the manner previously stated. The temperature and salinity dependences were similar to those observed with the use of Lyman's constants. Finally, by comparing the coefficients o f determination (R2) of the simplified equations with those for Lyman's equations, as expressed by Takahashi et al. (1976), we find that the data of Mehrbach et al. (1973) show the

14

971

~ 62i-

95!

....

"\-

~

27516 ~:

.~ 93P 6 ipI

$75,6 K

i

6o i

286,6 K

59'

298 16 K 30816 K 25

- - - -

35

91 I

28616 K

rl-

a88,6

89 i .......

45

Salinity (%o)

30816 K 315 Salinity (%°)

L. . . .

25

_____j

45

Fig. 2. pK~ vs. salinity for this work (solid line) and for Lyman (1956) (dashed line). Fig. 3. pK~ vs. salinity for this work (solid line) and for Lyman (1956) (dashed line).

greater degree of internal consistency. The (R 2 ) values for pK~ and pK~ were 0.992 and 0.996, while for Lyman's work they were 0.938 and 0,951. For this reason it was decided to use eqs. 4 and 5 in the remainder of this work. However, since these equations yield results quite similar to those of Lyman (see Figs. 2 and 3), an indication of compatibility of methods, and since Mehrbach et al. (1973) did not measure K~, the pK~ values from Lyman's work were employed in the present paper. The apparent solubility product o f calcite The K'~ data calculated from our experimental results are shown in Table I. They were first analyzed by a muttivariable linear analysis program (OSU--SIPS). This resulted in the following equation fit to the experimental results t

pKsp = 6.5795 -- 3.7159 x 10 -s (TS) + 0.91056(T/S) -- 22.110(1.1/S) (6)

where salinity is expressed in °/00 and temperature in kelvins. It should be pointed o u t that this t y p e of program may, when enough variables are used, perfectly fit any data with a single equation. However, this is n o t always desirable, since, as was pointed o u t earlier (e.g. Mehrbach et al., 1973), it can misrepresent the true trend of the data. A very complex e q u a t i o n can produce maxima and minima in the calculated curve, due to data scatter,

15

TABLE I r

Experimental results for the determination of Ksp of calcite T(K)

S(°/oo )

TA(meq 1-1 )

pH i

pHf

K~p(mol 2 kg seawater -2 ) × 106

298.16

34.57

2.212

24.45

1.708

18.29

1.233

34.57

2.212

24.45

1.708

18.29

1.233

34.57

2-.212

24.45

1.708

18.29

1.233

278.16

34.57

2.212

278.16

24.45

1.708

18.29

1.233

8.809 8.763 8.063 8.029 8.074 7.863 7.905 8.887 8.848 8.218 8.179 8.051 8.040 8.778 8.676 8.634 8.686 8.289 8.234 8.302 8.128 8.058 8.029 8.647 8.779 8.749 8.686 8.557 5.698 8.686 6.929 7.817 8.385 8.356 8.285 8.279 8.249 8.299

7.924 7.878 7.748 7.729 7.743 7.873 7.905 8.010 7.994 7.876 7.884 8.056 8.044 7.961 7.895 7.922 7.941 7.966 7.986 8.000 8.149 8.132 8.129 7.948 8.025 8.012 7.967 7.943 6.896 7.967 7.649 7.775 8.095 8.047 8.080 8.290 8.284 8.280

0.477 0.463 0.315 0.305 0.309 0.216 0.230 0.466 0.479 0.309 0.321 0.240 0.234 0.455 0.440 0.494 0.487 0.323 0.348 0.348 0.252 0.247 0.248 0.464 0.484 0.486 0.467 0.498 0.469 0.467 0.496 0.479 0.363 0.327 0.367 0.287 0.286 0.277

288.16

283.16

where a monotonic trend would be more representative of the system. T h e r e f o r e , in all c a s e s w e h a v e t r i e d t o c o m p r o m i s e b e t w e e n t h e f i t o f t h e e q u a t i o n a n d its s i m p l i c i t y . T h e s t a n d a r d d e v i a t i o n f o r t h i s l i n e is 1 . 7 7 x 1 0 -2 I t in p K w . T h i s c o r r e s p o n d s t o a n u n c e r t a i n t y in K sp o f a b o u t 4%. T h i s l i n e a n d t h e e x p e r i m e n t ~ , p o i n t s a r e s h o w n in F i g . 4. T a b l e I I gives t h e a v e r a g e e x p e r i m e n t a l v a l u e s f o r K'sp a n d t h e s t a n d a r d

16

6 7 r-

i

1o 66

SoHnity (%o1 t

Fig. 4. PKsp calculated from eq. 6 (T = 25°C, 15°C, 10°C and 5°C from top to bottom) and average experimentM results.

