Introduction
Hydrofluorocarbons (HFCs) have been developed as replacements for
chlorofluorocarbons and hydrochlorofluorocarbons (HCFCs) to protect the
stratospheric ozone layer from depletion. In particular, difluoromethane
(HFC-32, CH2F2) has been used as a refrigerant to replace HCFC-22
(CHClF2): azeotropic mixtures of CH2F2 with HFC-125
(CHF2CF3) and HFC-134a (CH2FCF3) have been used as
refrigerants for air-conditioning and refrigeration for a few decades, and
CH2F2 alone has recently been used as a refrigerant for air-conditioning.
However, HFCs can act as greenhouse gases, and thus there is concern about
emissions of CH2F2 and other HFCs to the atmosphere, where they
can accumulate and contribute to global warming (IPCC, 2013). Observational
data from the Advanced Global Atmospheric Gases Experiment (AGAGE) indicate
that the atmospheric concentration of CH2F2 has been increasing
every year since 2004; in 2012, the global mean mole fraction of
CH2F2 was 6.2 ± 0.2 ppt (parts per trillion), and the rate
of increase was 1.1 ± 0.04 ppt yr-1 (17 % yr-1) (O'Doherty
et al., 2014). By using AGAGE data in combination with a chemical transport
model such as the AGAGE 12-box model (Cunnold et al., 1994; Rigby et al.,
2013) and a value of 5.1 years as the atmospheric lifetime of
CH2F2, O'Doherty et al. (2014) estimated the global emission rate
of CH2F2 in 2012 to be 21 ± 11 Gg yr-1 with an increase
rate of 14 ± 11 % yr-1. Such estimates on the basis of long-term
observational data such as the AGAGE and the National Oceanic and
Atmospheric Administration Global Monitoring Division (NOAA GMD) network are
called top–down estimates and have been shown to provide an independent and
effective method for assessing the accuracy of globally and regionally
aggregated reductions or increases in emissions of individual HFCs, as well
as other greenhouse gases, compiled from national reports to the United
Nations Framework Convention on Climate Change (e.g., Prinn et al., 2000; Lunt
et al., 2015; Montzka et al., 2015).
The atmospheric lifetimes of HFCs are thus related to their estimated
emission rates. The currently accepted value of the atmospheric lifetime of
CH2F2, which was revised in 2014 (Carpenter et al., 2014), is
5.4 years. The partial atmospheric lifetime of CH2F2 with respect to
gas-phase reactions with OH in the troposphere is 5.5 years and that with
respect to stratospheric removal processes is 124 years. Other processes,
such as dissolution in seawater, are not considered to contribute
significantly to the atmospheric removal of CH2F2. Yvon-Lewis and
Butler (2002) estimated partial atmospheric lifetimes of some HCFCs and HFCs
with respect to irreversible dissolution in seawater by using
physicochemical properties such as solubility and aqueous reaction rates, as
well as meteorological data such as temperature and wind speed over the
ocean in grids. Their estimates indicated that dissolution in seawater is
not a significant sink of the HCFCs and HFCs that were evaluated in the
study. Because no aqueous reactions of CH2F2 have yet been
observed under environmental conditions, the dissolution of CH2F2 in seawater is considered to be reversible and cannot serve as a sink of
CH2F2. However, because CH2F2 is more soluble in water
than HCFCs and other HFCs (Sander, 2015), even reversible dissolution of
CH2F2 in seawater might influence a top–down estimate of
CH2F2 emission rates.
The objective of the present study is to experimentally determine the
seawater solubility of CH2F2, which is a physicochemical property
necessary for estimating the residence ratio of CH2F2 in the ocean
when the ocean mixed layer is at solubility equilibrium with the atmosphere.
Specifically, the Henry's law constants, KH (in M atm-1), of
CH2F2 and the salting-out effects of seawater-relevant ions on
CH2F2 solubility were experimentally determined. Values of
KH for CH2F2 have been reported in some review papers (Sander,
2015; Clever et al., 2005). The largest and smallest values at 298 K differ
from each other by a factor of approximately 3: 0.87 M atm-1 (Sander,
2015; Yaws and Yang, 1992) and 0.30 M atm-1 (Clever et al., 2005;
Miguel et al., 2000). To the author's knowledge, no data on the salting-out
effects of seawater-relevant ions on CH2F2 solubility have been reported.
