Evaluation of Solubility Data of the System CO2H2O from 273 K to the Critical Point of Water
This evaluation covers all of the literature sources for the solubility of carbon dioxide in water through the year 1989.
For describing the two-phase saturation solubility we select Henry's constant. From the equality of the chemical potentials of the solute in the vapor and liquid phase. Henry's constant k0H can be calculated from [see O'Connell (1) and Alvarez et al. (2)]
P
k0H = (yPφ1/γH1) exp ∫ (-V1/RT)dP. P*2(1)
From the equality of the chemical potentials of the solvent in the liquid and the vapor phase it follows that
P
(1-y) = [γR2 (1-x) P*2 φ*2 exp ∫ (V*2/RT) dP]/(Pφ2) P*2(2)
where the symbols are defined at the end of this evaluation. To calculate k0H from the experimental data usually available, namely P, T and x, equations (1) and (2) must be solved simultaneously. The common assumptions for low temperatures and low total pressures and concentrations are that the activity coefficients γ1H and γ2R equal unity, and that the partial molar volume, V1 equals the infinite dilution partial molar volume, V01 independent of pressure. Once an equation of state (EOS) is selected, Eq. (2) is solved for y by an iterative procedure described elsewhere (3). The explicit pressure dependence of the solubility can be accounted for either by using information on experimental partial molar volumes or by semiempirical perturbation methods (4). For this system experimental partial molar volumes (5,6) were used.
The virial EOS through the second virial coefficient was used for the mixed vapor phase for temperatures between 273 and 353 K. For the higher temperatures, 353 K to the critical temperature of the solvent, the Peng and Robinson (7) EOS was selected. The interaction parameter was chosen as 0.285. [For details on the sensitivity of the Henry's constant to different EOS, smoothing equation selection, and adjustment procedures, see Crovetto (8).] Up to about 500 K all of the EOS tested gave variations of about 1.5 % or less in the calculated values of k0H.
Another useful quantity in solubility and liquid/vapor equilibria is the isothermal distribution coefficient, KD, defined as
KD = y/x (3)
The infinite-dilution coefficient, K0D, is defined as
K0D = lim y/x x → 0(4)
and can be calculated from the same set of equations and assumptions already presented as (5)
K0D = k0H/ (P*2φ10)(5)
where φ01 is calculated from the selected EOS. In principle, K0D will be known with the same precision as k0H, but the effect of the selected EOS on the values of K0D and k0H, respectively, will be different.
Recently, Japas and Levelt Sengers (9) predicted the limiting asymptotic thermodynamic behavior for k0H and K0D and their temperature dependence near the critical temperature of the solvent. They demonstrated that asymptotically as T → Tc of the solvent, the following linear correlations will apply:
T ln (k0H/ƒ*2) = A + B(ρliq*2 = ρc2)(6)
T ln K0D = 2B(ρliq*2 - ρc2)(7)
where B(Rρ2c) = (∂ P/ ∂x)V,Tc ≡ - αcV,x.
The quantity acV,x is the second derivative of the Helmholtz energy with respect to the volume and the concentration. This relevant derivative can be related to the experimentally measurable initial critical-line slopes of the dilute solution and the pure solvent [see Japas and Levelt Sengers (9)]. The fact that K0D must equal unity for T = Tc, provides a valuable clue to whether the asymptotic behavior has been reached.
As stated by Harvey et al. (10), when dealing with experimental data the K0D factor, Eq. (7), gives a better estimate of the true asymptotic slope and a good agreement with acV,x from experimental critical-line data whereas the slope from the Henry’s constant, Eq. (6), does not.
