O'Neil J. R. ( 1986) Theoretical and experimental aspects of isotopic fractionation. In Stable ... Thode H. G., Shima M., Rees C. E., and Krishnamurty K. V. ( 1965).
Geochimica
et Cosmochimica
Acta, Vol. 61, No. 13, pp. 2691-2695, 1997 Copyright 0 1997 Elsevier Science Ltd
Pergamon
Printed in the USA. All rights reserved 0016.7037/97$17.00 + .OO
PI1 SOO16-7037(97)00107-S
Experimental
determination of carbon isotope equilibrium fractionation between dissolved carbonate and carbon dioxide STANISLAW HALAS*, JANINA SZARAN, and HALINA NIEZGODA
Mass Spectrometry Laboratory, Institute of Physics, Marie Curie Sklodowska University, 20-031 Lublin, Poland (Received February 15, 1996; accepted in revised form March 4, 1997)
Abstract-By mixing aliquots of pure Na2C03 and CO*, solutions with precisely known molal fractions of CO,, HCO,, and dissolved COz were prepared. The apparent fractionation factor between gaseous CO, and total carbon in the solution was determined mass spectrometrically from which the CO; - CO2 fractionation factor was calculated taking into account the known fraction of HCOT and respective isotope fractionation. Although the measurements have been made for a rather narrow temperature range, from 4 to 8o”C, a theoretical curve was fitted through the experimental points, and thereby, the isotopic partition function ratio of “CO; and ‘*COT molecules has been obtained for an extended temperature range. The results obtained for COT-CO, isotope fractionation are significantly lower than those for HC?&-CO2 exchange (with 103(~ -- l)-= 5.6 & 0.2 at 25°C and cross-over- point at about 63°C). Copyright 0 1997 Elsevier Science Ltd 1. INTRODUCTION a(T)
The stable isotope exchange reaction and gaseous carbon dioxide, ‘2co,
+ “co*
#
between
13c0,
carbonate
+ ‘*co2
ion
(1)
‘2C0,
in CO;
L ’
=
(3)
+
l3c
*
‘“co_;
+
“C
(4) (5)
Inasmuch as the ,?J factor for CO2 has been evaluated by Richet et al. (1977), it remains to evaluate the p-factor for CO;. In the harmonic approximation, which is correct at low temperatures, one obtains (Urey, 1947 )
1000
1 + 6’3CofC02
in CO2
Q('3C0d I Q( “C02)
‘2CO* + ‘3C 4+ “co ? + 1%.
, ~ S13Cof co, (“C/‘*C)
Q("CO;) Q( “CO;)
where Q stands for the reduced partition function of the molecular species given in parentheses. It is more convenient, however, to consider a(T) at thermodynamic equilibrium as the ratio of two (Yfactors (which are called p factors) for the following equilibria
was investigated theoretically and experimentally (Urey, 1947; Thode et al., 1965; Turner, 1982; Lesniak and Sakai, 1989; Zhang et al., 1995), but the data published so far are highly divergent. We experimentally determined the equilibrium fractionation factor
(y = (‘0°C)
=
(2)
1000 p = n
In this study, the carbon isotope equilibrium fractionation was measured in the presence of Na+ at a pH of about 10.3, at which the CO; fraction is as high as 0.82 while the partial pressure of CO? gas, P(CO,), is 1.8 10e4 atm (i.e., somewhat less than the partial pressure of atmospheric C02). The financial support of this research was just sufficient to investigate reaction 1 at low temperature (4-80°C). Therefore, theoretical calculations have been made to extend the plot of the value of t = lO”(a as a function of temperature 2. THEORETICAL
-
1)
towards the hydrothermal
(:)
exp[q)
sX(CO:)
(6)
where the product is extended over all six vibrational modes of the molecule, u, = hcq lkT, the prime refers to the isotopically substituted molecule ( ‘3COg), w, are vibrational frequencies in cm-‘, c is the speed of light in vacuum, h is Planck’s constant, k is the Boltzmann constant, and T is absolute temperature, X(C0,) is the excess factor (Richet et al., 1977). It should be emphasized that w: and u: are calculated from known w, and frequency shifts due to isotopic substitution. These calculations can be made using known molecular force field equations. In this paper, we shall repeat the procedure described by Urey ( 1947) but with recalculated frequency shifts Aw3/w3 and Aw4/w4, the sum of which should be equal to -0.03 1667 (see formula 20 in Urey, 1947 ) We will treat Awe as an adjustable parameter while Au3 is calculated from the equation
(2a) range.