TABLE II t

Average experimental results of Ksp and standard deviations T(°K)

This work 298.16

288.16

283.16

278.16

Ingle et al. (1973) 298.16 286.16 275.16

S(°/0o )

K~p(aV.) (tool 2 kg seawater -2 ) × 106

Standard deviation

34.57 24.45 18.29 34.57 24.45 18.29 34.57 24.45 18.29 34.57 24.45 18.29

0.470 0.310 0.223 0.473 0.315 0.237 0.470 0.340 0.249 0.479 0.352 0.284

0.010 0.005 0.010 0.009 0.008 0.004 0.030 0.010 0.003 0.013 0.020 0.006

35.0 35.0 35.0

0.450 0.477 0.465

0.010 0.009 0.010

17

deviation for each determination for this work as well as for that of Ingle et al. (1973) at atmospheric pressure. The data of Ingle et al. show about the same reproducibility at 350/00 salinity as the present data. However, there is a reversal evident in the temperature dependence of K'p in Ingle et al. at mid-temperatures (13°C). Figure 5 shows the effect of temperature on K:p at 350/oo salinity for this work and for that of Ingle et al. The present data show a greater degree of internal consistency, even though the standard 0.48

0.47 - / /

0

\\

/

\ \

7o` 0.46

\

045

x

0.44

[

I

I

280.16

290.16

30016

Temperature' ( K ) t

Fig. 5. Average experimental results of Ksp at 350/00 salinity vs. temperature work, o = Ingle et al., 1973).

Tu,

(n =

this

0.40

E

0.30

0.20

2'0

3o Salinity (%o)

Fig. 6. Average experimental values of K.'p. This work: A = 5°C; <> = 1 0 ° C ; [] --- 1 5 ° C ; o = 25°C; Ingle et al.: • = 13°C; X = 2°C;,o = 25°C.

18 deviations for the individual determinations are nearly identical for the two sets of results. In addition, it should be noted that at 24.45 and at 18.29%o salinity, the degree of internal consistency is greater than that seen at 35~/00 salinity, since at 35°/oo the temperature effect is at the limit of detection. It appears, therefore, that although the precision of these two works is the same, the results of Ingle et al. (1973) are subject to larger inherent systematic errors. Figure 6 shows a composite of the average K'sp data from this research and from that of Ingle et al. {1973). The data of Ingle et al. have been recalculated using the carbonate dissociation constants presented in this paper. This recalculation changed the previously reported trend in their data, pointing out the sensitivity of these calculations to changes in the dissociation constants.

Determination of 7+caco3/aca~ite from K's p Activity coefficients can be obtained as a by-product of solubility work. p In this case, Ksp is defined as !

gsp

:

(Ca2+)f(CO~-)f

(7)

where the subscript f refers to the total concentrations of the ions at equilibrium with CaCO3. Since the thermodynamic solubility product of calcite is defined as Ks°p = (aca:+)(aco]-)/acalcite

(8)

the following equation holds Ks°p = Ks; (TCa:+7col-)/acaleite

(9)

If acalcife is unity, then it is assumed that the surface of the solid is a pure calcite and not an Mg-calcite. Then the activity coefficient product can be simply calculated by dividing the thermodynamic solubility product by Kip. This is not strictly true, as Plummer and Mackenzie (1974) found the most stable calcites to actually contain 2--5 mol % MgCO3, and Thorstenson and Plummer (1977) concluded that the stable calcite in seawater is an Mgcalcite with about 4 mol % Mg. They further stated that the activity of calcite in this species is 0.745. A value of acalcite equal to unity is used as a rough estimate of the activity coefficients in this work. The equation of Jacobson and Langmuir (1974) was used for logKs°p logK°p = 1 3 . 5 4 3 - - 3 0 0 0 / ( T K) = 0.0401 (T K)

(10)

Now, using eq. 6 from this paper and the following equation log?caTco3

= logK°p + PKs'p + log(1 - - S / 1 0 0 0 ) :

(11)

log 7ca7co3 can be calculated. S is salinity (~(oo) and pKs'p is - - l o g K ~ . The purpose of the third term in eq. 11 is to Convert the effective units of

19 TABLE III .

t

.