First, the values of KH for CH2F2 were determined over the
temperature range from 276 to 313 K by means of an inert-gas stripping (IGS)
method. The KH values were also determined over the temperature range
from 313 to 353 K by means of a phase ratio variation headspace (PRV-HS)
method. The KH values obtained using the two methods could be fitted by an
equation representing the same temperature dependence. Second, salting-out
effects on CH2F2 solubility were determined over the temperature
range from 276 to 313 K for test solutions of artificial seawater prepared
over the salinity range from 4.5 to 51.5 ‰. The
salting-out effects were confirmed for the artificial seawater, but the
relationship between CH2F2 solubility and salinity of the
artificial seawater was found to be unusual in that the excessive free
energy for dissolution was not proportional to the salinity but rather was
represented by an equation involving the 0.5 power of the salinity. Over the
salinity range relevant to seawater, the solubility of CH2F2 in
the artificial seawater could be represented as a function of both salinity
and temperature. Third, on the basis of the solubility of CH2F2 in
seawater determined in this study and a global gridded dataset of monthly
mean values of temperature, salinity, and depth of the ocean mixed layer,
the amounts of CH2F2 dissolved in the ocean mixed layer were
estimated in each month for each lower-tropospheric semi-hemisphere of the
AGAGE 12-box model.
Experimental setup
Materials
CH2F2 gas (1010 or 1000 ppmv in synthetic air) was purchased
from Takachiho Chemical Industrial Co. (Tokyo, Japan). Sodium chloride
(NaCl, > 99.5 %), sodium sulfate (Na2SO4,
> 99 %), magnesium chloride (MgCl26H2O,
> 98 %), calcium chloride (CaCl22H2O, > 99.9 %), and
potassium chloride (KCl, > 99.5 %) were purchased from Wako
Pure Chemical Industries (Osaka, Japan) and used as supplied. Water was
purified with a Milli-Q Gradient A10 system (resistivity > 18 megohm-cm).
Synthetic artificial seawater was prepared as described by Platford (1965)
and was used to evaluate the salting-out effects on the solubility of
CH2F2 in the ocean. The prepared artificial seawater had the
following definite mole ratios: 0.4240 NaCl, 0.0553 MgCl2, 0.0291 Na2SO4,
0.0105 CaCl2, and 0.0094 KCl. The ionic strength of
the artificial seawater was set to between 0.089 and 1.026 mol kg-1 water,
that is, at molality base, with each salt at the aforementioned mole ratio;
the salinity (in ‰) of this artificial seawater was
between 4.45 and 51.53 ‰. This artificial seawater is referred to hereafter as a-seawater.
Inert-gas stripping method with a helical plate
An IGS method (Mackay et al., 1979) was used to
determine the solubility of CH2F2 in water and aqueous salt
solutions. A CH2F2–air–nitrogen mixture (mixing ratio of
CH2F2 ∼ 10-4) was bubbled into the aqueous
solution for a certain time period (e.g., 5 min), and then nitrogen gas (N2)
was bubbled through the resulting aqueous solution containing
CH2F2, which was stripped from the solution into the gas phase.
The gas-to-liquid partition coefficient (in M atm-1) at temperature T
(in K), Keq(T), was calculated from the rate of the decrease in the gas-phase
partial pressure according to Eqs. (1) and (2):
lnPt/P0=-k1t,k1=1Keq(T)RTFV,
where Pt / P0 is the ratio of the partial pressure of CH2F2
at time t to the partial pressure of CH2F2 at fixed time t0;
k1 is the first-order decreasing rate constant (in s-1); F is the
flow rate of N2 (in dm3 s-1); V is the volume of water or
aqueous salt solution (in dm3); and R is the gas constant
(0.0821 dm3 atm K-1 mol-1). The Keq(T) values in water correspond
to the Henry's law constants, KH(T) in molar per unit of standard atmosphere. The Pt values
typically ranged from 10-4 to 10-6 atm.
A stripping column apparatus with a helical plate was used to strip
CH2F2. This apparatus was described in detail by Kutsuna and Hori (2008)
and is described briefly here. The stripping column consisted of a
jacketed Duran glass column (4 cm i.d. × 40 cm height) and a glass
gas-introduction tube with a glass helix. Water or a-seawater (0.300 or
0.350 dm3) was added to the column for the test solution. The solution
was magnetically stirred, and its temperature was kept constant within
±0.2 K by means of a constant-temperature bath that had both heating
and cooling capabilities (NCB-2500, EYELA, Tokyo, Japan) and was connected
to the water jacket of the column.
Experiments were conducted at nine temperatures in the range of 276 to
313 K. A CH2F2–air mixture or N2 was introduced near the
bottom of the column through a hole (∼ 1 mm in diameter) in the
gas-introduction tube. The bubbles traveled along the underside of the glass
helix from the bottom to the top of the column, at which point they entered
the headspace of the column. The gas flow was controlled by means of
calibrated mass flow controllers (M100 Series, MKS Japan, Inc., Tokyo, Japan)
and was varied between 2.2 × 10-4 and
4.4 × 10-4 dm3 s-1 (STP at 25 ∘C and one
atmospheric pressure).
The volumetric flow rate of the gas (Fmeas) was calibrated with a
soap-bubble meter for each experimental run. The soap-bubble meter had been
calibrated by means of a high-precision film flow meter SF-1U with VP-2U
(Horiba, Kyoto, Japan). Errors in Fmeas are within ±1 %. To
prevent water evaporation from the stripping column, the gas was humidified
prior to entering the stripping column passage through a vessel containing
deionized water. This vessel was immersed in a water bath at the same
temperature as the stripping column. All volumetric gas flows were corrected
to prevailing temperature and pressure by Eq. (3) (Krummen et al., 2000).