CONSIDERATIONS
The equilibrium fractionation factor, LY,can be estimated by statistical mechanics on the basis of spectroscopic data (Urey, 1947 ) . Calculation formulae can be found in excellent review papers by Richet et al. (1977), O’Neil (1986), and references therein. For reaction 1, we may write
Aw31w3 + Aw4/w4 = - 0.031667 The choice of Awd is determined 2691
(7)
by the best fit to our experi-
S. Halas. .I. Szaran,
2692
and H. Niezgoda x2 = m(CO;)/DIC
mental data. Table 1 contains vibrational frequencies used in this paper and in the recent paper by Chacko et al. ( 1991). In order to obtain a more realistic ,0 factor for the CO, ion, the anharmonic correction and a correction for the influence of surrounding water molecules should be made. The estimation of this correction for the CO; ion will be made by combining the harmonic approximation (Eqn. 6) with experimental data for the COT - CO2 isotope fractionation. The experimental data for CO.7 - CO2 fractionation and known p-factor for CO2 will yield a multiplicative correction term to the harmonic approximation for COT:
If we know the carbon isotopic ratio of total dissolved inorganic carbon and that of CO* gas being in equilibrium with the solution, the isotopic fractionation between CO; and CO, can be obtained as follows. First, the apparent fractionation factor between DIC and CO2 is determined in the usual way: 1000 + 6”C(DIC) c&l =
that this factor may include slightly differs from unity.
Note
the excess
factor which
3. EXPERIMENTAL 3.1. Principle
012 = (aapp - XI(YI)/XZ
of the Measurement
This equation may also be rewritten (defined above) :
The carbonate ion, CO;, in aqueous solutions is always present in association with HCO, and COZ.s, the distribution of which is mainly dependent on the activity of hydrogen ions. In this experiment, the solution of pure Na2COI and CO, was prepared. This solution contains the following ion and neutral species: Na’, H+, CO;, HCO;, OH-, COz,uI, and H,O. The concentration of ion pairs was negligible at concentrations of carbon species used throughout the experiment. In equilibrium, the atmosphere over the solution contains only Hz0 vapour and CO, gas if the system was previously evacuated. The pressure of the CO, gas, P(CO*), depends mainly on the pH value, but also on the temperature of the system (T) and the concentration of ionic species expressed in terms of ionjc strength (I). Appropriate equations and equilibrium constants were adopted from Deines et al. ( 1974). Truesdell and Jones ( 1974)) Plummer and Busenberg (1982), Arnorsson et al. (1982), and Truesdell (1984). In the experiment, CO? gas was removed from above the solution for isotopic measurements. It is impossible to extract solely CO;, but only the sum of dissolved inorganic carbon species (DIC). The molal concentration of carbon in the solution can be expressed as the sum of molalities of the individual species: DIC = nz(CO,,,)
+ m(HC0,)
+ m(COf)
3.2. Preparation
(10)
X, = m(HCOF)IDIC
(11)
Molecule ‘Co; ‘COS
1. Vibrational WI 10070.00 10070.00 10070.00
freauencies d’z 881.00 853.38 853.38
(13)
(14) E values
(15)
of the Solution
Special attention was paid to the preparation of COT-rich solutions About 10 g of analytical grade Na2C03 was reacted with CO2 (prepared from 1 g of this reagent) and l/4 dm’ of water. Prior to use, the reagent was vacuum roasted at 120°C for 4 h to drive off adsorbed CO1 and water. Aliquots of CO* were prepared by standard techniques (McCrea, 1950). Distilled and boiled water was used throughout the experiment. We obtained the most reproducible results when the following steps in the preparation of the solution were taken: ( 1) A precisely weighed aliquot of roasted Na2C03 was placed into the lower vessel of the apparatus (Fig. I), and then the apparatus was connected to the vacuum line and evacuated. (2) CO* prepared from another aliquot of roasted NaZC03 was transferred from the reactor to the lower vessel of the apparatus by freezing with liquid nitrogen. Traces of air were evacuated and the stopcock between the upper and lower vessel was closed. (3) The apparatus was detached from the vacuum line, the upper stopcock opened, and 250 mL of water poured into the upper vessel. (4) The apparatus was again connected to the vacuum line to outgas water by pumping on the vessel through a constriction, then the upper stopcock was closed, and the outgassing of water repeated after 24 h. (5) Then water was allowed to react with NaZCOS and CO2 in the lower vessel to achieve chemical and isotopic equilibria. The apparatus was kept in a thermostated box (surrounded with a water mantle) for periods of 24 h to 1 week.
