Measurement of the diffusion coefficient of sulfur hexafluoride in water

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Introduction
Sulfur hexafiuoride (SF6) has been used extensively as a deliberate tracer in field and laboratory studies of air-sea exchange processes [Wanninkhof et al., 1987;Upstill-Goddard et al., 1990;Watson et al., 1991;Asher et al., 1992;Wanninkhof et al., 1993].SF 6 is an ideal tracer owing to its lack of chemical and biological reactivity, low natural levels, and low detection limit using gas chromatography with electron capture detection.The results of SF 6 studies have been used as the basis for deriving and testing a general relationship between wind speed and the gas exchange coefficient k, where

Flux= k (C -C• / c•)
(1) and C is the concentration in the liquid (I) or gas phase (g) and a is the dimensionless solubility of the gas in seawater [Liss and Slater , 1974].In these tracer studies, SF 6 is released into surface ocean or lake waters, and the evasion of the gas is monitored by the decrease in surface mixed layer concentration.For dual-tracer studies the concentration of 3He is also monitored, and the rate of decrease in 3He/SF6 is determined.There are significant differences between various expressions proposed for the magnitude and wind speed dependence of gas exchange [Smethie et al., 1985;Liss and Merlivat, 1986;Wanninkhof 1992], and this subject is currently the focus of some controversy.
The gas exchange coefficient has been found to be a function

Experimental Method
The experimental method for this measurement was based on the method developed by Barter [1941].The experimental method consists of monitoring the diffusion of a gas through an aqueous gel membrane (F-l).At steady state the flux of the gas through a planar membrane is given by the following expression:  [1987a] showed that experimental determinations of diffusi city using a gel were more reproducible than results obtained using a wetted-frit diaphragm.This is probably due to the lesser degree of convection and turbulence in the gel as compared with the diaphragm.However, the presence of the gel requires a correction.The gel decreases the solubility of the gas in the membrane and inhibits the diffusion path by the creation of a structure in the membrane.Langdon and Thomas [1971] have estimated that both of these effects combine to reduce the rate of diffusion by a factor of about 2% for a 0.7% gel.After the' diffusion coefficient has been calculated the value is increased by a factor of 1.90% for pure water and 2.03% for a NaC1 gel to correct for the presence of the gel.
The Ostwald coefficient of SF 6 in pure water was calculated

At all temperatures the difference between DSF 6 in 3596o
NaC1 and in pure water is not significant at the 95% confidence level, according to the t test [Havlicek and Crain, 1988].This is surprising because diffusivity should be lower in NaC1 than in pure water, owing to the increase in viscosity with increased ionic strength.This effect has been observed in previous studies of diffusivity.Ratcliff and Holdcroft [1963]  The calculated diffusivities of SF 6 in 3596o NaC1 at all temperatures imply that there is no difference in DSF 6 between pure water and NaC1 solutions.The lack of a difference emphasizes the lack of understanding of the process ef diffusion.There is no existing theory which can accurately predict the effect of parmeters such as temperature and ionic strength on the diffusion of a gas through a liquid membrane.

Schmidt Number of SF 6 in Seawater
The results of this study suggest that the diffusivity of SF 6 in seawater should be similar to that in pure water.The Schmidt numbers (kinematic viscosity divided by diffusivity, v/D)calculated for SF 6 in seawater using our pure water values over the temperature range 5-30øC are given in T-2.These Schmidt numbers were calculated using kinematic viscosities (v, the ratio of molecular viscosity to density) calculated from the viscosity of seawater from Millero [1974]

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relationships fit diffusivity data for nonelectrolytes in dilute solutions as a function of the molar volume of the diffusing gas and the viscosity of the solvent.Estimates for the diffusivity have been used because DSF 6 has not previously been measured.In this study we measured the diffusivity of SF 6 (DsF6) in pure water and compare the results to the estimations from the empirical formulas.We also measured DSF 6 in 35960 NaC1 and discuss the implications for estimating ScSF 6 in seawater.
Figure 1.a) Schematic cross section of the diffusion cell.The high-and low-concentration chambers are labeled as 1 and 2, respectively, as in equation (4).b) Schematic of the experimental apparatus.The gas flows from the cell are labeled as in equation (4).

Figure 2 .
Figure 2. Diffusion coefficients of SF 6 in pure water as measured in this study and from estimates made from empirical expressions from Wilke and Chang [1955] and Hayduk and Laudie [1974].Also plotted are the estimates from the Wilke-Chang relationship using an updated association factor for water prol:osed by Hayduk and Laudie [1974].The curve is a fit to the experimental data taking the form D=0.029 exp (-19.3/RT),where R is the gas constant and T is temperature (in kelvins).
measured the diffusivity of carbon dioxide (Dco2) in pure water and in various salt solutions at 25øC.They observed that diffusivity decreased with increasing salinity for all salts tested, including NaC1.Interpolating from their data, Dco 2 in a 3596o NaC1 solution was estimated to be about 6% lower than the pure water diffusivity.Jahne et al. [1987a] measured the diffusivities of H 2 and He in pure water and 35.596oNaCI from 5 to 35øC.They found diffusivities in the salt solutions to be lower by 5-8%, with the difference greatest at the lower temperatures.Jahne et al. [1987a] recommended an average correction of 6% when converting pure water diffusivities to seawater.Saltzman et al. [1993] compared the diffusivity of methane in 3596o NaC1 and in pure water at 15øC and found the values for NaC1 to be 4% lower than the pure water diffusivities.
and the density of seawater fromMillero and Poisson [1981 ].The uncertainty in each Schmidt number is dominated by the uncertainty in the diffusivity and ranges from 4.1 to 4.5% (l o) over the temperature range given in Table2.A least squares third-order polynomial fit to the Schmidt number data yields the following equation: is larger than the uncertainty in ore' values and ranges from 4.7% at 30øC to 12.4% at 5øC.SummaryThe diffusivity of SF 6 in pure water and 3596o NaC1 was measured in this study.The pure water results agree well with