Errors due to this correction are within ±1 %. Errors in F are thus
within ±1.4 %.
F=Fmeas×Pmeas-hmeasPhs-h×TTmeas,
where Pmeas and Tmeas are the ambient pressure and temperature,
respectively, at which Fmeas was calibrated; Phs is the headspace
total pressure over the test solution in an IGS method experiment with a
flow rate of F at temperature of T; and hmeas is the saturated vapor
pressure, in units of standard atmosphere, of water at Tmeas; h is the saturated vapor pressure,
in units of standard atmosphere, of water or a-seawater at T. Values of hmeas and h were calculated
by the use of Eq. (4), where S is salinity of a-seawater (Weiss and Price, 1980).
horhmeas=exp24.4543-67.4509×100T-4.8489×lnT100-0.000544×S
The purge gas flow exiting from the stripping column was diluted with
constant flow of N2 to prevent water vapor from condensing. The
CH2F2 in the purge gas flow thus diluted was determined by means
of gas chromatography–mass spectrometry (GC-MS) on an Agilent 6890N gas chromatograph with
5973 inert instrument (Agilent Technologies, Palo Alto, CA). A portion of the
purge gas containing CH2F2 stripped from the test solution was
injected into the GC-MS instrument in split mode (split ratio: 1 : 30) with
a six-port sampling valve (VICI AG, Valco International, Schenkon,
Switzerland) equipped with a stainless sampling loop (1.0 cm3). Gas was
sampled automatically at intervals of 10 to 11 min during an experimental
run (which lasted from 2 to 8 h), depending on the decay rate of the partial
pressure of CH2F2. Peaks due to CH2F2 were measured in
selected-ion mode (m / z = 33, CH2F+). A PoraBOND-Q capillary column
(0.32 mm i.d. × 50 m length, Agilent Technologies) was used to
separate CH2F2. The column temperature was kept at 308 K. Helium
was used as the carrier gas. The injection port was kept at 383 K.
If CH2F2 in the headspace over the test solution is redistributed
into the test solution, k1 should be represented by Eq. (5) instead of
Eq. (2) (Krummen et al., 2000; Brockbank et al., 2013).
k1=FKeq(T)RTV+Vhead,
where Vhead is headspace volume over the test solution. In this study,
the values of Vhead were 0.070 and 0.020 dm3 for V values of
0.300 and 0.350 dm3, respectively. Equations (6) and (7) are derived from
Eqs. (2) and (5), respectively:
Keq(T)=1k1RTFV,Keq(T)=1k1RTFV-VheadRTV.
As described in Sect. 3.1, CH2F2 in the headspace over the test
solution was not expected to be redistributed into the test solution. Hence, Eq. (6) was used to deduce Keq(T) from k1. Errors in T are estimated
to be within ±0.2 K. These errors in T may give potential systematic
bias of ca. ±1 % (δKeq/Keq) where
δKeq is the error in the value of Keq. Errors in F are estimated to be
less than 1.4 %, and these errors may give potential systematic bias of
less than 1.4 % (δKeq/Keq). Accordingly, for the IGS
methods, values of Keq may have potential systematic bias of
ca. ±2 %.
If the redistribution of CH2F2 in the headspace to the test solution
had occurred, the values determined using Eq. (6) would be overestimated.
Errors due to this redistribution are always negative values. The ratio of the
errors to the Keq values (%) is
100k1VheadF. Values of this
ratio increase as values of Keq decrease. Under the experimental
conditions here, this ratio is calculated to be from -2.0 % for water at
3.0 ∘C to -6.5 % for a-seawater at 51.534 ‰ and 39.5 ∘C.
Phase ratio variation headspace method
The KH values of CH2F2 in water were also determined by means
of the PRV-HS method (Ettre et al., 1993)
for comparison with the results obtained using the above-described IGS method.
The PRV-HS method experiments were performed over the temperature range from
313 to 353 K at 10 K intervals because the headspace temperature in the
equipment used here could not be controlled at less than 313 K. The
experimental procedure was the same as that described in detail previously
(Kutsuna, 2013), and it is described briefly here.
The determination was carried out by GC-MS on an Agilent 6890N gas chromatograph with
5973 inert instrument (Agilent Technologies) equipped with an automatic
headspace sampler (HP7694, Agilent Technologies). The headspace samples were
slowly and continuously shaken by a mechanical setup for the headspace
equilibration time (1 h; see below), and then the headspace gas (1 cm3)
was injected into the gas chromatograph in split mode (split ratio: 1 : 30).
The conditions used for GC-MS were the same as those described in Sect. 2.2.