(9)
x~) = m(COz,)lDIC
in terms of respective
t7_= (capp- X,(rl)IX>
The experiment was designed so that, for a given prepared solution, the molalities of individual carbon species can be calculated for any temperature. For this purpose, we have to know only the quantities of Na2C03, water, and CO, added. Calculated and measured pH were compared at room temperature only. The agreement was good (?O.Ol in pH units) Moreover, the P( CO,) was checked mass spectrometrically as described below at each temperature to ensure that the system was properly described by the set of equations. Let x0, x, , and x2 denote the mole fractions of individual carbon spectes, I.e.,
Table
1000 + 6’C(CO*)
The next step is to calculate o2 for carbon isotope fractionations between CO; and CO2 gas, using (Y,,and (Y, for CO,,-CO, gas and HCOT-CO, gas, respectively, which are known with high accuracy (Mook et al., 1974; Szaran, 1983; Vogel et al., 1970). Actually, the value of (Y”was meaningless for our purposes because we worked with highly basic solutions in order to obtain sufficient accuracy in the determination of (Ye. For example, at pH = 10.3 the mole fractions of COT, HCO,, Thus, and COzas were 0.817, 0.183, and l.19*10m5, respectively. we calculated (Yefrom a simplified formula in which the contribution of COz, was neglected. For a binary mixture of COT and HCO,, one obtains
(8)
1-++;
(12)
3.3. Measurements It was established that the isotopic composition of total carbon in the solution prepared as described above was identical to that of roasted Na,COS within the error of 6 “C measurement, i.e., about 0.05!% in our case. Thus, only COZ equilibrated with the solution
in cm-‘.
deaeneracies
are indicated
in oarentheses.
w,(2)
w‘!(2)
Ref.
1460.00 1421.66 1419.22
112.00 708.15 709.49
Chacko et al. (1991) This work Chacko et al. (1991)
Fractionation
of C isotopes
between
dissolved
carbonate
and CO?
2693
4. RESULTS
The results obtained for e2 as a function of temperature are plotted vs. temperature in Fig. 2. Our c2 values are significantly lower than those published previously (Table 2). Although our experimental results extend over a rather narrow temperature range, 4-80°C they may be used to fit three free parameters in the theoretical formula. One parameter is nw4 for COT in Eqn. 7, while the remaining are the coefficients in formula 8. The best fit was found for wi = 708.15 cm-’ instead of 709.49 cm-’ assumed by Bottinga (1968) and Chacko et al. ( 1991) (see Table 1). The correction factor has been obtained using formula 8:
, _5.l+ T
1620 T2
(16)
It should be noted that the coefficient of 1 lT* is much larger than the coefficient of 1 lT. Table 3 contains e2 values calculated on the basis of known p-factors for CO2 (Richet et al., 1977). This calculation has been made for an extended temperature range. 5. DISCUSSION
Fig. 1. Apparatus for isotopic equilibration rich solution. The two stopcocks are greased any contact with organic carbon.
of CO2 with a CO;with silicone to avoid
was analyzed. To take a CO, sample, the lower stopcock was closed and CO* was extracted cryogenically from the upper vessel of the apparatus, transferred into a small ampoule, and analyzed massspectrometrically for the amount of CO* and its 6°C value. The determination of the amount of CO, was performed by comparison of major beams in CO: spectra (m/e = 44) of the sample with that of a known amount of CO2 admitted to the same volume of the inlet system of the mass spectrometer. The measurement of S”C was performed using a double collector system. Thus, analyses of 6’sO were performed separately in order to introduce the correction for “0 contribution to the ‘%r60; peak (Craig, 1957) Immediately after these analyses, CO2 prepared from the roasted NaZCOZ was analyzed, and olapPwas evaluated. Finally, t2 was calculated from formula 15. The above procedure was then repeated at the same or another equilibration temperature. An improved inlet system on the mass spectrometer assured precise isotopic analysis of small samples of CO2 samples (Halas and Krause, 1983, 1984).
The fractionation factor (Y?,applied by isotope researchers thus far has apparently been too large. Our new results are consistent with physical properties of the molecules, namely, the molecule with a greater number of atoms, HCO;, has more vibrational modes, and thus a larger p-factor, than the CO; molecule. At 25”C, the best agreement is found with the result of Zhang et al. ( 1995). Thode et al. (1965) reported experimental results with wide fluctuations of t2 from 8.4 to 16.6 (Table 3). Most of their determinations were done at one temperature (27 ? 1’C) in the presence of Na+ in the solution. Therefore, Thode et al. ( 1965) recalculated the isotope equilibrium factors on the basis of the harmonic approximation, which yielded the following inequality at low temperatures (300K): (Y,, < (Y, < (Ye. In light of our present data, this order should be revised ( a2 < (Y,) Lesniak and Sakai (1989) investigated the isotope fractionation at two temperatures, 25 and 40°C but their results are questionable due to a probable departure from chemical equilibrium between the CO2 gas and the solution: first, because it is hard to prepare the solution by mixing aliquots of Na2C0, and NaHC03, which would have a precisely determined pH value; and second, even a slight departure of the partial pressure of CO*, which was bubbled through the solution with nitrogen carrier gas, from the equilibrium value can produce a significant kinetic effect until chemical equilibrium is reached. At low P( CO?) (pH = 9.9), the equilibration time would be unreasonably long in comparison to that in their experiment performed at pH = 7.2. Therefore, the data published by Lesniak and Sakai ( 1989) are probably highly biased by a kinetic effect for (Ye, while not much for [Y,. The rather large spread of our present experimental data requires detailed discussion. The final results were calculated from Eqn. 15 from which the standard error of E can be simply estimated by assuming no error in the determination
2694
S. Halas, J. Szaran,
?? ??
