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The partial molal volume of calcium carbonate in sea water
Geoehimica et CosmochimicaActa, 1972.Vol. 313, pp. 729to 734. Pergamon Press. Printed in Northern Ireland
The
partial molal volume of calciumcarbonate in sea
water*
I. W. DUEDALL~ Bedford Institute, Dartmouth, Nova Scotia (Received 8 November1971; acceptedin revisedform 21 Januag
1972)
Abstract-The partial molal volumes (a,) of K,CO, and Na,COs have been experimentally determined, at 20°C, for sea water (35x,) and for 0.725 M NaCl. For sea water, #g,oos equals 28.3 -+ 0.8 ml/mole and dNalCosequals 9.0 f l-5 ml/mole; for 0.725 M NaCl, ~&Co5 equals 23.17 & 0.35 ml/mole and #NsBCoS equals 174 f 0.23 ml/ mole. Using the sea water values and some literature values for other salts in sea water, flcaco8 for sea water was calculated to be -65 & 1.7 ml/mole. This value does not agree with 0~~~9, calculated from data for the effect of pressure on the solubility product of calcium carbonate m sea water. A possible explanation is that the data on the pressurecoefficientof the solubility of calcium carbonate may be in error.
IN RECENTpapers dealing with the problem of calcium carbonate saturation in sea water LI et al. (1969), HAWLEYand PYTKOWICZ(1969), and EDMONDand GIESKES (1970) calculated the volume change when calcium carbonate dissolves in sea water. Hawley and Pytkowicz’s and Edmond and Gieskes’ calculations were based on the effect of pressure on the stoichiometric solubility products of calcite and aragonite in sea water (PYTKOWICZand FOWLER, 1967; HAWLEY and PYTKOWICZ,1969); they used the following familiar equation which relates solubility product (K) to the partial molal volume change (A 7) and pressure (P) : hl
[211 =$gP_l)
If the thermodynamic solubility product concept is applied to equation (l), where the standard state is decked as infinite dilution in pure water, then AT equals ~o~o~,(inf. dil.) - PoaoO,; @ocaoo,(inf.dil.) and VoaoO, are the partial molal volume at infinite dilution in pure water and molar volume, respectively, of calcium carbonate. If the stoichiometric solubility product is used in equation (l), where now the standard state is defined as infinite dilution in normal sea water (i.e. 35x0 salinity), then, as PYTKO~ICZand FOWLER(1967) state, A7 for sea water (termed hereafter as AV(sw)) is not simply the change in volume due to ionization of calcium carbonate but includes a volume contribution to 5oc,oo,(inf. dil.) due to dissociation of carbonate ion-pairs. However, EDMONDand GIESKES (1970), who report a stoichiometric AP(sw) which is based on the solubility measurements made by PYTKOWICZand FOWLER(1967) and HAWLEY and PYTKOWICZ(1969), appear to obscure the meaning and usefulness of AP(sw) by saying that it is not defined in terms of ‘specific chemical reactions’. I should point out that in the derivation of equation (1) the condition for stoichiometric equilibrium (and also for thermodynamic equilibrium) for the dissolution of calcium carbonate in sea water is that * Bedford Institute Contribution. t Marine Ecology Laboratory and Chemical Oceanography Division. 729
I. W. DIJEDAIL
730
the free energies of the reactant and the product be equal. The fact that the dissolution of calcium carbonate in sea water leads to the formation of carbonate ion-pairs as well as other ionization products which therefore contribute to the overall ~~~~o,(sw) does not mean that each ‘specific chemical reaction’ has to be identified and assigned a specific free energy. The free energy of the dissolution products can be considered as the overall sum of the chemical potentials of all product species and GWZO &SW) represents the overall sum of the pressure derivatives of these fioCaCO,(sw)can therefore be calculated from the following chemical potentials. equation regardless of Edmond and Gieskes’ interpretation of A I : AP(sw)
= %Caco,(sw) -
LCO,
