COBISS: 1.01 PHYSICS AND CHEMISTRY OF CO2 OUTGASSING FROM A SOLUTION PRECIPITATING CALCITE TO A SPELEOTHEM: IMPLICATION TO 13C, 18O, AND CLUMPED 13C18O ISOTOPE COMPOSITION IN DIC AND CALCITE FIZIKA IN KEMIJA RAZPLINJANJA CO2 PRI ODLAGANJU SIGE, S POSEBNIM OZIROM NA SIGNALE IZOTOPA 18O IN IZOTOPSKEGA SKUPKA 13C18O V RAZTOPLJENEM ORGANSKEM OGLJIKU IN KALCITU Wolfgang DREYBRODT 12 Abstract UDC 552.545:556.114 Wolfgang Dreybrodt: Physics and chemistry of CO2 outgassing from a solution precipitating calcite to a speleothem: Implication to 13C, 18O, and clumped 13C18O isotope composition in DIC and calcite Outgassing of CO2 from thin water layers of a solution of CaCO3 in an H2O -CO2 system plays a crucial role in the precipitation of calcite. Understanding the process of outgassing of CO2 during precipitation of calcite to the surface of stalagmites is important for the interpretation of isotope signals in the calcite deposited to the speleothem. There is, however, some confusion in the literature about the physics and chemistry of this process. Indistinct terms like forced, enhanced, rapid, intense, slow, increased, equilibrium and progressive outgassing are used widely in the literature to explain the impact on isotope composition of the calcite deposited. It is shown that in all the variety of conditions occurring in nature only two distinct processes of outgassing exist. 1. Diffusion controlled outgassing: In the first step, whenever a thin water layer of calcareous solution is present, either on the cave wall or on the surface of a stalagmite, molecular CO2 escapes within several seconds by physical diffusion and after about 40 seconds pH and DIC in the solution achieve chemical equilibrium with respect to the CO2 in the cave atmosphere. 2.) Controlled by precipitation: In the second step this supersaturated solution precipitates calcite, whereby for each unit CaCO3 deposited one molecule of CO2 is generated and escapes from the solution by molecular diffusion. This precipitation controlled outgassing is active during precipitation only. All variations of outgassing mentioned in the literature can be explained Izvleček UDK 552.545:556.114 Wolfgang Dreybrodt: Fizika in kemija razplinjanja CO2 pri odlaganju sige, s posebnim ozirom na signale izotopa 18O in izotopskega skupka 13C18O v raztopljenem organskem ogljiku in kalcitu Razplinjanje CO2 iz tanke plasti raztopine sistema CaCO3 in H2O-CO2 je pomembno za izločanje kalcita in interpretacijo izotopskih signalov v odloženem kalcitu. V literaturi je precejšnja zmeda pri obravnavanju fizike in kemije procesa razplinjanja, saj raziskovalci uporabljajo različne izraze, kot so prisiljeno, poudarjeno, počasno, povečano in progresivno razplinjanje. V članku pokažem, da sta pri vseh različnih razmerah v naravi bistvena le dva procesa razplinjanja. 1) Difuzi-jsko razplinjanje: v prvem koraku molekularni CO2 v nekaj sekundah z difuzijo preide iz tanke plati vode, ki polzi ali po jamski steni ali po površini sige. Po približno 40 sekundah pH in raztopljeni organski ogljik v raztopini dosežeta ravnovesje z atmosferskim CO2. 2) Razplinjanje pri izločanju: v drugem koraku prenasičena raztopina izloča kalcit, pri čemer se za vsako odloženo molekulo CaCO3 iz raztopine sprosti molekula CO2, ki potem z difuzijo uide v jamsko atmosfero. S tema procesoma lahko pojasnimo vse druge načine razplinjanja, ki jih omenja literatura. Nato pokažem, da CO2, ki se razplini v prvem koraku, ne vpliva na izotopsko sestavo zaloge HCO3- v raztopini in zato tudi v izločenem kalcitu. Izotopska sestava HCO3- je tako za 13C in za 18O povsem določena z razplinjan-jem med izločanjem kalcita. Ujemanje količine razplinjenega CO2 in izločenega kalcita pokažem tudi s poskusom. Rezultati omogočajo kritično obravnavo uporabe termometra na osnovi 1 Faculty of Physics and Electrical Engineering, University of Bremen, Germany, 2 Karst Research Institute ZRC SAZU, Titov trg 2, 6230 Postojna, Slovenia, e-mail: dreybrodt@t-online.de Received/Prejeto: 03.02.2019 DOI: https://doi.org/10.3986/ac.v48i1.7208 ACTA CARSOLOGICA 48/1, 59-68, POSTOJNA 