Mean activity coefficient of CaCO3, ~'±CaCO3, m seawater. Calculated from the Ksp of this work and the thermodynamic solubility product of Jacobson and Langmuir (1974)

S(°/oo)

18 20 22 24 26 28 30 32 34 35

T(K) 298.16

293.16

288.16

283.16

278.16

0.1215 0.1145 0.1085 0.1032 0.0986 0.0944 0.0905 0.0870 0.0838 0.0822

0.1225 0.1158 0.1100 0.1049 0.1004 0.0963 0.0926 0.0891 0.0859 0.0844

0.1226 0.1163 0.1108 0.1060 0.1016 0.0977 0.0940 0.0906 0.0875 0.0860

0.1219 0.1160 0.1108 0.1062 0.1021 0.0983 0.0948 0.0915 0.0884 0.0870

0.1202 0.1148 0.1100 0.1057 0.1018 0.0982 0.0948 0.0917 0.0887 0.0873

TABLE IV Activity coefficient of Ca ion in seawater, 7Ca, calculated from ~'±CaCO3 (this work) and ~/co3 from Pytkowicz (1975)

S(°/oo )

25 27 29 31 33 35

T(K) 278.16

283.16

288.16

293.16

298.16

0.159 0.167 0.170 0.176 0.178 0.177

0.166 0.171 0.174 0.175 0.177 0.176

0.172 0.173 0.176 0.177 0.174 0.172

0.176 0.177 0.175 0.176 0.178 0.176

0.181 0.178 0.177 0.178 0.175 0.173

t h e activity c o e f f i c i e n t s f r o m m o l kg s e a w a t e r -l t o m o l kg I=I2 O - 1 . Since t h e activity c o e f f i c i e n t s are generally r e p o r t e d as 7±caco3, this c o r r e c t i o n has b e e n m a d e a n d t h e values p r e s e n t e d in T a b l e III. Historical values o f 7±caco3 a t 25°C a n d a p p r o x i m a t e l y 2 5 % salinity are 0 . 0 9 5 ( P y t k o w i c z , 1 9 7 5 ) . This value was r e c a l c u l a t e d using t h e c o r r e c t value o f k f r o m H a w l e y a n d P y t k o w i c z ( 1 9 7 3 ) o f 1.13, 0 . 0 6 9 ( L e y e n d e k k e r s , 1 9 7 3 ) , 0 . 0 6 5 (Berner, 1 9 6 5 ) a n d 0 . 0 8 3 ( J o h n s o n , 1 9 7 9 ) . We c a n n o w calculate ~/c~ using o u r 7±c,co3 a n d t h e ~fco3 values o f P y t k o w i c z (1975). T h e s e values are given in T a b l e IV. T h e values o f 7c~ c a l c u l a t e d h e r e are d e p e n d e n t o n t h e value o f t h e k f a c t o r , w h i c h a c c o u n t s f o r t h e c h a n g e s in t h e a s y m m e t r y a n d t h e liquid j u n c t i o n p o t e n t i a l s w h e n glass e l e c t r o d e s are t r a n s f e r r e d f r o m a dilute b u f f e r t o seawater. T h e value o f 7~caco3 f r o m J o h n s o n ( 1 9 7 9 ) was c a l c u l a t e d using an ion a s s o c i a t i o n m o d e l o f seawater. I t is i n d e p e n d e n t

20

! £] E]

ocl

c] meet, . . . . +--V ...... 10-6 -

',,e~:penmentol []

standard

dewohon

10-8

Y

[

0 I 046

I

I

048

K~p x

050 I 0 £"

Fig. 7. Scatter diagram of IP i vs Ksp : [] (determined from supersaturation); o (determined from undersaturation). TABLE V ¢