B~~~~,(sw) is the partial molal volume of calcium carbonate in sea water and as derived from equation (1) and as mentioned above it represents the sum of the pressure derivatives of the chemical potentials of the products of calcium carbonate where al’ is the overall dissolution. flcaCO*(SW) is also defined as ( ~V/iMfc,co,) incremental volume change of sea water due to the dissolution of an incremental mass, aM, of calcium carbonate. This latter definition which is a valid thermodynamic expression for a defined standard state is explicitly expressed in terms of measureable quantities (i.e. volume and mass). And, according to a review by HAMANN (1963) the ability of equation (1) to predict volume changes for the ionization of acids has been amply verified. This has also been shown for sea water in the recent paper by MILLERO and BERNER (1972). A comparison of ficiiCaCO,(sw) calculated from A I with fiCaCO,(~~) determined by a direct measurement therefore provides a method for determining the accuracy of the present data for the effect of pressure on the solubility of calcium carbonate in sea water. The measured [or calculated from AP(sw)] ficaco s(sw) will differ from a measured flccaco,(inf. dil.) (where the standard state is infinite dilution in pure water) for a few reasons one of which being the volume contributions to 5caC~,(s~) due to carbonate ion-pairs. Fundamental to this question of volume change is ficacO,(sw), the partial molal volume of calcium carbonate in sea water. Heretofore the only value for flc,cos(sw) available in the literature was given by OWEN and BRINKLEY (1941), an approximation which was based, in part, on the behaviour of other salts in sodium chloride solutions. In this paper I report a new value for ficCaCOI( SW) w m‘c h was calculated from the following additivity relationship : BCaco,(SW)
=
%c~(NO,),(~~) +
-
@KNO,(SW)
i!{FKsCO,(sw) +
+
flNaNO,(SW)}
BNa,COs(SW)}
(2)
(SW) have already been reported (DUEDALL, 1968) ~~~FN~No, of flx&O,(sw) and !!&CO, (SW) are reported here. Measurements of in 0.725 M NaCl (a solution having the same ionic strength as @K,CO, and @Na&O 35x,, sea water) ar”e also reported. The i~#‘sreported here are partial molal volumes which include volume contributions due to carbonate hydrolysis and carbonate ion pairs, and therefore, the values should not be misunderstood as being the sum of the volumes for the free ions, as reported by MILLERO (1969).
fb(NO,),(SW),
@KNO,(SW)
and measurements
The partial molal volume of calcium carbonate in sea water
MEASUREMENT
731
OF 4Jilrtco, AXD -tTNhco,
The method consists of measuring the change in volume on ~ssolution of additions of a known mass of salt to sea water contained in a specially designed dilatometer (DUEDALLand WEYL, 1965). The partial molal volume is determinedby extrapolation of the ratio of cumulative volume change (AV,) to cumulative mass addition (Anz)to zero salt addition. The dilatometer was first filled with either IAPSO Standard Sea Water, of salinity 35*00%,, or 0.725 M sodium chloride, and then placed in a 20°C thermostat in which the temperature was maintained to a constancy and accuracy of &0~005”C?. Fisher Certifiedreagents (l&CO, and NaaCOs) were used t~ughout. In experiments with O-725 M sodium chloride, about 0.15 g of salt per addition was dispensed into the dilatometer. However, for the salt additions to sea watex only about 0.05 g W&EIdispensed per addition because a cumulative salt addition of greater than 0.20 g caused calcium oarbonate to precipitate. Figures 1 and 2 show plots of AV,/Am vs Am &CO,
35%, sea water
i
25-
9 5
0.725
240 235
M NaCC
O* B
Cl 0
0 OA
A 0
n
u
cl
22-
I 0.1
21
I 0.2
I 0.3
I 0.4
I 0.5
1 0.6
I 07
I
Ah-f.9 Fig. 1. D&a for the partial molal volume of &CO,. Na, CO,
35 %o sea water
z 8
$6 1*
4
a-1 2
0.725 M NaCL ,B
I 0.1
v
I 0.2
"dour_
I 0.3 AM,
I o-4
j;j
I o-5
.I 06
I 0.7
6
I 0.8
t
W
Fig. 2. Data for the partial molal volume of NasCOs.