Headspace samples containing five different amounts of CH2F2 and
six different volumes of water were prepared for an experimental run at each
temperature as follows (30 samples total). Volumes (Vi) of 1.5, 3.0,
4.5, 6.0, 7.5, and 9.0 cm3 of deionized water were pipetted into six
headspace vials with a total volume (V0) of 21.4 cm3
(Vi/V0 = 0.070, 0.140, 0.210, 0.280, 0.350, and 0.421,
respectively). Five sets of six headspace vials were prepared and sealed. A
prescribed volume (vj) of a standard gas mixture of CH2F2 and
air was added to each set of five vials containing the same volume (Vi)
of water by means of a gas-tight syringe (vj = 0.05, 0.10,
0.15, 0.20, or 0.25 cm3). The headspace partial pressure of
CH2F2 thus prepared ranged from 10-5 to 10-6 atm.
The time required for equilibration between the headspace and the aqueous
solution was determined by analyzing the headspaces over the test samples as
a function of time until steady-state conditions were attained. In Fig. S1 in the Supplement,
the relative signal intensities of the GC-MS peaks for CH2F2, that
is, the ratio of the headspace partial pressure at time t to that at 60 min
(Pt/P60), are plotted against the time (th) during which samples
were placed in the headspace oven. The plot shows that the peak area did not
change after 60 min (Fig. S1). Therefore, the headspace equilibration time
was set at 1 h for all the measurements.
If Pij is the equilibrium partial pressure (in atm) of a CH2F2
sample in a vial with volume V0 (in cm3) containing a volume Vi
(in cm3) of water and a volume vj (in cm3) of a
CH2F2 gas mixture and if Pj is the equilibrium partial
pressure (in atm) of CH2F2 in a sample containing volume vj
(in cm3) of a CH2F2 gas mixture without water, then Eq. (8) applies:
PjV0RT=Keq(T)PijVi+PijV0-ViRT.
Because the signal peak area of CH2F2 (Sij) at partial
pressure Pij is expected to be proportional to vj for each set of
samples with the same Vi, a plot of Sij vs. vj should be a
straight line that intercepts the origin:
Sij=Liνj.
The slope of the line, Li, corresponds to Sij at vj = 1.0 cm3.
If L is the slope corresponding to Pi at Vi = 0, then
1Li=1L+RTKeq(T)-1LViV0.
Plotting 1/Li against Vi/V0 gives an intercept of 1/L and a slope
of [RTKeq(T) - 1]/L, and Keq(T) can be obtained from these two values.
Therefore, Keq(T) can be determined by recording the peak area Sij,
deriving Li from a plot of Sij vs. vj and then
applying regression analysis to plots of 1/Li vs. Vi/V0 with
respect to Eq. (10).
Furthermore, values of Keq(T) and errors in them were determined
by the nonlinear fitting of the data of Li and Vi/V0 by means of
Eq. (11), which was obtained from Eq. (10):
Li=L1+RTKeq(T)-1ViV0.
Errors in T are estimated to be within ca. 2 K. These errors in T may
give a potential systematic bias of ca. ±4 % (δKeq/Keq) at 313 K and ca. ±3 %
(δKeq/Keq) at 353 K. Errors in V0 are estimated to be less than
1 %, and these errors may give a potential systematic bias of less than
1 % (δKeq/Keq). Accordingly, for the PRV-HS methods, values
of Keq may have a potential systematic bias of ca. ±4 %.
Plots of values of F/(k1RTV) against F at each temperature for
0.350 and 0.300 dm3 of deionized water. Error bars represent
2σ due to errors in values of k1 as described in Sect. S2. Grey
symbols represent the data excluded for calculating the average.
Results and discussion
Determination of Henry's law constants
In the IGS method experiment, an aqueous solution was purged with N2 to
strip CH2F2 from the solution into the N2 purge gas flow, and
the partial pressure of CH2F2 (Pt) in the N2 purge gas
flow decreased with time. Typically, it took 20–100 min, depending on the
purge gas flow rate and the temperature of the solution, for the decrease to
show a first-order time profile. From the first-order time profile of
Pt for the following period of 2–7 h, during which Pt typically
decreased by 2 orders of magnitude, the first-order decreasing rate
constant, k1, was calculated according to Eq. (1). Values of k1 were
obtained at different volumes of deionized water (V), various purge gas flow
rates (F), and various temperatures. Figure S2 shows an example of the time
profile of Pt and how to calculate the k1 value.
Figure 1 plots values of F/(k1RTV), the right side of Eq. (6), against F for
V values of 0.350 and 0.300 dm3 at each temperature T (K). Table 1
lists the average values of F/(k1RTV) for V values of 0.350 and
0.300 dm3 at each temperature. The data with errors being > 10 %
of the data were first excluded. Next, some data were excluded for the calculation of the average so that the remaining data were inside the
2σ range. This procedure was iterated until all the data were inside
the 2σ range. The data points thus excluded were only for V values of
0.350 dm3, and there were eight or fewer of them at each temperature.