Ksp and IP i of seawater at 278.16 K and 34.57°/~ sMinity

Ksp 2 (mol kg seawater -2 ) × 106

[Pi

0.498 0.469 0.467 0.496 0.479

2.28 4.31 2.81 7.27 5.31

x 10-6 x 10-9 x 10-6 x 10-8 x 10-7

Ksp . (tool" kg seawater -2 ) × 106

IPi

0.464 0.484 0.486 0.467

2.64 3.23 3.09 2,81

x 10-6 x 10-7 x 10-6 x I0 -6

of the activity of calcite. Therefore, its good agreement with our value supports our assumption that the activity of calcite in the equilibrium solid is unity. In this section, it is assumed that thermodynamic equilibrium was reached during the experimental determination of Kip. It is very important that this assumption be tested. This could be accomplished if good experimental data for ~/caTco~ in addition to K°p were available. A soft electron microprobe study of surface coatings formed on large calcite crystals in seawater might yield an indication of the Ca to Mg mole ratio of the equilibrium state of the solid surface. This could be used to test the a u u m p t i o n that ac~cite = 1. Finally, a comparison of the Kip values obtained from supersaturation and undersaturation of calcite should yield the same value for a true equilibrium case. We made runs from a variety of initial ion products at 34.57°/o0 and 278.16 K and, within experimental error, the results were identical for

21 initially supersaturated and undersaturated seawater. The data for these determinations are given in Table V, and Fig. 7 shows a plot of the results. This can be interpreted as showing that the samples are reaching thermodynamic equilibrium. Nevertheless, the surface composition of the solid remains unknown. It is likely that it contains 2--5 mol % MgCO3, in accordance with the results of Plummet and Mackenzie (1974) and of Wollast and Reinhard-Derie (1977).

Determination o f AH' The change in lnK°p with respect to I/T is defined as d(lnK°p)/d(1/T) = - - A H ° / R

(12)

Since lng~p =

lnK°p -- lnTca 7co,

(13)

we can say d(lnKsp )/d(1/T) = d(lnK°p )/d(1/T) -- d(lnTca 7co3 )/d(1/T)

(14)

Thus, we can n o w define A H ' by t

d(lnKsp)/d(I/T)

=

(15)

-- A H ' / R

One should, therefore, be able to plot InK~p vs. l I T for the three salinities used here and obtain the values of ~H' with respect to salinity. Equation 6 was used to calculate the lines shown in Fig. 8. The slopes of these lin~s are equal to - - A H ' / R . These slopes yield values as follows: S = 18.29°/0o : A H ' = --1615.7 calmo1-1 ; S = 24.45~/o0 : A H ' = - - 1 0 5 0 . 2 c a l m o l -l ; S = 34.57°/00 : A H ' = - - 4 8 4 . 7 calmo1-1 . Plotting these A H ' values vs. the salinity and performing extrapolation to zero salinity gives a value of A H ° that is consistent - i5A

~ _c

18.29%o

-15.( "

-14.(

24.45%o

------.-._ 34.57

3.3

31.4 IITx

3:5 103

%.

' 5.6

Fig. 8. lnK:p versus lIT at 18.29°/oo, 24.450/o0 and 34.570/oo salinity (from eq.6).

22

300¢ I

t \\ \ i

\ \

\

E

\ \

<1

O

O

I000-

i

. . . . . .

~0

20

30

Salinily (%o)

Fig. 9. H ' vs. s a l i n i t y : © --- t h i s w o r k ; A : zk/-/° , J a c o b s o n a n d L a n g r n u i r ( 1 9 7 4 ) .

with that of Jacobson and Langmuir (1974) (see Fig. 9). This extrapolation is very rough as the activity coefficients of CaCO3 and MgCO3 change in an u n k n o w n manner with S°/oo and is, therefore, a tentative one.

Saturation profiles The percent saturation of seawater with respect to calcite is defined as %Saturation :

100% x (IP)~ situ/(K~p )m situ

(1)

where the in-situ ion product, (IP)m ~tu, equals the in-situ product of calcium ? and carbonate ions. The in-situ Ksp is the apparent solubility product of calcite presented in this paper, corrected for the effects of pressure and temperature at a given salinity. The percent saturation should n o t be confused with the quantity of calcite which must dissolve or precipitate in order to reach equilibrium. It must be remembered that the precipitation and dissolution of calcareous species change the carbonate and bicarbonate content of the water. The partitioning between these two species depends u p o n T,P,S and the CO2 ! c o n t e n t of the water. Ksp, on the other hand, is independent of pCO2. The in-situ ion product was calculated using the simplified equations for the carbonic acid dissociation constants of Mehrbach et al., presented earlier in this work, the borate constant of L y m a n (1956), and the pressure corrections for these constants determined by Culberson and Pytkowicz (1968). The in-situ pH was calculated from TA and TCO 2 data using the m e t h o d of

23 F

Culberson and Pytkowicz (1968). The in-situ Ksp was calculated for our I value of Ksp at atmospheric pressure using both the pressure correction of Hawley and Pytkowicz (1969) and that of Ingle (1975). While Ingle's pressure correction was calculated from experimental determinations with calcite, that of Hawley and Pytkowicz was derived from experimental measurements with aragonite and must be adapted for the present purpose. It is known that !