I.W.
732
DUEDALL
for several runs. The intercept values (at Am = 0) are the partial molal volumes, and these values were determined by fitting (by least squares) the combined data from all the runs to a linear equation. (Because so few data are available at low concentrationsfor each run, especially for sea water, I feel one has more confidencein the extrapolation when data from all the runs are combined rather than fitting the data from individual runs.) The partial volumes are given in Table 1. The uncertainty associated with each value is an absolute experimental error based Table 1. Partial molal volumes of K&O, and Na,CO, in NaCl (0.725 M) and sea water (35% salinity)
Solution
Partial molal volumes (ml/mole) K&O,
NaCl (0.725 M)
28.3 -&to.8 23.17 &0.35
Na,CO, 9.0 *1*5 l-74 &0.23
on the magnitude of the change in volume (AVJ, due to a salt addition, and on the absolute error in reading AV, (DUEDALL,1966). In sea water the errors are large because of the small volume changes measured, necessitated by having to add exceptionally small amounts of carbonate salt to sea water to avoid the precipitation of calcium carbonate. 6, is the linear extrapolationof AVJAm to zero salt addition, but the pH change of the solution in the dilatometer is not a linear function of the amount of carbonate salt added. Large pH changes occur for initial salt additions, and the extent of this effect is considerably greater for 0.725 M NaCl than for sea water. For sea water, this effect probably doesn’t significantly affect the extrapolation of AV,/Am because a linear extrapolation of pH to zero salt addition gives 8.7 whereas the initially measured pH of the sea water was 8.2. However, for 0.725 M NaCl, where the initially measured pH was 6.1, the extrapolated pH was about 10.4 which may have some measureable affect on B, (0,725 M NaCl). An obvious, but not too surprisingfeature of the f18results,is the significantdifferencebetween g8in sea water and 0, in 0.725 M NaCl. A major part of this differenceis probably because more carbonate ions are hydrolyzed in sea water to form bicarbonate ions than in 0.725 M NaCl. Therefore, the bicarbonate ion volume contribution to 8, must be greater in 9, (SW)than in 0, (0.725 M NaCI). Also, because of the presence of other cations in sea water, volume contributions to 0, due to bicarbonate and carbonate ion-pairs would be greater for sea water than for 0.725 M NaCI. CALCULATION OF Gino, f&,co,(sw) can be calculated from equation (2) using the flKSco,(sw) and T~~+~,(sw) reported here and the 20°C values of 5c,t,o,,,(sw), &o,(sw) and fiNaNO,(sw)reported previously (DUEDALL, 1968). The calculated BCaCO,(sw)equals -6-5 6 1.7 ml/mole. By comparison the frequently used fleaGo, (‘salt water’) reported by OWEN and BRINKLEY (1941) is - 13.9 ml/mole, which is probably close to BCaCO,(O-725 M NaCl) because fiKSco, (0.725 M NaCI) and &+oa (O-725 M NaCI) determined by the dilatometric method agree with the Owen and Brinkley data. flcCaCO,(sw)can also be calculated from the reported data on AP(sw) (HAWLEY and PYTKOWICZ, 1969; EDMOND and GIESKES, 1970) based on work (PYTKOWICZ and FOWLER, 1967; HAWLEY and PYTKOWICZ, 1969) to determine the effect of pressure on the stoichiometric solubility product of calcium carbonate in sea water.