The average of values of F/(k1RTV)
obtained for V values of 0.350 and 0.300 dm3 and the
KH(T) value derived from Eq. (13) at each temperature.
N represents the number of experimental runs for the average.
T (K)
F/(k1RTV)
KH(T) (M atm-1)
V = 0.350
V = 0.300
Averagea,b
Nc
Averagea
Nc
From Eq. (13)d,e
276.15
0.119 ± 0.006 (0.008)
21 (2)
0.117 ± 0.006 (0.008)
11 (0)
0.119 ± 0.003 (0.005)
278.35
0.107 ± 0.005 (0.007)
18 (3)
0.110 ± 0.005 (0.007)
14 (0)
0.111 ± 0.002 (0.004)
283.65
0.093 ± 0.003 (0.005)
27 (5)
0.092 ± 0.001 (0.003)
5 (0)
0.094 ± 0.002 (0.004)
288.65
0.082 ± 0.006 (0.008)
41 (5)
0.084 ± 0.006 (0.008)
12 (0)
0.082 ± 0.002 (0.004)
293.45
0.071 ± 0.001 (0.002)
15 (8)
0.071 ± 0.001 (0.002)
5 (0)
0.072 ± 0.002 (0.003)
298.15
0.064 ± 0.002 (0.003)
30 (6)
0.067 ± 0.005 (0.006)
12 (0)
0.065 ± 0.002 (0.003)
303.05
0.057 ± 0.003 (0.004)
16 (0)
0.056 ± 0.005 (0.006)
4 (0)
0.058 ± 0.002 (0.003)
307.95
0.051 ± 0.001 (0.002)
12 (6)
0.054 ± 0.004 (0.005)
10 (0)
0.052 ± 0.002 (0.003)
312.65
0.046 ± 0.001 (0.002)
13 (3)
0.047 ± 0.001 (0.002)
4 (0)
0.048 ± 0.001 (0.002)
a Errors are 2σ for the average only. b Number in parentheses
represents an error reflecting 2σ for the average plus potential
systematic bias (±2 %). c Number in parentheses represents number
of experimental runs excluded for the average. d Errors are 95 %
confidence level for the regression only. e Number in parentheses
represents an error reflecting errors at the 95 % confidence level for the regression plus potential systematic bias (±2 %).
As is apparent in Fig. 1 and Table 1, the F/(k1RTV) values for the two
V values (0.350 and 0.300 dm3) agreed at each temperature. This agreement
strongly suggests that Keq(T) is represented by Eq. (6) rather than by
Eq. (7) because, if Eq. (7) were applicable, the Keq(T) values calculated
for the V value of 0.300 dm3 would be inconsistent with those for the
V value of 0.350 dm3: the former would be smaller than the latter by
0.007–0.008 M atm-1. Redistribution of CH2F2 between the
headspace and the test solution was probably negligible under the
experimental conditions here; hence, values of Keq(T) should be
calculated from Eq. (6) rather than Eq. (7).
The abovementioned agreement also supports the idea that the gas-to-water
partitioning equilibrium of CH2F2 was achieved under the
experimental conditions used for the IGS method. As described later, the
achievement of gas-to-water partitioning equilibrium was also supported by
comparison of these data with Keq(T) values obtained using the PRV-HS
method. Hereafter only values of F/(k1RTV) for the V value of 0.350 dm3
are used to deduce Keq(T) values. Because the Keq(T) values in water
correspond to the Henry's law constants, KH(T) in molar per unit of standard atmosphere,
KH(T) is used instead of Keq(T) in this section.
Van't Hoff plot of the
KH values obtained using the IGS method and the PRV-HS method.
Solid curve displays the fitting of the data obtained using the IGS method
and the PRV-HS method (Eq. 13). Dashed curves display upper and lower 95 %
confidence limit of the above fitting by Eq. (12). Error bars of the data by
the IGS method represent 2σ for
the average plus potential systematic bias (±2 %). Error bars of
the data by the PRV-HS method represent errors at the 95 % confidence level
for the regression plus potential systematic bias (±4 %).
Figure 2 plots the average KH values for the V value of 0.350 dm3
against 100/T. Error bars of the data represent 2σ for the
average plus potential systematic bias (±2 %). Figure 2 also
displays the KH(T) values obtained using the PRV-HS method. The results of
the PRV-HS experiments are described in the Supplement (Figs. S3 and S4 and Table S1).
The KH value obtained using the PRV-HS experiments at each temperature and
its error were estimated at the 95 % confidence level by fitting the two
datasets at each temperature (Fig. S4) simultaneously by means of the
nonlinear least-squares method with respect to Eq. (11). Error bars of the
data by the PRV-HS method in Fig. 2 represent errors at the 95 % confidence
level for the regression plus potential systematic bias (±4 %).
