Measurements of the diffusion coefficients of CFC-11 and CFC-12 in pure water and seawater

eScholarship provides open access, scholarly publishing services to the University of California and delivers a dynamic research platform to scholars worldwide. Abstract: Trichlorofluoromethane (CCl 3 F; CFC-11) and dichlorodifluoromethane (CCl 2 F 2 ; CFC-12) have been widely used as tracers of oceanic circulation and mixing on decadal timescales. In order to estimate their transfer rate across the air-sea interface, liquid-phase diffusion coefficients are needed In this study the diffusivities of CFC-11 and CFC-12 in pure water were measured over the temperature range 0.6–30°C. Diffusivities of CFC-11 in pure water ranged from (5.24±0.25)×10 −6 cm 2 S −1 at 0.6°C to (1.13±0.05)×10 −5 cm 2 S −1 at 30.3°C and a fit to the data yielded the equation D CFC-11 = 0.015 exp (−18.1/ RT ), where R is the universal gas constant in kJ mol −1 K −1 and T is the temperature in Kelvin. Diffusivities of CFC-12 in pure water ranged from (5.38±0.22)×10 −6 cm 2 s −1 at 0.6°C to (1.26±0.05)×10 −5 cm 2 s −1 at 30.3°C Abstract. Trichlorofluoromethane (CC13F; CFC-11) and dichlorodifluoromethane (CC12F2; CFC-12) have been widely used as tracers of oceanic circulation and mixing on decadal timescales. In order to estimate their transfer rate across the air-sea interface, liquid-phase diffusion coefficients are needed. In this study the difthsivities of CFC- 11 and CFC-12 in pure water were measured over the temperature range 0.6-30øC. Diffusivities of CFC-11 in pure a fit to the data yielded the equation DcFc-(cid:127)= 0.015 exp (-18.1/RT), where R is the universal water ranged from (5.38+0.22)xl 0' cm s' at 0.6 C to (1.26+0.05)x10' cm s' at 30.3 C and the temperature dependence can be expressed as DcFc.12 = 0.036 exp (-20.1/RT). The estimated uncertainty in both equations is <3%. Experiments were also carried out in seawater for each compound. For CFC-11 the diffusivity in seawater was not significantly different from that in pure water. However, seawater estimated from the data. Molecular diffusivities


Abstract:
Trichlorofluoromethane (CCl 3 F; CFC-11) and dichlorodifluoromethane (CCl 2 F 2 ; CFC-12) have been widely used as tracers of oceanic circulation and mixing on decadal timescales. In order to estimate their transfer rate across the air-sea interface, liquid-phase diffusion coefficients are needed In this study the diffusivities of CFC-11 and CFC-12 in pure water were measured over the temperature range 0.6-30°C. Diffusivities of CFC-11 in pure water ranged from (5.24±0.25)×10 −6 cm 2 S −1 at 0.6°C to (1.13±0.05)×10 −5 cm 2 S −1 at 30.3°C and a fit to the data yielded the equation D CFC-11 = 0.015 exp (−18.1/RT), where R is the universal gas constant in kJ mol −1 K −1 and T is the temperature in Kelvin. Diffusivities of CFC-12 in pure water ranged from (5.38±0.22)×10 −6 cm 2 s −1 at 0.6°C to (1.26±0.05)×10 −5 cm 2 s −1 at 30.3°C and the temperature dependence can be expressed as D CFC-12 = 0.036 exp (−20.1/RT). The estimated uncertainty in both equations is <3%. Experiments were also carried out in seawater for each compound. For CFC-11 the diffusivity in seawater was not significantly different from that in pure water. However, the diffusivity of CFC-12 in seawater was found to be 7.2±3.0% lower than that in pure water. Schmidt numbers for both CFC-11 and CFC-12 in pure water and seawater were estimated from the data.
Abstract. Trichlorofluoromethane (CC13F; CFC-11) and dichlorodifluoromethane (CC12F2; CFC-12) have been widely used as tracers of oceanic circulation and mixing on decadal timescales. In order to estimate their transfer rate across the air-sea interface, liquid-phase diffusion coefficients are needed. In this study the difthsivities of CFC-11 and CFC-12 in pure water were measured over the temperature range 0.6-30øC. Diffusivities of CFC-11 in pure + -6 2 - Experiments were also carried out in seawater for each compound. For CFC-11 the diffusivity in seawater was not significantly different from that in pure water. However, the diffusivity of CFC-12 in seawater was found to be 7.2+3.0% lower than that in pure water. Schmidt numbers for both CFC-11 and CFC-12 in pure water and seawater were estimated from the data.