The partialrnolalvolume of oalciumcarbonateia.sea water
733
For calcite, Av(sw) equals -304 f 1 ml~mole at 20°C (ED~o~D and G~s~s, 1970). Therefore, using 36.9 ml/mole (WEAST, 1965) as the molar volume of calcite, the calculated poCaCo,(sw) is 6.1 f I ml/mole. However, @ocsoo,(sw)determined from dilatometer results is -65 -+ 1.7 ml/mole. The large difference between these two values appears greater than can be explained solely by the effect of pressure on iiCaCO,(sw). For instance, although data are not available for calcium carbonate, data (HAMANN, 1957) for sodium chloride show that f&o&nf. dil.) in pure water increases by only 3 ml/mole at 1000 bar. Some of the discrepancy between the two values for fjcaco, (SW) could be explained if chemical equilibrium was never quite reached in the solubility experiments done by PYTKOWICZand FOWLER(1967) and HAWLEYand PYTHOWICZ (1969). This would have the effect of producing a smaller calculated (equation 1) volume change than the equilibrium AP(sw), and conse(SW), based on the effect of pressure on the solubility quently, the calculated ficCaCo, of calcium carbonate, would be greater than what is determined from dilatometer measurements. Very recently I learned that MILLERO and BEENER (1972) have also calculated the volume change for calcium carbonate ~ssolution. Their calculations were based on an ion-pair model and available data for the effect of pressure on the ionization of bicarbonate in sea water. From their results, fiCaCo,(sw),at 25’C, equals -25 If 2.4 ml/mole, which is in good agreement with the ~cCaCo,(~~)determined from dilatometer results considering the assumptions they made and the available data, and also taking into account that the dilatometer result is a 20°C value while the (SW)is at 25°C and that salts in sea water exhibit positive expansibiliestimated gcCaoo, ties (~~1~~~0, 1969). Also, because IVIillero and Berner’s cocoon differed conoaCO,(sw) calculated from calcium carbonate solubility data, they siderably from 8 suggested that the effect of pressure on the solubility of calcium carbonate in sea water may be in error. Acknowledgements-I thank A. R. COOTE,R. C. COOKE,F. J. MILLEROand D. KESTER for their helpful discussionsand also thank A. WALTON for readingthe manuscriptand offeringsuggestions for its improvement.
DUEDALL I. W. (1966) The partial equivalent volumes of salts in sea water. MSc. Thesis, Oregon State University, 47 pp. DT~DALL I. W. (1968) Partial modalvolumes of 16 salts in sea water. Enuiron. Sci. Tech. 2, 706-707. DUEDALL I. W. and W~YL P. K. (1965) Apparatus for determining the partial equivalent volumes of salts in aqueous solutions. Rev. Sci. In&r. 36, 528-531. EDXOND J. M. and GIESKES 5. M. T. M. (1970) On the calculation of the degree of saturation of sea water with respect to calcium carbonate under in situ conditions. ~e~~~~~~.Cos~oeh~~. Acta 34, 1261-1291. IZANANN S. D. (1957) Physica-Chemical E#ects of Pressure,Buttorworths, 246 pp. IXAMANN S. D. (1963) Chemical equilibria in condensedsystems. In High Pressure Physic.g aad Chemistry. (editor R. S. Bradley), 361 pp. Academic Press. HAWLEY J. and PVTKOW~CZ R. M. (1969) Solubility of calcium carbonate in sea water at high pressuresand 2%. Geochim. Cosmochim. Acta 33, 1557-1561. Lx Y. -H., TA~ARASRI T. and BROEKXRW. S. (1969) Degree of saturationof CaCOsin the ooe&ng. J. Geophys. Res. ‘X,5507-5525.
734
I. W. BIJEDAIZ
MILLEROF. J. (1969) The partial molal volumes of ions in sea water. Limnol. Ocecmogr.14, 376-385. MILLEROF. J. and BERNERR. A. (1972) Effects of pressureon carbonate equilibriain sea water. Geochim. Coamochim.Acta 33, 92-98. OVEN B. B. and BRINKLEYS. R. (1941) Calculationof the effect of pressureupon ionic equilibria in pure water and salt solutions. Chem. Rev. 29, 461-474. PYTKOWICZR. M. and FOTVLERG. A. (1967) Solubility of foraminifera in sea water at high pressures. &o&em. J. 1, 169-182. WEAST R. C. (1965) Handbook of Chemistry and Physics, Chemical Rubber Co.