All the KH values were regressed with respect to the van't Hoff equation
(Eq. 12) with no weighting (Clarke and Glew, 1965; Weiss, 1970):
KH(T)=expa1+a2×100T+a3×lnT100.
The regression with respect to Eq. (12) gave Eq. (13).
lnKH(T)=-49.71+77.70×100T+19.14×lnT100
The square root of variance, that is, the standard deviation for each fitting
coefficient in Eq. (12), is as follows:
δa1=5.5;δa2=8.3;δa3=2.8.
In Fig. 2, the solid curve was obtained using Eq. (13). The KH(T) values
calculated using Eq. (13) are listed in Table 1. Equation (13) can reproduce
the average of KH values at each temperature within an error of 5 %.
The dashed lines in Fig. 2 represent 95 % confidence limits of the
regression for fitting the KH(T) values by Eq. (12). Taking into
consideration errors in the KH values, the KH values obtained using the
two methods were within the 95 % confidence limits of the regression by
Eq. (12); this result supports the idea that the values determined by the
IGS method and the PRV-HS method were accurate.
Plots of values of F/(k1RTV) against F at each temperature for
0.350 dm3 of a-seawater at 36.074 ‰. Error bars
represent 2σ due to errors in the values of k1 as described in
Sect. S2. Grey symbols represent the data excluded for calculating the average.
The Gibbs free energy for the dissolution of CH2F2 in water at
temperature T (ΔGsol(T)) and the enthalpy for the dissolution of
CH2F2 in water (ΔHsol) can be deduced from
KH(T) by means of Eqs. (14) and (15):
ΔGsol(T)=μlo(T)-μgo(T)=-RTlnKH(T)ΔHsol(T)=-R∂lnKH(T)∂(1/T),
where μlo(T) is the chemical potential of CH2F2 under the
standard-state conditions at a concentration of 1 M in aqueous solutions at
temperature T; and μgo(T) is the chemical potential of CH2F2
under the standard-state conditions at 1 atm of partial pressure in the gas
phase at temperature T. The KH(T) and ΔHsol(T) values at
298.15 K were calculated by means of Eqs. (13) and (15) and are listed in Table 2.
KH(298.15) is represented by KH298 hereafter.
Table 2 also lists literature values of KH298 and
ΔHsol at 298.15 K for CH2F2 reported in two reviews (Clever et
al., 2005; Sander, 2015) and by Anderson (2011); the units of the literature
data were converted to M atm-1 for KH298 and kilojoule per mole for
ΔHsol. The KH298 value determined in this study was
6–7 % smaller than the values reported by Maaßen (1995),
Reichl (1995), and Anderson (2011), whereas the value reported by Yaws and Yang (1992),
that reported by Hilal et al. (2008), and that reported by Miguel et
al. (2000) were 1.3, 1.3, and 0.46 times, respectively, as large as the value
determined here. The absolute value of ΔHsol at 298.15 K
determined here was 1.4–3.4 kJ mol-1 less than the values
determined by Maaßen (1995), Reichl (1995), Kühne et al. (2005), and Anderson (2011), whereas it was 10 kJ mol-1 less than the value
reported by Miguel et al. (2000).
KH298 and ΔHsol values derived from
Eqs. (13) and (15), along with literature data for
KH298 and ΔHsol.
KH298
ΔHsol
(M atm-1)
(kJ mol-1)
0.065
-17.2
This work
0.070
-20
Maaßen (1995)a
0.070
-19
Reichl (1995)a
0.069c
-20.6
Anderson (2011)
0.085
Hilal et al. (2008)a
-18.6, -19.7
Kühne et al. (2005)a
0.087
Yaws (1999)a
0.087
Yaws and Yang (1992)a
0.030
-27.2
Miguel et al. (2000)b
a Reviewed by Sander (2015). b Reviewed by Clever et
al. (2005). c The value was obtained by extrapolation of the data reported at
284.15–296.15 K (Supplement in Anderson, 2011) with respect to the van't Hoff equation.
The average of values of F/(k1RTV) obtained for V values of 0.350 dm3
and the KeqS(T) value derived from Eq. (23) at each salinity
and temperature. N represents the number of experimental runs for the average.