2019 WOLFGANG DREYBRODT by one of these two types of outgassing. Furthermore it is shown that the first step of outgassing driven by diffusion has no influence on the isotope composition of the HCO3- reservoir in the solution and consequently on that of calcite precipitated from it. The isotope composition of HCO3 for 13C as well as for 18O solely is determined by the second step of precipitation controlled out-gassing. An experiment is presented proving that the amount of CO2 escaping from the solution during precipitation of calcite at any time is equal to the amount of calcite precipitated. The results are used for a critical application to the A47 clumped isotope thermometer that explains why in most stalagmites the calcite is not a good candidate to obtain correct temperatures at the time of its deposition. Key words: isotope, clumped isotope, speleothem, calcite, pa-leo-thermometer. izotopskega skupka A47 in pojasnjujejo, zakaj kalcit ni primeren za določanje temperature v času izločanja.. Ključne besede: izotop, izotopski skupek, siga, kalcit, paleo temperatura. INTRODUCTION Outgassing of CO2 from thin water layers containing a solution of CaCO3 in a water-CO2 system plays a crucial role in the precipitation of calcite. During deposition of calcite from thin water layers, as they occur on stalagmites, two different processes of CO2 outgassing are active. First, when a calcareous solution drips to the stalagmite, aqueous CO2 escapes from the water film by molecular diffusion into the cave atmosphere with low pCO2 until chemical equilibrium between the CO2 in the solution and that in the atmosphere is established. In chemical equilibrium the concentration, Ceq , of aqueous CO2 in the water is related to the partial pressure, Pcoi of CO2 in the cave by Henry's law, c = KH • , where KH is Henry's constant. For water layers with a depth, 5, of several tenths of a millimeter this process is fast and takes about ten seconds in agreement to the theoretically predicted exponential time constant, Tdiff = 452/(n2D), where D = 2-10-5 cm2s-1 is the diffusion constant of aqueous CO2 (Dreybrodt 1988; Dreybrodt 2011; Hansen et. al. 2013). Note that the time constant, Tdiff, for outgassing is independent of the difference between the pCO2 in the solution and the pCO2 in the cave atmosphere. During this first step of diffusive outgassing of dissolved molecular CO2 the solution remains undersaturated and calcite cannot be precipitated. Therefore, the Ca2+-con-centration remains constant. The HCO3-concentration remains constant also because it is tied to the Ca2+-con-centration by electro neutrality. After outgassing is completed the concentration of H2CO3 is reduced also. Therefore pH rises and the concentrations [HCO 3- ] and [CO 32- ] are no longer in equilibrium with respect to the lower concentration of CO2 in the solution. Establishing chemical equilibrium needs the time, Teq of about 40 s, independent of the depth, 5, of the water layer (Hansen et al. 2013) and causes supersaturation with respect to calcite. The pH-value after completion of this process is above 8. These processes have been explored experimentally (Hansen et al. 2013). After establishment of supersaturation calcite is precipitated to the surface of the stalagmite until after the time 3Tprec, 95% of the calcite is precipitated and equilibrium with respect to calcite is obtained. During precipitation, stoichiometry of the reaction Ca2+ + 2HCO3-CaCO3 + CO2 + H2O requires that for each molecule of CaCO3 deposited one molecule of CO2 must be released into the solution from where it outgasses by molecular diffusion into the surrounding atmosphere. This second step of outgassing is controlled by calcite precipitation, which releases CO2 molecules into the water. These escape from the solution by molecular diffusion and the amount of CO2 released into the atmosphere is equal to the amount of calcium withdrawn from the solution by precipitation into calcite. These two different types of outgassing have caused confusion in the speleothem research community. Indistinct