The
partial molal volume of calciumcarbonate in sea
water*
I. W. DUEDALL~ Bedford Institute, Dartmouth, Nova Scotia (Received 8 November1971; acceptedin revisedform 21 Januag
1972)
Abstract-The partial molal volumes (a,) of K,CO, and Na,COs have been experimentally determined, at 20°C, for sea water (35x,) and for 0.725 M NaCl. For sea water, #g,oos equals 28.3 -+ 0.8 ml/mole and dNalCosequals 9.0 f l-5 ml/mole; for 0.725 M NaCl, ~&Co5 equals 23.17 & 0.35 ml/mole and #NsBCoS equals 174 f 0.23 ml/ mole. Using the sea water values and some literature values for other salts in sea water, flcaco8 for sea water was calculated to be -65 & 1.7 ml/mole. This value does not agree with 0~~~9, calculated from data for the effect of pressure on the solubility product of calcium carbonate m sea water. A possible explanation is that the data on the pressurecoefficientof the solubility of calcium carbonate may be in error.
IN RECENTpapers dealing with the problem of calcium carbonate saturation in sea water LI et al. (1969), HAWLEYand PYTKOWICZ(1969), and EDMONDand GIESKES (1970) calculated the volume change when calcium carbonate dissolves in sea water. Hawley and Pytkowicz’s and Edmond and Gieskes’ calculations were based on the effect of pressure on the stoichiometric solubility products of calcite and aragonite in sea water (PYTKOWICZand FOWLER, 1967; HAWLEY and PYTKOWICZ,1969); they used the following familiar equation which relates solubility product (K) to the partial molal volume change (A 7) and pressure (P) : hl
[211 =$gP_l)
If the thermodynamic solubility product concept is applied to equation (l), where the standard state is decked as infinite dilution in pure water, then AT equals ~o~o~,(inf. dil.) - PoaoO,; @ocaoo,(inf.dil.) and VoaoO, are the partial molal volume at infinite dilution in pure water and molar volume, respectively, of calcium carbonate. If the stoichiometric solubility product is used in equation (l), where now the standard state is defined as infinite dilution in normal sea water (i.e. 35x0 salinity), then, as PYTKO~ICZand FOWLER(1967) state, A7 for sea water (termed hereafter as AV(sw)) is not simply the change in volume due to ionization of calcium carbonate but includes a volume contribution to 5oc,oo,(inf. dil.) due to dissociation of carbonate ion-pairs. However, EDMONDand GIESKES (1970), who report a stoichiometric AP(sw) which is based on the solubility measurements made by PYTKOWICZand FOWLER(1967) and HAWLEY and PYTKOWICZ(1969), appear to obscure the meaning and usefulness of AP(sw) by saying that it is not defined in terms of ‘specific chemical reactions’. I should point out that in the derivation of equation (1) the condition for stoichiometric equilibrium (and also for thermodynamic equilibrium) for the dissolution of calcium carbonate in sea water is that * Bedford Institute Contribution. t Marine Ecology Laboratory and Chemical Oceanography Division. 729
I. W. DIJEDAIL
730
the free energies of the reactant and the product be equal. The fact that the dissolution of calcium carbonate in sea water leads to the formation of carbonate ion-pairs as well as other ionization products which therefore contribute to the overall ~~~~o,(sw) does not mean that each ‘specific chemical reaction’ has to be identified and assigned a specific free energy. The free energy of the dissolution products can be considered as the overall sum of the chemical potentials of all product species and GWZO &SW) represents the overall sum of the pressure derivatives of these fioCaCO,(sw)can therefore be calculated from the following chemical potentials. equation regardless of Edmond and Gieskes’ interpretation of A I : AP(sw)
= %Caco,(sw) -
LCO,