T (K)
KeqS (M atm-1)
Salinity, 4.452 ‰
Salinity, 8.921 ‰
Averagea,b
Nc
Eq. (23)d,e
Averagea,b
Nc
Eq. (23)d,e
276.15
0.108 ± 0.006 (0.008)
8 (0)
0.107 ± 0.003 (0.005)
0.103 ± 0.006 (0.008)
21 (0)
0.103 ± 0.003 (0.005)
278.35
0.099 ± 0.004 (0.006)
12 (0)
0.100 ± 0.002 (0.005)
0.095 ± 0.006 (0.008)
26 (1)
0.096 ± 0.002 (0.004)
283.65
0.086 ± 0.003 (0.005)
9 (0)
0.085 ± 0.002 (0.004)
0.083 ± 0.007 (0.009)
24 (0)
0.082 ± 0.002 (0.004)
288.65
0.075 ± 0.004 (0.006)
12 (0)
0.074 ± 0.002 (0.003)
0.072 ± 0.005 (0.006)
33 (0)
0.071 ± 0.001 (0.002)
293.45
0.065 ± 0.002 (0.003)
10 (0)
0.066 ± 0.002 (0.003)
0.063 ± 0.003 (0.004)
27 (5)
0.063 ± 0.002 (0.003)
298.15
0.058 ± 0.002 (0.003)
13 (0)
0.059 ± 0.002 (0.003)
0.056 ± 0.004 (0.005)
26 (2)
0.056 ± 0.002 (0.003)
303.05
0.052 ± 0.001 (0.002)
8 (0)
0.053 ± 0.002 (0.003)
0.049 ± 0.004 (0.005)
14 (6)
0.051 ± 0.001 (0.002)
307.95
0.047 ± 0.002 (0.003)
13 (1)
0.048 ± 0.001 (0.002)
0.046 ± 0.004 (0.005)
23 (1)
0.046 ± 0.001 (0.002)
312.65
0.042 ± 0.001 (0.002)
7 (0)
0.044 ± 0.001 (0.002)
0.040 ± 0.003 (0.004)
12 (8)
0.042 ± 0.001 (0.002)
Salinity, 21.520 ‰
Salinity, 36.074 ‰
Averagea,b
Nc
Eq. (23)d,e
Averagea,b
Nc
Eq. (23)d,e
276.15
0.095 ± 0.006 (0.008)
20 (0)
0.095 ± 0.003 (0.005)
0.088 ± 0.005 (0.007)
21 (0)
0.089 ± 0.002 (0.004)
278.35
0.087 ± 0.005 (0.007)
22 (0)
0.088 ± 0.002 (0.004)
0.079 ± 0.006 (0.008)
20 (3)
0.083 ± 0.002 (0.004)
283.65
0.075 ± 0.004 (0.006)
15 (1)
0.076 ± 0.001 (0.003)
0.069 ± 0.002 (0.003)
18 (2)
0.071 ± 0.001 (0.002)
288.65
0.066 ± 0.004 (0.005)
20 (0)
0.066 ± 0.001 (0.002)
0.062 ± 0.004 (0.005)
19 (4)
0.062 ± 0.001 (0.002)
293.45
0.058 ± 0.003 (0.004)
14 (0)
0.058 ± 0.001 (0.002)
0.054 ± 0.002 (0.003)
19 (4)
0.055 ± 0.001 (0.002)
298.15
0.052 ± 0.003 (0.004)
20 (0)
0.052 ± 0.001 (0.002)
0.049 ± 0.002 (0.003)
24 (4)
0.049 ± 0.001 (0.002)
303.05
0.046 ± 0.003 (0.004)
16 (0)
0.047 ± 0.001 (0.002)
0.044 ± 0.002 (0.003)
16 (0)
0.044 ± 0.001 (0.002)
307.95
0.042 ± 0.003 (0.004)
16 (0)
0.043 ± 0.001 (0.002)
0.040 ± 0.002 (0.003)
15 (2)
0.040 ± 0.001 (0.002)
312.65
0.038 ± 0.002 (0.003)
16 (0)
0.039 ± 0.001 (0.002)
0.036 ± 0.002 (0.003)
16 (0)
0.037 ± 0.001 (0.002)
Salinity, 51.534 ‰
Averagea,b
Nc
Eq. (23)d,e
276.15
0.081 ± 0.003 (0.005)
10 (0)
0.084 ± 0.002 (0.004)
278.35
0.077 ± 0.003 (0.005)
15 (0)
0.078 ± 0.002 (0.004)
283.65
0.067 ± 0.001 (0.003)
9 (1)
0.067 ± 0.001 (0.002)
288.65
0.059 ± 0.002 (0.003)
14 (1)
0.059 ± 0.001 (0.002)
293.45
0.052 ± 0.001 (0.002)
7 (3)
0.052 ± 0.001 (0.002)
298.15
0.047 ± 0.002 (0.003)
15 (0)
0.047 ± 0.001 (0.002)
303.05
0.042 ± 0.001 (0.002)
8 (0)
0.042 ± 0.001 (0.002)
307.95
0.038 ± 0.002 (0.003)
12 (0)
0.038 ± 0.001 (0.002)
312.65
0.036 ± 0.001 (0.002)
7 (1)
0.035 ± 0.001 (0.002)
a Errors are 2σ for the average only. b Number in parentheses
represents an error reflecting 2σ for the average plus potential
systematic bias (±2 %). c Number in parentheses represents number
of experimental runs excluded for the average. d Errors are 95 %
confidence level for the regression only. eNumber in parentheses
represents an error reflecting errors at the 95 % confidence level for the regression plus potential systematic bias (±2 %).
