IUPAC-NIST Solubilities Database

IUPAC-NIST Solubility Database
NIST Standard Reference Database 106

Solubility System: Carbon dioxide with Sea Water

Components:
   (1) Sea Water; ; []  NIST Chemistry WebBook for detail
   (2) Carbon dioxide; CO2; [124-38-9]  NIST Chemistry WebBook for detail

Evaluator:
   Denis A. Wiesenburg, Center for Marine Sciences, University of Southern Mississippi, Stennis Space Center, MS 39529 USA
January, 1995

Critical Evaluation:

    AN EVALUATION OF THE SOLUBILITY OF CARBON DIOXIDE IN SEA WATER AT PARTIAL PRESSURE OF 101.3 kPa

In spite of the importance of carbon dioxide in the ocean, only a few measurements have been made of the solubility of carbon dioxide in seawater at partial pressure of gas of 101.3 kPa. References 1-6 are considered to be of historical interest. They were not used in the present evaluation although they contain some data of value. Since the early measurements, most authors have chosen to extrapolate from data based on the solubility of carbon dioxide in aqueous sodium chloride solutions. This situation persisted until the 1970’s when four independent solubility data sets for carbon dioxide in seawater were produced using a variety of techniques.

These four sets of modern measurements were considered for this evaluation. Three of these are of carbon dioxide solubility in natural sea water and one in synthetic or artificial sea water. Two of the independent data sets are extensive enough to allow evaluation and computation of a smoothing equation. Li and Tsui (9) analyzed compositions of equilibrium solutions using infrared spectroscopy, while Murray and Riley (10) used a gravimetric determination. Unfortunately, the agreement between the two sets of measurements is poor: the data of Murray and Riley are as much as 3.8 % lower than those of Li and Tsui at higher temperatures and salinities. The agreement is better at lower temperatures and in distilled water. Weiss (11) examined both data sets and made measurements of his own to determine which were most accurate. Weiss also noted that neither Murray and Riley nor Li and Tsui made corrections for the non-ideal behavior of carbon dioxide. For carbon dioxide, the departure from the ideal gas approximation is much larger than the precision with which its solubility can be measured. Also, neither Murray and Riley nor Li and Tsui made corrections for the dissociation of dissolved hydrated carbon dioxide to form bicarbonate in distilled water. Making these corrections reduces the distilled water values for both of the published data sets by ~ 0.18 % at 273.15 K to ~ 0.46 % at 313.15 K. The 15 measurements that Weiss (11) made confirmed the accuracy of the measurements of Murray and Riley (10). The values of Li and Tsui (9) were shown to be in error by as much as 4 % at the higher temperatures and salinities. The data of Murray and Riley (10), after correction for the effects of non-ideal behavior and for dissociation in the distilled water measurements (11), are believed to be accurate enough to develop a smoothing equation.

Stewart and Munjal (7) made measurements of the solubility of carbon dioxide in synthetic seawater which the evaluator calculated to have a salinity of 34.42 ‰. The compiler estimated the error of these measurements to be ± 1 %, which is greater than the error of the better methods. A comparison of their data with the measurements of Murray and Riley (10) and Weiss (11) revealed their artificial seawater solubility values to be low by and average of 6 %. For this reason, the data of Stewart and Munjal (7) were not considered further.

Solubilities of carbon dioxide are generally used in calculations of chemical equilibria and are given typically as amount concentration (c₁ = n₁/V) or amount per unit mass of solution or as mass fractions. Weiss (11) evaluated the solubility of carbon dioxide in sea water in terms of the equilibrium constant K₀, defined as the amount of solute per liter or kilogram of solution, when the fugacity (f) of the solute and the total pressure are both 1 atm. According to the modified form (11) of Henry’s law, m₁ = K₀f, where m₁ is the concentration of dissolved gas in molar or gravimetric units and f is the fugacity. In terms of the Bunsen coefficient, K₀ = a/V^• in molar units, or K₀ = α/V^•p in gravimetric units, where V^• is the molar volume of the pure really gas at standard temperature and pressure and p is the density of the solution. Weiss (11) fitted the corrected Murray and Riley (10) data to the smoothing equation:

ln (K₀ / mol dm^-3 atm^-1) = -58.0931 + 90.5069 (100 K /T) + 22.2940 ln (T/100 K)
+ (S/%)[ 0.027766 – 0.025888 (T/100 K) + 0.0050578 (T/100 K)²]