It is a fact that the hydration and dissociation of CO2 in water cannot be separated from its dissolution. In this treatment only the total CO2 dissolved is considered, regardless of the species present in solution. This assumption can be made because any species other than CO2(aq) [the not yet isolated, so-called “carbonic acid” (H2CO3)aq, the H+, and the HCO3-] in a solution of CO2 in water exist in negligible amounts. These species can be ignored because the ratio of the molalities of “(H2CO3)aq” and ions to CO2 is about 3/1000 at 298.15 K (11). Also, experimental and theoretical arguments of Kruse and Franck (12) indicate that (H2CO3)aq is not an important species at higher temperatures. The acidity constant of CO2 goes through a maximum value of 6.3x10-7 mol kg-1 at 353 K and decreases at higher temperatures. The acidity constant of CO2 goes through a maximum value of 6.3x10-7 mol kg-1 at 353 K and decreases at higher temperatures (13, 14) so that the quantity of ionic species should become smaller as the temperature increases beyond 353 K.
Wherever necessary, values for the pure water properties, ρ, ƒ2•, P2• were taken from Haar et al. (15).
The goal of this evaluation was to cover with one equation the solubility of CO2 in water for the liquid range of water 273 K to 647.126 K. This was not possible within the precision of the available measurements. The data for low temperature solubilities, 273 K to 353 K, are always significantly more precise, i.e., at least by a factor of ten than the high temperature ones. For this system there are no data at low temperatures of very high precision similar to those available for inert non-polar gases in water (16, 17).
At the present time equations for the temperature dependence of gas solubilities in water are only empirical showing limiting asymptotic critical behavior and tendencies (9). The parameters for this Eq. (9) must be adjusted from the data.
The original data were retrieved as mole fraction, total pressure in the system, and temperature. From these data, the selected EOS, and Eqs. (1) and (2), k0H was calculated. For the low temperature data set (273-353 K), the equation is
ln (k0H/bar) = 4.800 + 3934.4(T/K)-1 - 941290.2 (T/K)-2.(8)
The standard deviation of the fit is 1.1 % in k0H. The coefficients were calculated by a least squares method. A further increase in the number of coefficients in Eq. (8) was not statistically significant. The references used for Eq. (8) are listed alphabetically in Table 1, entitled “Sources of data.” For the low-temperature set, the correction for non-ideality of the vapor phase does not amount more than 0.5 %.
There is available a low-temperature low-pressure evaluation for the carbon dioxide/water system done by Wilhelm et al. (18). They made different choices for the number of sources considered and the smoothing equation used. Differences between k0H values calculated from Eq. (8) and theirs are important only at the end of the temperature interval of the fitting, i.e., at 273 K and 353 K, amounting to 2 % at 353 K.
Any formulation that attempts to cover the entire liquid range of the solvent should be consistent with the facts that the derivative [d(1n k0H)/dT]s diverges to - ∞ as T→Tc [Japas and Levelt Sengers (9)], that the infinite dilution solute partial molar isobaric heat capacity of dissolution in the saturated liquid,C0p1, diverges to + ∞ as T→Tc, and that the value of k0H at Tc, is a constant equal to P•2 times Φ01.
For the high temperature data set, 353 K to the critical temperature of water, the system was anchored at the low temperature by adding to the sources used five k0H values calculated from Eq. (8) at 273.15, 293.15, 303.15, 323.15, and 353.15 K. They were given the same weight as any other experimental points. However, they were not used for Eq. (7). For the CO2/H2O system the linear relationship is Eq. (7) in obtained starting at densities which correspond to 373 K.
The high-temperature data set is best represented in K0D by
T ln K0D = 91.22 K(mol/L)-1 (ρliq*2 - ρc2)(9)
which gave a standard deviation of 8.6 % (in Henry’s constant) and in k0H by
ln (k0H/bar) = 1713.53 (1-Tr)1/3(T/K)-1 + 3.875 + 3680.09 (T/K)-1 = 1198506.1 (T/K)-2
(10)
with a standard deviation of 5.1 % in k0H. In Eq. (10) Tr = T/Tc. The asymptotic leading term is adjusted by the results obtained from fitting the data to the form of Eq. (7). Coefficients for Eq. (10) were obtained from a least squares procedure with no weighting applied. The list of sources used is given in Table 1.