(d lnKsp/dP)T = - - A ~ J / R T

(17)

Integrating this gives ln(g,p

,1 )calcite /Ksp

=

--ACJ&P/RT

:

--(Vcalcite

- - V--CO3 - - f f C a ) & P / R T

(18)

This can also be written for aragonite. Then, by combining eqs. 17 and 18 we get ln(g'~

,1 )arag. /Ksp

--

,p ,1 )calcite ln(Ksp/Ksp

-_-

(V-calcite - - ~arag. ) & P / R T

(19)

Therefore ln(g'~P /Ksp ,1 )calcite

:-

,p ,1 )arag. ln(Ksp/Ksp

- - (V'calcite - - f f a r a g . ) Z ~ P / R T

(20)

?

where the superscripts p and 1 refer to the values of Ksp at in-situ pressure and 1 atmosphere and V'-calcit e a n d V'-arag"are partial molar volumes (Owen and Brinkley, 1941). While the correction presented by Hawley and Pytkowicz (1969) was derived from fewer experimental determinations than that of Ingle, the use of aragonite as a basis makes it theoretically appealing, since for pure calcite compositional changes due to surface reactions with Mg ion are noted (Weyl, 1961; Bemer, 1976a). However, the use of calcite may be more sound, since it represents better the conditions which a calcitic particle would actually encounter under general oceanic conditions. The experimental values of Hawley and Pytkowicz for i~T. .(s p'Pt . ~IT-(" s p )Ia1. r a g . after adaption for use with calcite were fitted to an equation of the form rp ~1 ln(K~p/Ksp)calcite

= 1.6220 × 10 -2 + 5.4627 x 1 0 - 3 P - - 1.4656

x 10-SPT- (O.03379/T)(P-

1)

(21)

Those of Ingle (1975) were fitted to rp t1 ln(K~p/Ksp )calcite

=

0.071320 + 0 . 0 0 8 0 4 1 2 P - 2.2544 x 1 0 - S p T

(22)

where P is the pressure in atmospheres and T is the absolute temperature. The log function was used for the fit since Ks'p is an exponential function of pressure. Figure 10 shows station 70 of Yaloc 69. The three profiles represent the same station as calculated first by Ingle (1975) and then using the two pressure corrections as stated earlier. As the temperature decreases (depth increases) the difference between Ingle's profile and ours using her pressure

24 ~o SAT URATIQr~ 60

80

iOO

120

]40

/ r

I000~-

~ 2000p

r

'~ D

t

~,

o

3000H

4000

l-

Fig. 10. Yaloc 69, station 70. Saturation profiles: o = this work, pressure correction of Hawley and Pytkowicz (1969); []L--'this work, pressure Correction of Ingle (1975); a = profile from Ingle (1975). TABLE

VI

100% s a t u r a t i o n h o r i z o n , lysocline and c a r b o n a t e c o m p e n s a t i o n d e p t h ( C C D ) f o r several GEOSECS stations

Station

214 215 319 269 115 116 32 33

NC NC SE SW NE NE NW NW

Pac Pac Pac Pac Atl Atl Atl Atl

100% Saturation horizon (m)

Lysocline

CCD

Ingle

Hawley et al.

(m)

(m)

(1975)

(1969) ? ? 3750a--4000 b 4200 b 4900 d 4900 d 4750 d 4750 d

4400 4400 4200 4300 5600 5600 6000 6000

745 706 1800 1580 3854 3585 3630 3536

768 730 2850 2116 5300 4500 4585 4600

a Berger (1970). b Parker and Berger (1971). c Berger (1976). (1978). e Biscaye et al. (1976).

d

c c c c e e e e

Broecker and Takahashi

correction decreases. This is expected since the Kspt values for the two cases agree well at low temperatures. Using the pressure correction of Hawley and Pytkowicz (1969) yields consistently greater percent saturation values. In order to further investigate the effect of the different pressure corrections, eight G E O S E C S stations were taken for which profiles of percent saturation were calculated in the manner outlined above. The 1 0 0 % saturation horizons obtained at each station and for each pressure correction are shown in Table VI, along with the lysocline and the carbonate compensation depths for each area. W h e n the 1 0 { ~ saturation horizon is less than 1 0 0 0 m in depth the effect of pressure is small. Thus, the two pressure corrections