terms like forced, enhanced, rapid, intense, slow, fast, minimal, increased, equilibrium and progressive out-gassing are scattered throughout the literature without clear definitions of their meaning. In a large number of papers the term outgas or degas is used this way many times. As an example, the book "Speleothem Science" referencing the current literature (Fairchild & Baker 2012) uses the term "degas" 148 times, but does not give a clear description of its meaning. In a similar way the term degas is used in a recent paper 90 times (Mickler et al. 2019). There is consensus in the scientific community that understanding of the physics and the chemistry in cave 60 ACTA CARSOLOGICA 48/1 - 2019 PHYSICS AND CHEMISTRY OF CO2 OUTGASSING FROM A SOLUTION PRECIPITATING CALCITE TO A SPELEOTHEM: IMPLICATION TO 13C, 18O, AND CLUMPED 13C18O ISOTOPE COMPOSITION IN DIC AND CALCITE processes is of utmost importance to decipher paleo-cli-matic information from time series of 18O and 13C signals recovered from stalagmites. In this paper I discuss the processes of outgassing of CO2 from thin water layers on the top of a stalagmite. In addition I present an experiment elucidating that outgassing related to precipitation of calcite is controlled by precipitation and ceases when precipitation stops. MATERIALS AND METHODS H2O-CO2 -CaCO3 SOLUTIONS In order to study chemical equilibration and precipitation of calcite in a batch experiment, we prepared a supersaturated H2O-CO2 -CaCO3 solution with Milli-Q water in a 5 L-Duran borosilicate glass vessel. To get the desired concentration of Ca2+ the corresponding amount of Baker analyzed CaCO3 was added to the water and stirred with a magnetic mixer. Subsequently, the solution was sparged with high purity CO2-4.5 (Linde). After a few hours, the solution becomes clear and translucent indicating complete dissolution of CaCO3. To obtain a solution slightly supersaturated with respect to calcite nitrogen is bubbled through the solution until pH of about 7 is established. This solution can be kept in the bottle for several days without changing pH and Ca2+ concentration. (Hansen et. al. 2013). As can be calculated by PHREEQC2 (Parkhurst and Appelo 1999), the specific conductivity of the solution, a, is linearly related to its Ca2+ concentration, c. For pH = 8 and Ca2+ concentrations between 1 and 8 mmol/L at a temperature of 25 °C, one finds experimentally the relation a = 60 + 153c between specific conductivity, a (^S/cm), and Ca2+ concentration, c, in mmol/L (Hansen et al. 2013). EXPERIMENTAL SET-UP Fig. 1 shows the experimental set up. A box with a volume of 67 L closed to the outside atmosphere contains a beaker with 0.7 L of the solution that is stirred by a magnetic stirrer. A membrane pump bubbles the air in the box through this solution from where it turns back to the atmosphere in the box. The specific conductivity of the solution is measured with a Mettler-Toledo* InLab*738 Conductivity Probe. The CO2 concentration in the box is monitored during the experiment using a Vaisala* CO2-sensor. Prior to the experiment, the box is flushed with pure N2 or Ar until CO2 was zero. Then 67ml of CO2 are injected by a syringe to obtain a pCO2 = 10-3 atm. After several hours the solution was in equilibrium with the surrounding pCO2 in the box. To initiate precipitation of calcite 2.5g of calcite seed crystals (Baker analysed) are added to the supersaturated solution through a funnel. Precipitation of calcite to the surface of the seed crystals starts immediately. The temporal evolution of electrical conductivity and pCO2 is measured until no further change occurred. The experiment was performed at ambient temperature of 25°C that was constant within 0.5°C during the experiment. Fig. 1: Experimental set up. ACTA CARSOLOGICA 48/1 - 2019 61 WOLFGANG DREYBRODT EXPERIMENTAL RESULTS Fig. 2 depicts the temporal evolution of the total amount of CO2 in the atmosphere in the box and the total amount of calcium in the solution. Both curves show an expo- nential approach to equilibrium. The exponential times within the limit of error of about 5% are equal. Figure 3 illustrates the amount of CO2 released from the solution Fig. 2: Temporal evolution of the amount of CO2 contained in the atmosphere in the box and the amount of Ca contained in the solution. Fig. 3: Amount of CO2 released into the atmosphere versus the amount of Ca precipitated from the solution. 