A group of sources exist that are at low temperatures, but higher pressures. This group consists of eight different sources and is listed alphabetically in Table 1. From the experimental data, 23 values of Henry’s constant were calculated at different temperatures. This group was difficult to evaluate because for some experimental conditions CO2 itself is very near its critical point. This group was not included in the fitting.
For this system we estimate an uncertainty in the fitting equations of 1 % for k0H between 273 K and 353 K, and an uncertainty of about 5-10 % between 353 K and 600 K. For temperatures above 600 K the uncertainty increases rapidly to at least 20 % near the critical point of water.
A high-temperature deviation plot versus temperature shows that there may be some systematic errors between experimental data from different sources.
Smoothed values for ln(k0H/bar) calculated from Eq. (8), at 10 K intervals between 273 K and 353 K are given in Table 2.
Smoothed values for ln(k0H/bar) between 353 K and 647 K at 15 K intervals calculated from Eqs. (9) and (10) are given in Table 3.
Recommended values for k0H calculated from the selected fitting Eq. (8), considering all sources, at 5 K intervals from 273.15 K to 353.15 K are given in Table 4.
List of symbols
αv,x second derivative with respect to the volume and composition of the Helmholtz energy
kH Henry’s constant
x mole fraction of the soute in the liquid phase
y mole fraction of solute in the vapor phase
ƒ fugacity
Cp,1 partial molar isobaric heat capacity for the solute
KD isothermal distribution coefficient
P total pressure
R gas constant
T temperature
Tc critical temperature of the solvent
Tr = T/Tc reduced temperature
V molar volume
Vi partial molar volume of i
Greek symbols:
ρ molar density
φI fugacity coefficient in the gaseous mixture of component i
γH activity coefficient in the liquid phase on the scale defining ideality by means of Henry’s law
γR activity coefficient in the liquid phase on the scale defining ideality by means of pure solvent behavior or Raoult’s law
Subscripts: 1:solute, 2:solvent, c:critical
Superscripts: 0: infinite dilution, *:pure substance, g: vapor phase, liq: liquid phase, s:saturation, c:critical
TABLE 1. Sources of data.
Group A: (273 K < 353 K, P < 2 bar)
AUS(63):Austin, W.H.; Lacombe, E.; Rand, P.W.; Chatterjee, M., J. Appl. Physiol. 1963, 18, 301-4
(5:5)
BO(891):Bohr, C.; Bock, J., Ann. Phys. Chem., NF 1891, 44, 318-43.
(2:0)
BO(899):Bohr, C., Ann. Phys. Chem. 1899, 68, 500-25.
(15:15)
BU(855):Bunsen, R.W.E., Phil. Mag. 1855, 9, 116-30, 181-201; Gasometrische Methoden, Braunschweig 1857. The same experimental points are also published in Bunsen, R.W.E. Justus Liebig's Annalen der Chemie (also Ann. Chem.) 1855, 93, 1-50.
(6:5)
BUC(28):Buch, K., Nordiska Kemistmo¨tet (Finland) 1926, 184-92.
(14:7)
CRA(82):Cramer, S.D., U.S. Bur. Mines Rep. Invest. 1982, RI 8706.
(1:0)
CUR(38):Curry, J.; Hazelton, C.I., J. Am. Chem. Soc. 1938, 60, 2771-3.
(4:2)
HAR(43):Harned, H.S.; Davis, R., Jr., J. Am. Chem. Soc., 1943, 65, 2030-7.
(18:18)
KH(867):de Khanikof, M.M.N.; Louguinine, V., Ann. Chim. Phys. (ser. 4) 1867, 11, 412-33.
(10:1)
KOB(35):Kobe, K.A.; Williams, J.S., Ind. Eng. Chem. (Anal. Edition) 1935, 7(1), 37-8.
(1:1)
KOC(49):Koch, H.A., Jr.; Stutzman, L.F.; Blum, H.A.; Hutchings, L.E., Chem. Eng. Prog. 1949, 45(11), 677-82.