25

give similar results. However, at depths of 3000 m or more the pressure effect is pronounced and differences of up to 1500 m in the 100% saturation horizon can be seen. In the case of stations 115 and 33 the 100% saturation horizon, based on the correction of Hawley and Pytkowicz (1969) is close to or deeper than the lysocline. This means that the calcite solubility data derived from their aragonite pressure coefficient data may not be valid perhaps because they refer to an ideal pure calcite. Alternatively, the values deeper than the lysocline may simply reflect uncertainties in the data. However, Millero (1976) has stated that the change in molar volume, V*, calculated from Ingle's (1975) measurements agrees well with direct measurements of partial molar volumes in seawater. Therefore, the use of Ingie's pressure correction is preferred by the authors for oceanic applications to calcite. There are several errors inherent in the calculation of the 100% saturation I horizon depth. The first is the uncertainty of the Ksp at one atmosphere and t in the Ksp at depth. From this work we know that the standard deviation of the K~p at one atmosphere is ~3--4%, and the uncertainty in the pressure-corrected Ks'p is ~6%, determined by Ingle (1975). Secondly, the error in the in-situ ion product contributes to the overall uncertainty in depth. This is primarily due to the uncertainties in the experimental determinations of titration alkalinity, borate alkalinity and a H . The standard deviations for these measurements were calculated by Johnson et al. (1977) and are +0.13%, +1.89% and +1.89%, respectively. Together these errors give a combined error for the determination of the carbonate concentration, the largest error in the ion product determination, of +2.68%. Finally, the largest uncertainty in the 100% saturation horizon depth calculation is due t to the angle at which the ion product and Ksp curves cross. Figure 11 shows o

(tool kg - I SW) 2 x I0 6 I

t

2

Fig. 11. Ksp (solid line) and IPin situ (dashed line) vs. depth for station 33. Shading indicates uncertainties in Kip and IP.

26 that the resolution of the saturation horizon when it occurs in deep waters {Atlantic and south Pacific) by the indirect m e t h o d is limited to about 750 m. The method is indirect when based upon the measurement of the ion product in the field compared with Kip obtained at pressure in the labora. tory. Improvements in experimental precision are likely to be limited. Nevertheless, the method yields general indications of the degree of saturation of oceanic water which may serve for rough studies of the lysocline and the carbonate compensation depth, the latter being definitely deeper than the 100% saturation horizon. In the north Pacific the saturation horizon is better defined because the onset of undersaturation occurs at shallower depths. In this case, the IP and the Ksp lines cross at a wider angle, as is illustrated in Fig. 10. Here the uncertainty in the 100% saturation horizon depth is less than 50 m. t

DISCUSSION OF IN-SITU SATUROMETRY Broecker and Takahashi {1978) defined the 'critical carbonate' as the CO~-) concentration at the lysocline. Later they identified it also with the 100% saturation horizon by equating their lysocline-based results with the pseudo-100% saturation results of Ben-Yaakov et al. (1974). These results can easily be seen not to have reached a steady state due to the brevity of their runs. Thus, the two concepts embraced by the definition of Broecker and Takahashi, the carbonate concentration at the lysocline and the carbonate concentration at 100% saturation, may not coincide. The first concept may be referred to as the 'lysocline carbonate' and the second as the 'critical carbonate'. Ben-Yaakov and Kaplan {1971) showed that, in the region of the 100% saturation horizon, a steady state was reached with in-situ saturometry after equilibration times of 15--30 min. The uncertainty in this case was ~ 2 mV. However, visually approximating the fit to the examples presented in BenYaakov and Kaplan (1971) and assuming 5 m i n stagnation periods as the runs in Broecker and Takahashi (1978) did, we find that the final EMF deviates from the asymptotic value (derived from the visual estimates) by 2 mV in the region of the 100% saturation horizon to 13 mV at the surface. Therefore, we can see that for short equilibration times the best Values for in-situ saturometry occur near the 100% saturation horizon. As one moves away from this depth the accuracy of this m e t h o d becomes increasingly dependent on the dissolution and precipitation kinetics of calcium carbonate. If the sedimentary lysocline is kinetically controlled, as are the carbonate concentrations arrived at by in-situ saturometry, then we should expect these results to diverge from the true critical carbonate values as we move away from the 100% saturation horizon. Thus, agreement between lysocline concentrations and the pseudo-critical carbonate values determined by insitu saturometry does not mean these values represent the actual critical carbonate concentrations.