60 ACTA CARSOLOGICA 48/1 - 2019 PHYSICS AND CHEMISTRY OF CO2 OUTGASSING FROM A SOLUTION PRECIPITATING CALCITE TO A SPELEOTHEM: IMPLICATION TO 13C, 18O, AND CLUMPED 13C18O ISOTOPE COMPOSITION IN DIC AND CALCITE during precipitation of calcite versus the amount of calcium removed from the solution by precipitation. As one can see from the straight line with slope 1, the amount of CO2 released is equal to the amount of CaCO3 precipitated during the entire experiment. DISCUSSION The two different processes of outgassing are both limited in time. 1) Outgassing by molecular diffusion into the atmosphere depends on the depth of the water layer, 5, by Td¡ff= 452/(n2D). For water layers with depth as they are common on speleothems one finds times, Tdiff of outgassing between 2 s up to 32 s for 0.01 cm < 5 < 0.04 cm. (2) Outgassing controlled by precipitation of calcite proceeds with exponential precipitation time constant, t = 5/a. a is the kinetic rate constant of prec the rate law for precipitation, R = a(c-ceq), where c in mol cm-3 is the calcium concentration in the water layer, ceq the equilibrium concentration of calcium with respect to the pCO2 (atm) in the cave atmosphere and with respect to calcite (Buhmann and Dreybrodt 1985; Dreybrodt 1988). The kinetic constant depends on temperature by the relation a = (0.52+0.04T+0.004T2)-10-5 cm/s and increases by about a factor of ten from 0°C to 25°C. T is temperature in °C. (Baker et al. 1998). With these data precipitation times range between 2000 s and 250 s for 5 = 0.01 cm at T = 0°C and 25°C, respectively. For all temperatures Tprec is larger than Tdiff by one order of magnitude. If the drip intervals T,. << t ,+ t the residence 1 drip din eq time of the water on top the stalagmite will be short and there may not be sufficient time for the solution to outgas and to become supersaturated with respect to calcite (provided this has not happened by prior cal-cite precipitation on the cave walls) and consequently precipitation of calcite is not active. This means that during fast dripping, Tdrip << Tdiff + Teq stalagmites may exhibit a hiatus at the apex. Calcite precipitation starts after supersaturation has been attained. It ceases after the time 3-t during which 95% of the calcite avail- prec ° able have been deposited. Therefore isotope signals imprinted for drip times T,. > 3-t + t,.a + t will all 1 1 drip prec din eq be independent of drip time. Only for T,. < 3-t + drip prec Tdiff + Teq the isotope signal in the calcite does depend on drip time, because for times larger than 3-Tprec, 95% of the calcite is deposited and further precipitation of the remaining 5% has no significant impact (Dreybrodt 2011; Dreybrodt 2016). It may be instructive to consider the amounts of CO2 outgassing during the two steps of outgassing. Using the program EQUILIBRIUM (Dreybrodt 1988), updated by F. Gabrovsek, I find the following numbers. When the water enters into the cave, calcium concentrations of about 2 mmol/L and CO2 concentrations in the solution of about 0.5 mmol/L are common. After outgassing by diffusion into a cave atmosphere with pCO2 of 0.0004 atm these solutions contain 2 mmol/L of calcium but only about 0.02 mmol/L of aqueous CO2. Thus typical amounts of CO2 lost from the solutions in the first step by diffusion is about 0.48 mmol/L. In the second step of precipitation controlled outgassing, the calcium concentration changes from 2 mmol/L to 0.63 mmol/L. The corresponding amount of CO2 lost during precipitation is therefore 1.37 mmol/L. This is about three times more than what is lost during the first step of diffusion driven outgassing. Within this concepts of outgassing there is no need to consider forced, enhanced, rapid, intense, slow, increased, equilibrium, or