(6:1)
KUN(22):Kunerth, W., Phys. Rev. 1922 2, 512-24.
(8:6)
LI(71):Li, Y.-H,; Tsui, T.-F., J. Geophys. Res. 1971, 76(18), 4203-8.
(5:5)
MAR(41):Markham, A.; Kobe, K., J. Am. Chem. Soc. 1941, 63, 449-54.
(3:3)
MOR(30):Morgan, J.L.R.; Pyne, H.R., J. Phys. Chem. 1930, 34, 1578-82.
(2:0)
MOR(31):Morgan, O.M.; Maass, O., Can. J. Res. 1931, 5, 162-99.
(19:4)
MOR(52):Morrison, T.J.; Billett, F., J. Chem. Soc. 1952, 3819-22.
(19:19)
MUR(71):Murray, C.N.; Riley, J.P. Deep-Sea Res. 1971, 18, 533-41.
(8:8)
NOV(61):Novak, J.; Fried, V.; Pick, J. Collect. Czech. Chem. Commun. 1961, 26, 2266-70, Measurements at different pressures at 8 different constant temperatures. From the slope of kH vs. x, k0H is calculated.
(8:0)#
ORC(36):Orcutt, F.S.; Seevers, M.H., J. Biol. Chem. 1936, 117, 501-7.
(1:1)
POW(70):Power, G.G.; Stegall, H., J. Appl. Physiol. 1970, 29, 145-9.
(1:1)
PR(895):Prytz, K.; Holst, H., Ann. Phys. Chem., NF 1895, 54, 130-8.
(2:0)
SHE(35):Shedlovsky, T.; MacInnes, D.A., J. Am. Chem. Soc. 1935, 57, 1705-10.
(1:1)
VAN(39):Van Slyke, D.D., J. Biol. Chem. 1939, 130, 545-54.
(6:6)
VE(855):Verdet, M.; report of Bunsen, M., Ann. Chim. Phys. 1855, 43 496-508.
(21:0)#
YEH(64):Yeh, S.-Y.; Peterson, R.E., J. Pharmac. Sci. 1964, 53, 822-4.
(4:3)
# See text for details about source rejection.
Group B: (low-temperature, 273 K < T 353 K, P > 2 bar)
This group was not considered for data fitting.
KRI(35):
Kritchewsky, I.R.; Shaworonkoff, N.M.; Aepelbaum, V.A.Z., Physik. Chem. A 1935, 175, 232-8,
i, P = 5-30 bar, (2:0)
MAT(69):Matous, J.; Sobr, J.; Novak, J.P.; Pick, J., Collect. Czech. Chem. Commun. 1969,
34, 3982-5.
ii, P = 9-39 bar, (3:0)
SHA(82:Shaiachmetou, R.A.; Tarzimanov, A.A., Deposited Doc. 1981, SPSTL 200 khp-D81 1982.
ii, P = 100-400 bar, (1:0)
STE(70):Stewart, P.B.; Munjal, P., J. Chem. Eng. Data 1970, 15 67-71,
ii, P1 = 10, 40 bar, (12:0)
VIL(67):Vilcu, R.; Gainar, I., Rev. Rown. Chim. 1967, 12(2), 181-9,
ii, P1 = 25, 70 bar, (20:0)
WIE(39):Wiebe, R.; Gaddy, V.L., J. Am. Chem. Soc. 1939, 61, 315-8.
i. P = 25-700 bar, (2:0)
WIE(40):Wiebe, R.; Gaddy, V.L., J. Am. Chem. Soc. 1940, 62, 815-7.