27

(pmoLkg-tSW) I00 ~50

CRITICAL CARBONATE

0 ~50

I000

1

'

2000

500C

400C 500C Fig. 12. Calculated critical carbonate from this work (o); in-situ saturometry (n) of BenYaakov et al. (1974); lysocline carbonate values (A) of Broecker and Takahashi (1978). The star represents the value of Ksp at I atm, from eq. 6.

The critical carbonate concentrations for GEOSECS station 233 (central north Pacific) have been calculated in order to prove the inaccuracies of in situ saturometry caused by kinetic effects. These calculations were made f using the values of K~p from the present work, the pressure coefficients of Culberson and Pytkowicz (1968), the carbonate dissociation constants presented in this paper, the borate dissociation constant of Lyman (1956), f the pressure correction for Ksp of Ingle (1975), and the titration alkalinity and total CO2 data from the GEOSECS preliminary report (1973). The critical carbonate was calculated by first iteratively solving eq. 1 for aH until t the condition that eq. 2 is equal to the in-situ Ksp was met. Then, eq. 3 was used to calculate the critical carbonate. The authors have shown that the 100% saturation horizon occurs between 500 and 1000 m depth in this area of the Pacific. Our critical carbonate results are shown with the lysocline carbonate and in-situ saturometry data presented by Broecker and Takahashi (1978) in Fig. 12. Broecker and Takahashi's lysocline carbonate concentrations agree well with the in-situ saturometry determinations of Ben-Yaakov et al. (1974). However, from Fig. 12 it may be seen that these results deviate, in the predicted manner, from our calculated critical carbonate curve. This suggests that the lysocline is deeper than the 100% saturation horizon. This could be a result of the dissolution kinetics of calcite as pointed out earlier with respect to in-situ saturometry. This supports the t h e o r y of the kinetic origin of the lysocline. ACKNOWLEDGEMENTS

This work was done under the auspices of NSF Grant OCE-77D0018A02 and Office of Naval Research Contract N00014-76-C-0067. Thanks are also

28 due to Elliot Atlas for discussions on the use of the saturometer design.