Introduction
Industrially produced CFC-11 (CC13F) and CFC-12 (CC12F2) have well-known time histories of emissions and inferred atmospheric concentrations. In seawater they are chemically inert and have been shown to be useful tracers in the study of oceanic circulation and mixing on decadal timescales [Gammon et al., 1982;Bullister and Weiss, 1983;Weiss et al., 1985;Fine et al., 1988;Fine, 1993;Molinari et al., 1992;Rhein, 1991Rhein, , 1994. They have also recently been found to be useful as tracers and age-dating tools for groundwater [Busenberg and Plutnmer, 1992;Busenberg et al., 1993]. In most regions of the oceans, CFC-11 and CFC-12 concentrations in surface seawater are close to being in equilibrium with atmospheric concentrations [Bullister, 1984;Weiss et al., 1985;Pickart et al., 1989]. However, this is not always the case. Measurements in newly formed Labrador Sea water [Wallace and Lazier, 1988], the Greenland Sea [Rhein, 1991], the Weddell Sea [Bullister, 1989, the Ross Sea [Trumbore et al., 1991], and the eastern Mediterranean Sea [Schlitzer et al., 1991] have shown that equilibrium saturation is not achieved in high-latitude deep water formation areas and upwelling regions. In these cases, the oceanic uptake of CFC-11 and CFC-12 is controlled by their air-sea exchange rate. Air-sea gas transfer rates are determined by the air-sea concentration gradient and the transfer velocity, which reflects the physical state of the interface and the physical/chemical properties of the gas. experimentally. In this study the diffusivities of CFC-11 and CFC-12 in pure water and seawater were measured over the temperature range of 0.6ø-30øC. The results were compared to predictions from semiempirical formulae.