(1)

0 where S is the salinity (‰) and T is the Kelvin temperature. Weiss (11) also fitted the same data to an equation that represented the solubility in terms of mass of the solution rather than volume,

ln (K₀ / mo1 kg^-1 atm^-1) = –60.2409 + 93.4517 (100 K / T) + 23.3585 ln (T /100 K)
+ (S/ ‰)[ 0.023517 –0.023656 (T /100 K) + 0.0047036 (T /100 K)²].

(2)

The Murray and Riley (10) data show a standard error of estimate of about 0.3 %, or 1.4 x 10^-4 mol dm^-3 atm^-1 in terms of K₀. Weiss (11) gives extensive tables of the carbon dioxide solubility in sea water at various temperatures and salinities from both of the above equations. These equations are recommended for calculation of the solubility of carbon dioxide in seawater.

Although the solubility coefficients of carbon dioxide in seawater are well defined by the above equations, for practical purposes oceanographers and atmospheric scientists require the atmospheric equilibrium solubility for their work. Weiss (8) has proposed equations similar to the above which express the atmospheric equilibrium solubility from moist air at 1 atm total pressure in units of volume (STP), as a function of temperature and salinity. In working with samples from depths in the ocean, it is also advantageous to express atmospheric solubilities in terms of mol kg^-1, which are pressure and temperature independent (8). Weiss and Price (12) produced a smoothing equation for carbon dioxide solubility in sea water from the Murray and Riley (10) data in terms of the function F, for a total pressure of 1 atm where m₁ = x₁F and x₁ is the mole fraction of carbon dioxide in dry air:

ln (F / mo1 dm^-3 atm^-1) = –160.7333 + 215.4152 (100 K / T) + 89.8920 ln (T /100 K)
–1.47759 (T /100K)² + (S/ ‰)[ 0.029941 – 0.027455 (T / 100 K)
+ 0.0053407 (T / 100 K)²]

(3)

Weiss and Price (12) also fitted the Murray and Riley (10) data to an equation that represented the solubility in terms of mass of the solution rather than volume:

ln (F / mol kg^-1 atm^-1) = -162.8301 + 218.2968 (100 K / T) + 90.9241 ln (T / 100 K)
-1.47696 (T / 100 K)² + (S/‰)[ 0.025695 – 0.025225 (T / 100 K)
+0.0049867 (T / 100 K)²]

(4)

These two equations can be used to calculate accurately the atmospheric equilibrium solubility of carbon dioxide in sea water between 272.15 K and 313.15 K and salinities between 0 and 40 ‰.

In the following table some numerical values, calculated from Eqs. (1), (2) and (4), are presented for the solubility coefficient K₀. More extensive tables can be found in Refs. 11 and 12.

Added by the editor:

  Note that Weiss (11) defined the Bunsen coefficient as the volume of gas (STP) absorbed per unit volume of the solution at the temperature of the measurement, when the total pressure and the fugacity are both 1 atm. According to the usual definition, Bunsen coefficient is the volume of gas (STP) absorbed per unit volume of the solvent at the temperature of measurement and 1 atm partial pressure of gas.

  Concerning the thermodynamics of the carbon dioxide system in seawater, there exist several articles in the literature. See for instance the recent paper of Millero (18) and the references therein.

  The definitions of salinity and chlorinity have been changed during the years. For these definitions and the salinity – chlorinity relationship, see for instance Refs. 13, 14, 15, and 16.