progressive outgassing as relevant processes. They all can be defined either by diffusion controlled or by precipitation controlled out-gassing. The influence of pCO2 in the cave atmosphere to the isotope composition of calcite is often discussed in the PCO2 in cave atmosphere atm C eqi h mmol/L Precipitation rate,R, for c = 2 mmol/L mmol cm-2 s-1 3.540-4 0.64 1.70-10-8 2-10"3 1.17 1.04-10-8 5-10"3 1.62 4.75-10-9 8-10"3 1.92 1.00-10-9 M0-2 2.07 -8.75-10-10 Tab. 1: Equilibrium concentration of Ca with respect to calcite and precipitation rates in dependence on partial pressure, pC02, of C02 in the cave atmosphere. c. = 2 mmol/L, T = 10°C. ACTA CARSOLOGICA 48/1 - 2019 61 WOLFGANG DREYBRODT literature in terms of outgassing rates associated with the pCO2 difference (gradient) between solution and the cave atmosphere. In this sense rates are called enhanced, when pCO2 in the cave is low. This, however, has no impact on the isotope composition of the calcite deposited for the following reasons. A change of pCO2 causes a change of, ceq, the equilibrium concentration of calcium by the relation C =k-■\]pC02 where k is a constant depending on temperature (Dreybrodt 1988). ceq is listed in Tab. 1 for various pCO2 at a temperature of 10°C. For a solution impinging to the stalagmite with concentration, cto = 2 mmol/L, using the rate law for calcite deposition, R = a(cin-ceq), (Buhmann & Dreybrodt 1985; Dreybrodt 1988) and employing a = 1.25-10-5 cm/s at 10°C one finds the initial precipitation rates as listed in Tab. 1. Precipitation rates decrease with increasing pCO2 and at pCO2 > 0.01 atm the solution becomes corrosive. The corresponding rates of CO2 outgassing controlled by calcite precipitation are equal to the withdrawal rates of calcium from the solution by precipitation of calcite. During precipitation of calcite outgassing is determined by the precipitation rates and not by pCO2 difference (gradient) between solution and cave atmosphere. At that point it is important to realize that only out-gassing controlled by precipitation has an impact on the isotope composition of both 13C as well as 18O in HCO3-in the solution and consequently to the calcite precipitated. Equilibration of 18O in HCO3 with water proceeds on time scales of several thousand seconds (Beck 2004) and can be neglected during the short time scales considered here. For pH < 8.3 there are two large reservoirs of carbon: HCO3- dominant for pH > 7.5 and aqueous CO2 dominant for pH < 6. Water entering into the cave with 2 mmol/L of calcium exhibits a pH of about 7.3 with 4 mmol/L of HCO3- and 0.5 mmol/L aqueous CO2. The first step of diffusion controlled outgassing of CO2 takes about 10 s. During this time the reservoir of HCO3- remains unaffected as electro neutrality requires CHC03 = 2-CCa and calcite has not yet been removed by precipitation. The reservoir of aqueous CO2 is depleted to 0.02 mmol/L. After this first step of outgassing pH rises to 8.25 and precipitation starts. Since diffusive out gassing of aqueous CO2 is accomplished by molecular diffusion of two non interacting independent species, the heavy and the light isotope, isotope equilibrium between the gas and the aqueous CO2 is attained after the short time of Tdiff. Subsequently the reservoir of HCO3- approaches chemical and isotope equilibrium on the order of several 10 s (Zeebe et al. 1999). During equilibration the concentrations CHC03 and Cc02 remain constant. Cc02 is fixed due to the constant pCO2 in the cave atmosphere and the concentration of HCO3 is tied to the calcium concentration, cCa, by electro neutrality, CHC03 =2-CCo, at pH about 8. During the time of equilibration the system is closed. Neither calcium and HCO3- nor CO2 are removed from the solution. Therefore, SDIC must remain constant. After outgassing one has ¿out r X -i-r S1 rout _ HCQ3 ' HCQ3 "*" C CQ2 '°CQ2 IC I -I- \ \CHC03 + C C021 After equilibration S^¡c is given by r .Seq +C ■Seq req _ HCQ3 HCQ3 T ° CQ2 UCQ2 DIC ~ (CHC03 C C02 ) Equating both one obtains the change in &SHC03 as (1) (2) -lôout-âeq) (3) » C02 C02I v a e _