Experimental Method
The experimental approach is based on the agar gel technique developed by Barrer [1941] and modified by Jahne et al. [1987a] and Saltznmn et al. [1993]. The diffusion cell used in this experiment is a stainless steel housing, consisting of two chambers on either side of an aqueous gel membrane. Details of cell construction and operation were given by Saltznmn et al. [1993]. In this experiment, CFC-11 or CFC-12 is passed continuously over one side of an aqueous gel membrane while where D is the diffusivity, L is the gel thickness, and C• is the aqueous gel concentration on the high-concentration side of the membrane. In terms of measurable parameters, the diffusivity can be expressed as [Saltzman et al., 1993] D= C2sf2 L C•søtA where C•g and C2g are the gas-phase concentrations on the highconcentration side and low-concentration side of the gel, respectively, f2 is the gas flow through the low-concentration chamber, A is the gel cross-sectional area, and a is the dimensionless Ostwald solubility coefficient. Gels were prepared by dissolving 0.7% agar in water or seawater, yielding measured densities of 0.992 g cm '3 (1(•=0.1%) and 1.019 g cm '3 (1(•--0.1%), respectively. The thickness of the gel membrane was calculated from the mass of the gel and the diameter of the cell (3.8 cm). Gel loss due to evaporation during an experiment was less than 1% by mass. The gel thickness at the end of the experiment was used in the calculation of the diffusion coefficient. Pure water experiments were carried out using Milli-Q water. Seawater experiments were carried out using Gulf Stream surface water, after filtration with 0.2 gan pore size membrane filters. The measured salinity of the seawater was 35.0%o (1(•=0.5%). Measured diffusion coefficients were increased by a factor of 1.9% for pure water and 2.0% for seawater to correct for the decreased solubility of CFC-11 and CFC-12 in the agar gel and hindrance of the threedimensional agar structure [Langdon and Thomas, 1971].
The solubilities of CFC-11 and CFC-12 in water mad seawater were obtained from Warner and Weiss [1985], with a quoted estimated accuracy and relative precision of 1.5% and 0.7% (lc•), respectively. In this experiment there was an additional uncertainty of 0.65% in the solubilities used for seawater due to the variation of salinity during the preparation of seawater gels. The concentration of the diffusing gas was determined in the outflow of the low-concentration side of the cell by gas chromatography with photoionization (CFC-11) or thermal conductivity (CFC-12) detection. A 1/8" stainless steel Porasil B (100/150 mesh) column was used isothermally at 85øC with a carrier gas (helium) flow rate of 20 mL min 4.
During an experiment the pressure in the diffusion cell is approximately 1 arm. The vapor pressure of CFC-11 is less than 1 arm at temperatures below about 24øC. To prevent CFC-11 condensing out in the cell on the high concentration side of the gel during an experiment, a 10% mixture of CFC-11 in ultrapure helium was used in all CFC-11 experiments. Since the vapor pressure of CFC-12 is significantly higher than 1 arm at all experimental temperatures, pure CFC-12 was used in all CFC-12 experiments.
Before each experiment, helium gas was introduced across both sides of the gel to remove the air dissolved in the gel during preparation. During the experiment the flow across the high-concentration side of the gel was kept at approximately 2 mL min 4 for CFC-11 and 5 mL min '• for CFC-12. On the low.concentration side of the gel, the helium was mass flow controlled at a constant flow rate between 10 and 20 mL min 4. Tests showed that the measured diffusivity was independent of flow rate in this range. The helium was bubbled through a water reservoir prior to the cell to saturate the helium stream with water vapor before entering the cell.
This minimized evaporation of the gel during an experiment.
A stirred, thermostated water bath controlled the experimental temperature, between 0.6øC and 30øC. A mercury thermometer monitored the cell temperature in the bath with an estimated uncertainty of :t:0.1øC. When the experimental temperature was higher than room temperature, a counterflow Nation membrane dryer (Permapure product) was used to dry the outflow of the low-concentration chamber. Measured concentrations were corrected for H20 vapor loss in the dryer (3% at 25øC; 4% at 30øC). Experiments were carried out with and without the dryer at room temperature to determine if CFC-11 or CFC-12 was lost in the dryer. No loss was observed.
A calibration was run immediately at'ter each experiment by serially diluting the effluent of the high-concentration side of the gel with pure helium in glass gas-tight syringes. A tank of reference gas mixture (CFC-11 and He) was used to monitor day-to-day variation in detector response and to correct for changes in laboratory temperature and pressure. Gas volumes and partial pressure-fugacity corrections were made to account for the nonideality of the pure CFC-12 used in these experiments. 'Two corrections were made to the data. First, the volume of pure gas used in the first stage of serial dilutions to generate calibration mixtures had to be corrected to account for CFC-12 molecule-molecule interactions. This correction increased the diffusivity by 1.9%. Second, a partial pressurefugacity correction had to be made to the gas phase on the highconcentration side of the gel in order to use the solubility data of Warner and Weiss [1985]. Their measurements were made using a dilute gas phase. This correction also increased the diffusivity, ranging from 1.7% at 30.3 øC to 2.4% at 0.6 øC. Both these corrections are based on the virial equation of state expanded up to the second virial coefficient [Guggenheim, 1967] and follow the approach of Weiss and Price [1980]. Virial coefficients were obtained from Dymond and Smith [1980]. For CFC-11, deviations from ideality were negligible because the experiments were carried out in dilute mixtures of helium and were therefore essentially ideal.
The total uncertainty for a measured DCFC-ll in pure water was estimated to be 3.7%-5.3% (lg), with the largest contribution from the determination of the concentration ratio (C2dC•g), which ranged up to 3.7%. The total uncertainty for a single measured Dcl•½-12 was estimated to be 3.5% -4.6% (lg).

Diffusivity of CFC-11 and CFC-12 in Pure Water
The experimentally determined diffusion coefficients of CFC-11 and CFC-12 in pure water at 0.6 ø, 5 ø, 10 ø, 15 ø, 20 ø, 25 ø and 30øC are shown in Figure 1. Three replicates were carried out at each temperature. A least squares exponential fit to the data yields the equations:

DH. i•= cm 2 s '1 (6)
Here q is a dimensionless association factor equal to 2.6 for water, Ms is the molecular weight of water, T is the temperature in Kelvin, r/s is the viscosity of water in centipoise and Va is the molar volume of the gas at its boiling point. The W-C expression is 2-14% and 6.2-11.6% higher than our measurements for CFC-11 and CFC-12, respectively. For CFC-11, the Hayduk-Laudie (H-L) estimate is 19.5% lower than our measurements at 0.6øC and 13.5% higher than our measurements at 30øC. For CFC-12, the H-L expression generates diffusion coefficients that are 14.8% lower than our measurements at 0.6øC and 10.8% higher than our measurements at 30øC. The updated W-C expression gives the best overall agreement with our data for both gases. For CFC-11 the expression is 6.6% lower than our measurement at 0.6øC and 6.3% higher at 30øC. For CFC-12 the updated W-C expression is 1% lower than our measurement at 0.6øC and 4% higher at 30øC.
As mentioned in the introduction, air-sea gas transfer rates are commonly parameterized in terms of Schmidt numbers, where the Schmidt number is the kinematic viscosity of seawater divided by the diffusivity of the species. Using diffusivities generated from (3) and (4) and kinematic viscosities calculated from the pure water viscosities and densities of Millero [1974] and Weast et al. [1984], Schmidt numbers were calculated for CFC-11 and CFC-12 in pure water (Table 1). The uncertainty in each Schmidt number is dominated by the uncertainty in the diffusivity and is therefore estimated to be -3%. A least squares polynomial fit to the calculated Schmidt numbers give the following expressions'

Diffusivity of CFC-11 and CFC-12 in Seawater
The diffusivity of gases in liquids is strongly dependent on the viscosity of the liquid [W/Ike and Chang, 1955; Hayduk and Laudie, 1974]. Over the temperature range from 5 ¸ to 30øC, the viscosity of seawater is 3-5% greater than that of pure water [Millero, 1974]. As shown in (5) and (6), seawater gas diffusivities are therefore expected to be smaller than the corresponding pure water diffusivities. There have been limited experimental studies of this effect. The expected reduction of diffusivity in seawater relative to pure water has been observed for He and H2 by Jahne et al. [1987a], for CO2 by Ratcliff and Holdcroft [1963], and for CH4 by Saltznmn et al. [1993]. Essentially no difference was observed between seawater and pure water diffusivities for SF6  and for CH3Br [De Bruyn and Saltzman, 1997]. These results are discussed in more detail by . Several runs were carried out using seawater gels to examine this effect for CFC-11 and CFC-12 (Table 2). Three runs at 9.4øC for CFC-11 gave a mean diffusion coefficient of (6.80-3:0.12)x10 '6 cm 2 s'l(l•J). The corresponding pure water value is (6.86+0.39)x10 '6 cm 2 s4(l•J), which is not significantly different at the 95% confidence level. The same experiment was repeated at a later time, using the thermal conductivity detector (TCD) in place of the photoionization detector, with similar results. Four seawater runs at 12.6øC gave a mean diffusivity of  (7.47_+0.18)x10 '6 cm 2 s'l(l(l). Four pure water runs gave a mean value of (7.62_+0.21)x10 '6 cm 2 s'l(l(l). Once again, these values are not significanfiy different at the 95% confidence level. For CFC-12, the expected viscosity effect was observed. Four seawater runs at 9.1øC gave a mean diffusivity of (6.26550.12)x10 '6 cm 2 s4(lo). Three pure water runs at the same temperature gave a mean value of (6.75550.17)x10 '6 cm 2 s'l(l(I). This is 7.2_-*3.0% higher than the seawater value. The difference in behavior between CFC-11 and CFC-12 with respect to their diffusivity in seawater is not understood.
Assuming that the measured difference in diffusivity can be extrapolated to all temperatures, we have corrected our measured pure water diffusivities to generate seawater diffusivities as a function of temperature and have used the corrected diffusivities to calculate seawater Schmidt numbers for both CFC-11 and CFC-12 as a function of temperature (Table  1). No correction was made to the CFC-11 diffusivities, but the CFC-12 diffusion coefficients in pure water were decreased by 7.2% to generate seawater diffusivities. Seawater viscosities and seawater densities were obtained from Millero [1974 Schmidt numbers are within 2% of Schmidt numbers determined in this work above 25øC. Below 25øC they are higher, ranging from 4.3% higher at 20øC to 15% higher at 0øC.
As mentioned, Schmidt numbers determined in this work are calculated assuming the measured difference between seawater and pure water diffusivity at a single temperature can be extrapolated to all temperatures. In light of our inability to explain the lack of a difference between seawater and pure water diffusivity for compounds like CFC-11, it is difficult to assess the validity of this assumption. It would certainly be useful to measure seawater diffusivities across the whole temperature range. However, in earlier work with this apparatus  it was clear that measurement precision in seawater gels decreased at both ends of our measurable temperature range. The reason for this decrease in sensitivity is unknown. In future work we hope to examine and improve measurement precision in seawater gels to allow for the measurement of seawater diffusivities across a much wider temperature range.