B~~~~,(sw) is the partial molal volume of calcium carbonate in sea water and as derived from equation (1) and as mentioned above it represents the sum of the pressure derivatives of the chemical potentials of the products of calcium carbonate where al’ is the overall dissolution. flcaCO*(SW) is also defined as ( ~V/iMfc,co,) incremental volume change of sea water due to the dissolution of an incremental mass, aM, of calcium carbonate. This latter definition which is a valid thermodynamic expression for a defined standard state is explicitly expressed in terms of measureable quantities (i.e. volume and mass). And, according to a review by HAMANN (1963) the ability of equation (1) to predict volume changes for the ionization of acids has been amply verified. This has also been shown for sea water in the recent paper by MILLERO and BERNER (1972). A comparison of ficiiCaCO,(sw) calculated from A I with fiCaCO,(~~) determined by a direct measurement therefore provides a method for determining the accuracy of the present data for the effect of pressure on the solubility of calcium carbonate in sea water. The measured [or calculated from AP(sw)] ficaco s(sw) will differ from a measured flccaco,(inf. dil.) (where the standard state is infinite dilution in pure water) for a few reasons one of which being the volume contributions to 5caC~,(s~) due to carbonate ion-pairs. Fundamental to this question of volume change is ficacO,(sw), the partial molal volume of calcium carbonate in sea water. Heretofore the only value for flc,cos(sw) available in the literature was given by OWEN and BRINKLEY (1941), an approximation which was based, in part, on the behaviour of other salts in sodium chloride solutions. In this paper I report a new value for ficCaCOI( SW) w m‘c h was calculated from the following additivity relationship : BCaco,(SW)
=
%c~(NO,),(~~) +
-
@KNO,(SW)
i!{FKsCO,(sw) +
+
flNaNO,(SW)}
BNa,COs(SW)}
(2)
(SW) have already been reported (DUEDALL, 1968) ~~~FN~No, of flx&O,(sw) and !!&CO, (SW) are reported here. Measurements of in 0.725 M NaCl (a solution having the same ionic strength as @K,CO, and @Na&O 35x,, sea water) ar”e also reported. The i~#‘sreported here are partial molal volumes which include volume contributions due to carbonate hydrolysis and carbonate ion pairs, and therefore, the values should not be misunderstood as being the sum of the volumes for the free ions, as reported by MILLERO (1969).
fb(NO,),(SW),
@KNO,(SW)
and measurements
The partial molal volume of calcium carbonate in sea water
MEASUREMENT
731
OF 4Jilrtco, AXD -tTNhco,
The method consists of measuring the change in volume on ~ssolution of additions of a known mass of salt to sea water contained in a specially designed dilatometer (DUEDALLand WEYL, 1965). The partial molal volume is determinedby extrapolation of the ratio of cumulative volume change (AV,) to cumulative mass addition (Anz)to zero salt addition. The dilatometer was first filled with either IAPSO Standard Sea Water, of salinity 35*00%,, or 0.725 M sodium chloride, and then placed in a 20°C thermostat in which the temperature was maintained to a constancy and accuracy of &0~005”C?. Fisher Certifiedreagents (l&CO, and NaaCOs) were used t~ughout. In experiments with O-725 M sodium chloride, about 0.15 g of salt per addition was dispensed into the dilatometer. However, for the salt additions to sea watex only about 0.05 g W&EIdispensed per addition because a cumulative salt addition of greater than 0.20 g caused calcium oarbonate to precipitate. Figures 1 and 2 show plots of AV,/Am vs Am &CO,
35%, sea water
i
25-
9 5
0.725
240 235
M NaCC
O* B
Cl 0
0 OA
A 0
n
u
cl
22-
I 0.1
21
I 0.2
I 0.3
I 0.4
I 0.5
1 0.6
I 07
I
Ah-f.9 Fig. 1. D&a for the partial molal volume of &CO,. Na, CO,
35 %o sea water
z 8
$6 1*
4
a-1 2
0.725 M NaCL ,B
I 0.1
v
I 0.2
"dour_
I 0.3 AM,
I o-4
j;j
I o-5
.I 06
I 0.7
6
I 0.8
t
W
Fig. 2. Data for the partial molal volume of NasCOs.