\
and H. Niezgoda
? 8 “‘s ??
0
6-
:k:
~
calculated 0
measured
??
__ ?? e ?? ??
:
??
?ee 0
~
_____j_
??
1
4
I
0
I
I
I
20
??
40
I
I
80
60
100
T [“Cl Fig. 2. Plot of t2= 103(a
-
1) vs. temperature.
The curve represents
of x1 and x2 fractions. Also, E, is known with high precision in comparison to e2. Hence, the standard error of e2 may be estimated as follows: 462
1 =
(17)
dEapp)/X2
where ~(E,~J = do2[6’3C(C02)]
+ cr2[SL3C(DIC)]
(18)
The standard error of S13C(DIC) in our case was usually less than 0.1%~ but cr of 613C( C02) was largly dependent on the amount of C02, varying typically from 0.2 to 0.6%0. Inasmuch as x2 for various solutions prepared varied from 0.80 to 0.87, the expected error was larger by a factor of 1.2. This estimate refers to each single point plotted in Fig.2 for temperatures below 40°C. The error of the curves was further reduced approximately threefold by statistical treatment of the data. There is a large scatter in our experimental
calculated
values as described
data at high temperatures. We noticed severe difficulties in obtaining good reproducibility using glass apparatus with greased stopcocks due to small leaks or diffusion of CO, through the softened grease. This study was restricted to a rather narrow temperature range and to one cation in the solution (Na’ ) . As was suggested by Thode et al. (1965), the presence of Mg++ ions leads to formation of a neutral complex, MgCOi, which may increase the equilibrium isotope fractionation oz. Seawater
Table 3. Calculated carbon isotope fractionation between CO; and CO, over an extended range of temperature. In brackets are extrapolated values beyond temperatures of this experiment.
T (“(2 0
Table 2. Comparison tionation between CO; EL1 8.3 to 16.6 6.45 ? 0.4 8.38 2 0.1 5.9 -t 1.0 5.0 2 0.2
of published experimental data on 13C fracand CO* at room temperature. T (“C)
Ref.
21 25 25 25 25
Thode et al. (1965) Turner (1982) Lesniak and Sakai (1989) Zhang et al. (1995) This work
in the text
10 20 30 40 50 60 70 80 100 120 150 200
f2
9.12 7.34 5.14 4.28 2.96 1.75 0.65 -0.35 -1.26 (-2.84) (-4.17) (-5.74) (-1.52)
Fractionation
of C isotopes
between
Table 4. Estimated values of apparent carbon isotope fractionation between sea water and gaseous carbon dioxide (carp = xocO + ~,t, + X& as a function of temperature and pH. Data for E,, and t, were taken from Vogel et al. (1970) and Mook et al. (1974). T (“0
PH
X0
0 0 0 20 20 20
7.6 8.0 8.4 7.6 8.0 8.4
0.033 0.013 0.005 0.022 0.009 0.003
xi 0.946 0.935 0.875 0.943 0.903 0.800
X2 0.021 0.052 0.120 0.035 0.088 0.197
C”PP 10.48 10.61 10.57 8.20 8.16 7.91
contains M&O! in which the amount of COT is nearly 75% of total CO; (Garrels et al., 1961). Assuming tentatively, however, that the effect of MgCOy on isotopic fractionation is negligible, we calculated c,rp for model seawater and CO* (Table 4). Direct measurements of eappfor seawater (Zhang et al., 1995 ) yield results about 0.2%0 higher than that calculated here (Table 4). It seems that the production of MgCO: ion pairs may lead to an increase of the c2 value because the /3 factor for MgCOi should be higher than that for pure CO,. Another significant application of our new t* values is in the modelling of highly basic natural brines with pH above 8 and occasionally even 10 (Halas and Lis, 1980). Acknowledgments-We thank Dr. H. Roy Krouse, The University of Calgary, for corrections to the manuscript. We are grateful to Dr. T. Vennemann and one anonymous referee for thorough reviews. This study (project 2 0348 91 01) was supported by the State Committee for Scientific Research, Warsaw. Editorial
handling:
T. K. Kyser REFERENCES
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