c e l l o f his

REFERENCES Ben-Yaakov, S. and Kaplan, I.R., 1971. Deep sea in-situ calcium carbonate saturometry. J. Geophys. Res., 76: 722--731. Ben-Yaakov, S., Ruth, E. and Kaplan, I.R., 1974. Carbonate compensation depth: relation to carbonate solubility in oceanic waters. Science, 184: 982--984. Berger, W.H., 1970. Planktonic foraminifera: selective solution and the lysocline. Mar. Geol., 8: 111--138. Berger, W.H., 1976. Distribution of carbonate in surface sediments of the Pacific Ocean. J. Geophys. Res., 81: 2617--2627. Berner, R.A., 1965. Activity coefficients of bicarbonate, carbonate, and calcium ions in seawater. Geochim. Cosmochim. Acta, 29: 947--965. Berner, R.A., 1976. The solubility of calcite and aragonite in seawater at atmospheric pressure and 3 4 . 5 % salinity. Am. J. Sci., 276: 713--730. Biscaye, P.E., Kolla, V. and Turekian, K.K., 1976. Distribution of calcium carbonate in surface sediments of the Atlantic Ocean. J. Geophys. Res., 8: 2595--2603. Broecker, W.A. and Takahashi, T., 1978. The relationship between lysocline depth and in situ carbonate ion concentration. Deep-Sea Res., 25: 6 5 - 9 5 . Culberson, C.H., 1968. Pressure dependence of the apparent dissociation constants of carbonic and boric acids in seawater. M.S. Thesis, Oregon State Univ., Corvallis, OR, 85pp. Culberson, C.H. and Pytkowicz, R.M., 1968. Effect of pressure on carbonic acid, boric acid and the pH in seawater. Limnol. Oceanog., 13: 403--417. G E O S E C S , 1973. Preliminary data report, sponsored by IDOE. Hawley, J.E. and Pytkowicz, R.M., 1969. Solubility of calcium carbonate in seawater at high pressure and 2°C. Geochim. Cosmochim. Acta, 33: 1557--1561. Hawley, J.E. and Pytkowicz, R.M., 1973. Interpretation of p H measurements in concentrated electrolyte solutions. Mar. Chem., 1 : 245--250. Ingle, S.E., 1975. Solubility of calcite in the ocean. Mar. Chem., 3: 301--319. Ingle, S.E., Culberson, C.H. Hawley, J.E. and Pytkowicz, R.M., 1973. The solubility of calcite in seawater at atmospheric pressure and 35O/oo salinity.Mar. Chem., 1: 295-307. Jacobson, R.L. and Langmmr, D., 1974. Dissociation constant of calciteand Ca(HCO3 )+ from 0 ° to 50°C. Geochim. Cosmochim. Acta, 38: 301--318. Johnson, K.S., 1979. Ion association and activity coefficients in electrolyte solutions. Ph.D. Dissertation Oregon State Univ., Corvallis,O R (in preparation). Johnson, K.S., Voll, R., Curtis, C.A. and Pytkowicz, R.M., 1977. A criticalexamination of the N B S p H scale and the determination of titration alkalinity. Deep-Sea Res., 24: 9 1 5 - 9 2 6 . Leyendekkers, J.V., 1972. The chemical potentials of seawater components. Mar. Chem., 1 : 75--88. Lyman, J., 1956. Buffer mechanism of seawater. Ph.D. Dissertation Univ. California, Los Angeles, CA, 160 pp. MacIntyre, W.G., 1965. The temperature variation of the solubility product of calcium carbonate in seawater. Fish. Res. Board Can., Rep. No. 2 0 0 , 1 5 3 pp. Mehrbach, C., Culberson, C.H., Hawley, J.E. and Pytkowicz, R.M., 1973. Measurement of the apparent dissociation constants of carbonic acid in seawater at atmospheric pressure. Limnol. Oceanog., 18: 897--907. Millero, F.J., 1976. The effect of pressure on the solubility of calcite in seawater at 25°C. Geochim. Coamochim. Acta, 40: 9 8 3 - 9 8 5 . Morse, J.W. and Berner, R.A., 1972. Dissolution kinetics of calcium carbonate in seawater. II. A kinetic origin for the lysocline. Am. J. Sci., 272: 840---851.

29 Owen, B.B. and Brinkley, S.R., Jr., 1941. Calculation of the effect of pressure upon the equilibria in pure water and in salt solutions. Chem. Rev., 29: 461--472. Parker, F.L. and Berger, W.H., 1971. Faunal and solution patterns of planktonic foraminifera in surface sediments of the south Pacific. Deep-Sea Res., 18: 73--107. Plummet, L.N. and Mackenzie, F.T., 1974. Predicting mineral solubility from rate data: application to the dissolution of magnesian calcites. Am. J. Sci., 274: 61--82. Pytkowicz, R.M., 1975. Activity coefficients o f bicarbonates and carbonates in seawater. Limnol. Oceanog., 20: 971--975. Pytkowicz, R.M. and Cole, M., 1980. Heterogeneous equilibria in mixed electrolyte solutions. Am. Chem. Soc. Symp. Ser., Washington, DC (in press). Pytkowicz, R.M. and Fowler, G.A., 1967. Solubility of foraminifera in seawater and high pressures. Geochim. J., 1: 169--182. Pytkowicz, R.M. and Hawley, J.E., 1974. Bicarbonate and carbonate ion pairs and a model of seawater at 25°C. Limnol. Oceanogr., 19: 223--234. Takahashi, T., Kaiteris, P., Broecker, W.S. and Bainbridge, A.E., 1976. An evaluation of the apparent dissociation constants of carbonic acid in seawater. Earth Planet. Sci. Left., 32 : 458--467. Thorstenson, D.C. and Plummer, L.N., 1977. Equilibrium criteria for two component solids reacting with fixed composition in an aqueous phase. Example: the magnesium calcites. Am. J. Sci., 277: 1203--1223. U.S. Naval Oceanographic Office, 1966. Handbook of Oceanographic Tables, SP-68. Weyl, P.K., 1961. The carbonate saturometer. J. Geol., 69: 32--44. Wollast, R. and Reinhard-Derie, D., 1977. Equilibrium and mechanism of dissolution of Mg-calcites. In: N.R. Anderson and A. Malahoff (Editors), The Fate of Fossil Fuel CO 2 in the Oceans. Plenum Press, New York, NY, pp. 479--496.