I.W.
732
DUEDALL
for several runs. The intercept values (at Am = 0) are the partial molal volumes, and these values were determined by fitting (by least squares) the combined data from all the runs to a linear equation. (Because so few data are available at low concentrationsfor each run, especially for sea water, I feel one has more confidencein the extrapolation when data from all the runs are combined rather than fitting the data from individual runs.) The partial volumes are given in Table 1. The uncertainty associated with each value is an absolute experimental error based Table 1. Partial molal volumes of K&O, and Na,CO, in NaCl (0.725 M) and sea water (35% salinity)
Solution
Partial molal volumes (ml/mole) K&O,
NaCl (0.725 M)
28.3 -&to.8 23.17 &0.35
Na,CO, 9.0 *1*5 l-74 &0.23
on the magnitude of the change in volume (AVJ, due to a salt addition, and on the absolute error in reading AV, (DUEDALL,1966). In sea water the errors are large because of the small volume changes measured, necessitated by having to add exceptionally small amounts of carbonate salt to sea water to avoid the precipitation of calcium carbonate. 6, is the linear extrapolationof AVJAm to zero salt addition, but the pH change of the solution in the dilatometer is not a linear function of the amount of carbonate salt added. Large pH changes occur for initial salt additions, and the extent of this effect is considerably greater for 0.725 M NaCl than for sea water. For sea water, this effect probably doesn’t significantly affect the extrapolation of AV,/Am because a linear extrapolation of pH to zero salt addition gives 8.7 whereas the initially measured pH of the sea water was 8.2. However, for 0.725 M NaCl, where the initially measured pH was 6.1, the extrapolated pH was about 10.4 which may have some measureable affect on B, (0,725 M NaCl). An obvious, but not too surprisingfeature of the f18results,is the significantdifferencebetween g8in sea water and 0, in 0.725 M NaCl. A major part of this differenceis probably because more carbonate ions are hydrolyzed in sea water to form bicarbonate ions than in 0.725 M NaCl. Therefore, the bicarbonate ion volume contribution to 8, must be greater in 9, (SW)than in 0, (0.725 M NaCI). Also, because of the presence of other cations in sea water, volume contributions to 0, due to bicarbonate and carbonate ion-pairs would be greater for sea water than for 0.725 M NaCI. CALCULATION OF Gino, f&,co,(sw) can be calculated from equation (2) using the flKSco,(sw) and T~~+~,(sw) reported here and the 20°C values of 5c,t,o,,,(sw), &o,(sw) and fiNaNO,(sw)reported previously (DUEDALL, 1968). The calculated BCaCO,(sw)equals -6-5 6 1.7 ml/mole. By comparison the frequently used fleaGo, (‘salt water’) reported by OWEN and BRINKLEY (1941) is - 13.9 ml/mole, which is probably close to BCaCO,(O-725 M NaCl) because fiKSco, (0.725 M NaCI) and &+oa (O-725 M NaCI) determined by the dilatometric method agree with the Owen and Brinkley data. flcCaCO,(sw)can also be calculated from the reported data on AP(sw) (HAWLEY and PYTKOWICZ, 1969; EDMOND and GIESKES, 1970) based on work (PYTKOWICZ and FOWLER, 1967; HAWLEY and PYTKOWICZ, 1969) to determine the effect of pressure on the stoichiometric solubility product of calcium carbonate in sea water.