In 1981 the joint panel of Experts on Oceanographic Tables and Standards proposed a new definition of salinity and recommended the use of a new salinity scale – the Practical Salinity scale 1978 (PSS 78) (13). The Practical Salinity 1978 was defined for the salinities within the salinity range 2 – 42. An extension of the Practical Salinity Scale 1978 to salinities up to 50 is given in reference 17.

T/K

T/K	Salinity S/%
	0	34	35	36	38
Eq. (1). Solubility Coefficient 10² K₀/ mol dm^-3 atm^-1
273.15	7.758	6.498	6.465	6.431	6.364
283.15	5.366	4.529	4.507	4.485	4.440
293.15	3.910	3.337	3.322	3.306	3.275
303.15	2.983	2.583	2.572	2.561	2.540
313.15	2.370	2.090	2.082	2.074	2.059
Eq. (2). Solubility Coefficient 10² K₀ / mol kg^-1 atm^-1
273.15	7.758	6.325	6.287	6.249	6.175
283.15	5.367	4.413	4.328	4.363	4.313
293.15	3.916	3.258	3.241	3.223	3.189
303.15	2.995	2.530	2.517	2.505	2.480
313.15	2.389	2.054	2.045	2.036	2.018
Eq. (4). Function F for moist air at 1 atm, 10² F / mol kg^-1 atm^-1
273.15	7.681	6.264	6.226	6.189	6.115
283.15	5.280	4.342	4.318	4.293	4.244
293.15	3.814	3.174	3.157	3.140	3.106
303.15	2.862	2.419	2.407	2.395	2.371
313.15	2.209	1.902	1.894	1.886	1.869

Experimental Data: (Notes on the Nomenclature)