I, P1 = 25-500 bar, (5:0)
ZAW(81):Zawisza, A.; Malesinska, B., J. Chem. Eng. Data 1981, 26, 388-91.
ii, P1 = 25 bar, (9:0)
Group C: (T > 373 K, any P)
BO(891):BC.; Bock, J., Ann. Phys. Chem., NF 1891, 44, 318-43.
ii, T = 373 K, (1:0)
CRA(82):Cramer, S.D., U.S. Bur. Mines. Rep. Invest. 1982, RI 8706.
ii, T = 399-486 K, (6:2)
CRO(90):Crovetto, R.; Wood, R.H. Fluid Phase Equil. 1992, 74, 271-88.
ii, T = 623-640 K, P = 170-220 bar, (3:3)
ELL(63):Ellis, A.J.; Golding, R.M., Am. J. Sci. 1963, 261, 47-60.
ii, T = 450-607 K, (15:14)
MAL(59):Malinin, S.D., Geokhimiya 1959 (3) 235-45.
i, T = 473-603 K, P = 100-500 bar, (4:2)
SHA(82):Shaiachmetou, R.A.; Tarzimanov, A.A., Deposited Doc. 1981, SPSTL 200 khp-D81 1982.
i, T = 373-423, K, P = 100-800 bar, (2:2)
TAK(65):Takenouchi, S.; Kennedy, G., Am. J. Sci. 1965, 263, 445-54.
I, T = 423-623 K, P = 200-1400 bar, (5:4)
WIE(39):Wiebe, R.; Gaddy, V.L., J. Am. Chem. Soc. 1939, 61, 315-8.
i, T = 373 K, P = 25-700 bar, (1:1)
ZAW(81):Zawisza, A.; Malesinska, B., J. Chem. Eng. Data 1981, 26, 388-91.
ii, T = 373-473 K, (9:0)
The meaning of the symbols used in the table follows:
For Group A: The numbers in parenthesis, (m:n), are m= the number of experimental points given in the source, and n = the number of points actually considered in the evalution.
For Group B and C: i: several isothermal solubility measurements are available for different pressures. When feasible, a graphical extrapolation for Henry’s constant, kH, to the solvent vapor pressure was performed. The numbers in parenthesis, (m:n), are m = the number of k0H’s obtainable from the source, n = the number actually considered.
ii: only pressure, or a very small pressure range, was experimentally studied in the source. The numbers in parenthesis, (m:n), are in this case m = the number of experimental partial molar volume of the solute is considered for calculating k0H in Eq. (1).
In Group C the range of T and P of the measurements is given. In Group B, only the range of P is given.
There are also compiled data sources which were not used in the evaluation: (1) Setchenov, J [Sechenov, I.M.] Pflügers Arch. Gesamte Physiol. Menschen Tiere 1874, 8, 1-39; Mem. Acad. Imp. Sci., St. Petersburg 1879, 26, 1-62; Akad. Nauk SSSR, Mem. Acad. Imp. Sci., St. Petersburg 1887 35, 1-59; Mosk. Obsh. Spyt. Prirody. Nouv. Mem. Soc. Imp. Nat. Moscow 1889, 15, 203-74; (2) Hantzsch, A., Vagt, A. Z., Phys. Chem. 1901, 38, 705-40; (3) Sander, W. Z., Phys. Chem. 1911-1912, 78, 513-49; (4) Findlay, A., Shen, B., J. Chem. Soc. 1912, 101, 1459-68; (5) Findlay, A., Howell, O. R. J. Chem. Soc. 1915, 107, 282-84; (6) Wiebe, R., Gaddy, V.L., J. Am. Chem. Soc. 1940, 62, 1055-74; (7) Shchennikova, M. K., Devyatykh, G. G., Korshunov, I. A., J. Appl. Chem. USSR (Engl. Transl.) 1957, 30, 881-6; (8) Ellis, A. J. Am. J. Sci. 1959 257, 217-34; (9) Bartels, H., Wrbitzky, R. Pflügers Arch. 1960, 271 162-8; (10) Barton, J. R., Hsu, C. C., J. Chem. Eng. Data 1971, 16 93-5; (11) Weiss, R. F., Marine Chemistry 1974, 2, 203-15; (12) Postigo, M. A., Katz, M., J. Solution Chem. 1987, 16, 1015-24; and (13) Yuan, C., Yang. J., Gaodene Xuexiao Huaxue Xuebao, 1993, 14, 80-83.