The partialrnolalvolume of oalciumcarbonateia.sea water
733
For calcite, Av(sw) equals -304 f 1 ml~mole at 20°C (ED~o~D and G~s~s, 1970). Therefore, using 36.9 ml/mole (WEAST, 1965) as the molar volume of calcite, the calculated poCaCo,(sw) is 6.1 f I ml/mole. However, @ocsoo,(sw)determined from dilatometer results is -65 -+ 1.7 ml/mole. The large difference between these two values appears greater than can be explained solely by the effect of pressure on iiCaCO,(sw). For instance, although data are not available for calcium carbonate, data (HAMANN, 1957) for sodium chloride show that f&o&nf. dil.) in pure water increases by only 3 ml/mole at 1000 bar. Some of the discrepancy between the two values for fjcaco, (SW) could be explained if chemical equilibrium was never quite reached in the solubility experiments done by PYTKOWICZand FOWLER(1967) and HAWLEYand PYTHOWICZ (1969). This would have the effect of producing a smaller calculated (equation 1) volume change than the equilibrium AP(sw), and conse(SW), based on the effect of pressure on the solubility quently, the calculated ficCaCo, of calcium carbonate, would be greater than what is determined from dilatometer measurements. Very recently I learned that MILLERO and BEENER (1972) have also calculated the volume change for calcium carbonate ~ssolution. Their calculations were based on an ion-pair model and available data for the effect of pressure on the ionization of bicarbonate in sea water. From their results, fiCaCo,(sw),at 25’C, equals -25 If 2.4 ml/mole, which is in good agreement with the ~cCaCo,(~~)determined from dilatometer results considering the assumptions they made and the available data, and also taking into account that the dilatometer result is a 20°C value while the (SW)is at 25°C and that salts in sea water exhibit positive expansibiliestimated gcCaoo, ties (~~1~~~0, 1969). Also, because IVIillero and Berner’s cocoon differed conoaCO,(sw) calculated from calcium carbonate solubility data, they siderably from 8 suggested that the effect of pressure on the solubility of calcium carbonate in sea water may be in error. Acknowledgements-I thank A. R. COOTE,R. C. COOKE,F. J. MILLEROand D. KESTER for their helpful discussionsand also thank A. WALTON for readingthe manuscriptand offeringsuggestions for its improvement.
DUEDALL I. W. (1966) The partial equivalent volumes of salts in sea water. MSc. Thesis, Oregon State University, 47 pp. DT~DALL I. W. (1968) Partial modalvolumes of 16 salts in sea water. Enuiron. Sci. Tech. 2, 706-707. DUEDALL I. W. and W~YL P. K. (1965) Apparatus for determining the partial equivalent volumes of salts in aqueous solutions. Rev. Sci. In&r. 36, 528-531. EDXOND J. M. and GIESKES 5. M. T. M. (1970) On the calculation of the degree of saturation of sea water with respect to calcium carbonate under in situ conditions. ~e~~~~~~.Cos~oeh~~. Acta 34, 1261-1291. IZANANN S. D. (1957) Physica-Chemical E#ects of Pressure,Buttorworths, 246 pp. IXAMANN S. D. (1963) Chemical equilibria in condensedsystems. In High Pressure Physic.g aad Chemistry. (editor R. S. Bradley), 361 pp. Academic Press. HAWLEY J. and PVTKOW~CZ R. M. (1969) Solubility of calcium carbonate in sea water at high pressuresand 2%. Geochim. Cosmochim. Acta 33, 1557-1561. Lx Y. -H., TA~ARASRI T. and BROEKXRW. S. (1969) Degree of saturationof CaCOsin the ooe&ng. J. Geophys. Res. ‘X,5507-5525.
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MILLEROF. J. (1969) The partial molal volumes of ions in sea water. Limnol. Ocecmogr.14, 376-385. MILLEROF. J. and BERNERR. A. (1972) Effects of pressureon carbonate equilibriain sea water. Geochim. Coamochim.Acta 33, 92-98. OVEN B. B. and BRINKLEYS. R. (1941) Calculationof the effect of pressureupon ionic equilibria in pure water and salt solutions. Chem. Rev. 29, 461-474. PYTKOWICZR. M. and FOTVLERG. A. (1967) Solubility of foraminifera in sea water at high pressures. &o&em. J. 1, 169-182. WEAST R. C. (1965) Handbook of Chemistry and Physics, Chemical Rubber Co.