Numerical values for solubility coefficient K₀
T/K	10² * Henry's law constant, K [mol/dm**3 atm]	Salt Effect	Equation(s)
273.15	7.758	0 %	Eq. (1) Solubility Coefficient 10**2 K<0>
273.15	6.498	34 %	Eq. (1) Solubility Coefficient 10**2 K<0>
273.15	6.465	35 %	Eq. (1) Solubility Coefficient 10**2 K<0>
273.15	6.431	36 %	Eq. (1) Solubility Coefficient 10**2 K<0>
273.15	6.364	38 %	Eq. (1) Solubility Coefficient 10**2 K<0>
283.17	5.366	0 %	Eq. (1) Solubility Coefficient 10**2 K<0>
283.17	4.529	34 %	Eq. (1) Solubility Coefficient 10**2 K<0>
283.17	4.507	35 %	Eq. (1) Solubility Coefficient 10**2 K<0>
283.17	4.485	36 %	Eq. (1) Solubility Coefficient 10**2 K<0>
283.17	4.440	38 %	Eq. (1) Solubility Coefficient 10**2 K<0>
293.15	3.910	0 %	Eq. (1) Solubility Coefficient 10**2 K<0>
293.15	3.337	34 %	Eq. (1) Solubility Coefficient 10**2 K<0>
293.15	3.322	35 %	Eq. (1) Solubility Coefficient 10**2 K<0>
293.15	3.306	36 %	Eq. (1) Solubility Coefficient 10**2 K<0>
293.15	3.275	38 %	Eq. (1) Solubility Coefficient 10**2 K<0>
303.15	2.983	0 %	Eq. (1) Solubility Coefficient 10**2 K<0>
303.15	2.583	34 %	Eq. (1) Solubility Coefficient 10**2 K<0>
303.15	2.572	35 %	Eq. (1) Solubility Coefficient 10**2 K<0>
303.15	2.561	36 %	Eq. (1) Solubility Coefficient 10**2 K<0>
303.15	2.540	38 %	Eq. (1) Solubility Coefficient 10**2 K<0>
313.15	2.370	0 %	Eq. (1) Solubility Coefficient 10**2 K<0>
313.15	2.090	34 %	Eq. (1) Solubility Coefficient 10**2 K<0>
313.15	2.082	35 %	Eq. (1) Solubility Coefficient 10**2 K<0>
313.15	2.074	36 %	Eq. (1) Solubility Coefficient 10**2 K<0>
313.15	2.059	38 %	Eq. (1) Solubility Coefficient 10**2 K<0>
273.15	7.758	0 %	Eq. (2) Solubility Coefficient 10**2 K<0>
273.15	6.325	34 %	Eq. (2) Solubility Coefficient 10**2 K<0>
273.15	6.287	35 %	Eq. (2) Solubility Coefficient 10**2 K<0>
273.15	6.249	36 %	Eq. (2) Solubility Coefficient 10**2 K<0>
273.15	6.175	38 %	Eq. (2) Solubility Coefficient 10**2 K<0>
283.17	5.367	0 %	Eq. (2) Solubility Coefficient 10**2 K<0>
283.17	4.413	34 %	Eq. (2) Solubility Coefficient 10**2 K<0>
283.17	4.328	35 %	Eq. (2) Solubility Coefficient 10**2 K<0>
283.17	4.363	36 %	Eq. (2) Solubility Coefficient 10**2 K<0>
283.17	4.313	38 %	Eq. (2) Solubility Coefficient 10**2 K<0>
293.15	3.916	0 %	Eq. (2) Solubility Coefficient 10**2 K<0>
293.15	3.258	34 %	Eq. (2) Solubility Coefficient 10**2 K<0>
293.15	3.241	35 %	Eq. (2) Solubility Coefficient 10**2 K<0>
293.15	3.223	36 %	Eq. (2) Solubility Coefficient 10**2 K<0>
293.15	3.189	38 %	Eq. (2) Solubility Coefficient 10**2 K<0>
303.15	2.995	0 %	Eq. (2) Solubility Coefficient 10**2 K<0>
303.15	2.530	34 %	Eq. (2) Solubility Coefficient 10**2 K<0>
303.15	2.517	35 %	Eq. (2) Solubility Coefficient 10**2 K<0>
303.15	2.505	36 %	Eq. (2) Solubility Coefficient 10**2 K<0>
303.15	2.480	38 %	Eq. (2) Solubility Coefficient 10**2 K<0>
313.15	2.389	0 %	Eq. (2) Solubility Coefficient 10**2 K<0>
313.15	2.054	34 %	Eq. (2) Solubility Coefficient 10**2 K<0>
313.15	2.045	35 %	Eq. (2) Solubility Coefficient 10**2 K<0>
313.15	2.036	36 %	Eq. (2) Solubility Coefficient 10**2 K<0>
313.15	2.018	38 %	Eq. (2) Solubility Coefficient 10**2 K<0>
273.15	7.681	0 %	Eq. (3) Function F for moist air at 1 atm, 10**2 F, where m<1> = x<1> F
273.15	6.264	34 %	Eq. (3) Function F for moist air at 1 atm, 10**2 F, where m<1> = x<1> F
273.15	6.226	35 %	Eq. (3) Function F for moist air at 1 atm, 10**2 F, where m<1> = x<1> F
273.15	6.189	36 %	Eq. (3) Function F for moist air at 1 atm, 10**2 F, where m<1> = x<1> F
273.15	6.115	38 %	Eq. (3) Function F for moist air at 1 atm, 10**2 F, where m<1> = x<1> F
283.17	5.280	0 %	Eq. (3) Function F for moist air at 1 atm, 10**2 F, where m<1> = x<1> F
283.17	4.342	34 %	Eq. (3) Function F for moist air at 1 atm, 10**2 F, where m<1> = x<1> F
283.17	4.318	35 %	Eq. (3) Function F for moist air at 1 atm, 10**2 F, where m<1> = x<1> F
283.17	4.293	36 %	Eq. (3) Function F for moist air at 1 atm, 10**2 F, where m<1> = x<1> F
283.17	4.244	38 %	Eq. (3) Function F for moist air at 1 atm, 10**2 F, where m<1> = x<1> F
293.15	3.814	0 %	Eq. (3) Function F for moist air at 1 atm, 10**2 F, where m<1> = x<1> F
293.15	3.174	34 %	Eq. (3) Function F for moist air at 1 atm, 10**2 F, where m<1> = x<1> F
293.15	3.157	35 %	Eq. (3) Function F for moist air at 1 atm, 10**2 F, where m<1> = x<1> F
293.15	3.140	36 %	Eq. (3) Function F for moist air at 1 atm, 10**2 F, where m<1> = x<1> F
293.15	3.106	38 %	Eq. (3) Function F for moist air at 1 atm, 10**2 F, where m<1> = x<1> F
303.15	2.862	0 %	Eq. (3) Function F for moist air at 1 atm, 10**2 F, where m<1> = x<1> F
303.15	2.419	34 %	Eq. (3) Function F for moist air at 1 atm, 10**2 F, where m<1> = x<1> F
303.15	2.407	35 %	Eq. (3) Function F for moist air at 1 atm, 10**2 F, where m<1> = x<1> F
303.15	2.395	36 %	Eq. (3) Function F for moist air at 1 atm, 10**2 F, where m<1> = x<1> F
303.15	2.371	38 %	Eq. (3) Function F for moist air at 1 atm, 10**2 F, where m<1> = x<1> F
313.15	2.209	0 %	Eq. (3) Function F for moist air at 1 atm, 10**2 F, where m<1> = x<1> F
313.15	1.902	34 %	Eq. (3) Function F for moist air at 1 atm, 10**2 F, where m<1> = x<1> F
313.15	1.894	35 %	Eq. (3) Function F for moist air at 1 atm, 10**2 F, where m<1> = x<1> F
313.15	1.886	36 %	Eq. (3) Function F for moist air at 1 atm, 10**2 F, where m<1> = x<1> F
313.15	1.869	38 %	Eq. (3) Function F for moist air at 1 atm, 10**2 F, where m<1> = x<1> F

References: (Click a link to see its experimental data associated with the reference)

   1  McLeod, H., J. Chem. Soc. 1869, 22, 307.
   2  Hamberg, A., J. Prakt. Chem. 1885, [2] 33, 433.
   3  Krogh, A., Medd. om Gronland 1904, 26, 331.
   4  Fox, C. J. J., Trans. Faraday Soc. 1909, 5, 68.
   5  Coste, J. H., J. Soc. Chem. Ind. 1917, 36, 846.
   6  McClendon, J. F., J. Biol. Chem. 1917, 30, 259.
   7  Stewart, P.B.; Munjal, P., J. Chem. Eng. Data 1970, 15, 67-71.
   8  Weiss, R. F., Deep-Sea Res. 1970, 17, 721.
   9  Li, Y.-H.; Tsui, T.-F., J. Geophys. Res. 1971, 76, 4203-7.
   10  Murray, C. N.; Riley, J. P., Deep-Sea Res. 1971, 18, 533-41.
   11  Weiss, R. F., Mar. Chem. 1974, 2, 203-15.
   12  Weiss, R. F., Price, B. A., Mar. Chem. 1980, 8, 347.
   13  UNESCO Technical Papers in Mar. Sci. 1981, 37, 1.
   14  Lewis, E.L.; Perkin, R.G., Deep-Sea Res. 1981, 28A, 307.
   15  Millero, F.J., Ocean Sci. Eng. 1982, 7, 403.
   16  Grasshoff, K.; Ehrhardt, M.; Kremling, K., Editors, Methods of Seawater Analysis, 2nd Edition, Verlag Chemie, 1983.
   17  Poisson, A.; Gadhoumi, M.H., Deep-Sea Res. 1993, 40, 1689.
   18  Millero, F.J., Geochim, Cosmochim. Acta 1995, 59, 661.