Van't Hoff plot of the KeqS values for
a-seawater at each salinity. Dashed curve represents the
KH values by Eq. (13). Solid curves represent the fitting
obtained using Eq. (23). Error bars of the data represent 2σ for the
average plus potential systematic bias (±2 %).
Plots of ln(KH(T)/KeqS(T)) vs. salinity in a-seawater
at each temperature. Solid curves represent the fitting obtained using Eq. (22).
Error bars represent errors reflecting 2σ for the average plus potential systematic bias (±2 %) of KeqS.
Determination of salting-out effects in artificial seawater
The solubility of CH2F2 in a-seawater (Sect. 2.1) was determined
by means of the IGS method (Sect. 2.2). According to Eq. (6), the
Keq(T) values at an a-seawater salinity of S in per mill were
obtained by averaging the F/(k1RTV) values for the V value of 0.350 dm3
at each salinity and temperature in a similar way as described in Sect. 3.1.
Figure 3 plots values of F/(k1RTV) at each temperature against F for V values
of 0.350 dm3 at an a-seawater salinity of 36.074 ‰.
Figures S5–S8 represent such plots at an a-seawater salinity of 4.452,
8.921, 21.520, and 51.534 ‰. The Keq(T) value at an
a-seawater salinity of S in per mill is represented by KeqS(T)
hereafter. Table 3 lists the KeqS(T) values.
Figure 4 plots the KeqS(T) values against 100/T. The plots indicate a
clear salting-out effect on CH2F2 solubility in a-seawater: that
is, the solubility of CH2F2 in a-seawater decreased with
increasing a-seawater salinity. For example, the solubility of
CH2F2 in a-seawater at a salinity of 36.074 ‰ was
0.74–0.78 times the solubility in water at 3.0 to 39.5 ∘C.
In general, the salting-out effect on nonelectrolyte solubility in an
aqueous salt solution of ionic strength I can be determined empirically by
means of the Sechenov equation:
lnKH(T)/KeqI(T)=kII,
where KeqI(T) is the Keq(T) at ionic
strength I in mol kg-1; and kI is the Sechenov
coefficient for the molality- and natural-logarithm-based Sechenov equation
and is independent of I (Clegg and Whitfield, 1991). For a-seawater, a
similar relationship between KeqS(T) and S is
expected:
lnKH(T)/KeqS(T)=kSS,
where kS is the Sechenov coefficient for the salinity- and natural-logarithm-based Sechenov equation and is independent of S. Figure 5 plots
ln(KH(T)/KeqS(T)) against S at each temperature. Table S2 lists
values of kS determined by fitting the data at each temperature by the use
of Eq. (17). If the KeqS(T) values obeyed Eq. (17), the data at each
temperature in Fig. 5 would fall on a straight line passing through the
origin, but they do not. Figure 5 reveals that the salinity dependence of
CH2F2 solubility in a-seawater cannot be represented by Eq. (17).
When the same data were plotted on a log–log graph (Fig. S9), a line with a
slope of about 0.5 was obtained by linear regression. This result suggests
that ln(KH(T)/KeqS(T)) varied according to Eq. (18):
lnKH(T)/KeqS(T)=ks1×S0.5.
Values of ks1 may be represented by the following function of T:
ks1=b1+b2×100T.
Parameterizations of b1 and b2 obtained by fitting all the
ln(KH(T)/KeqS(T)) and S data at each temperature simultaneously by
means of the nonlinear least-squares method gives Eq. (20).
lnKH(T)/KeqS(T)=0.0127+0.0099×100T×S0.5
The standard deviation for each fitting coefficient in Eq. (19) is as
follows: δb1 = 0.0106; δb2 = 0.0031.
Since 2 × δb1 > b1, the parameterization
by Eq. (19) may be overworked. Accordingly, all the
ln(KH(T)/KeqS(T)) and S data at each temperature are fitted
simultaneously using Eq. (21) instead of Eq. (19). The nonlinear
least-squares method gives Eq. (22).
ks1=b2×100TlnKH(T)/KeqS(T)=0.134×100T×S0.5
The standard deviation for the fitting coefficient in Eq. (21) is as
follows: δb2 = 0.001. As seen in Fig. 5, Eqs. (21) and (22)
reproduced the data well.
ln(KH(T)/KeqS(T)) depends on S0.5 and follows Eq. (22) rather
than the Sechenov dependence (Eq. 17). Table S2 compares values of
KeqS calculated using Eq. (22) with those by Eq. (17). The difference
between these values of KeqS at 35 ‰ of salinity
was within 3 % of the KeqS value. Decreases in values of KeqS
are calculated to be 7–8 and 4 %, respectively, by Eqs. (17) and (22)
as salinity of a-seawater increases from 30 to 40 ‰ at each temperature.
The reason for this salting-out effect of CH2F2 solubility in
a-seawater is not clear. Specific properties of CH2F2 – small
molecular volume, which results in little work (free energy) for cavity
creation (Graziano, 2004, 2008), and large solute-solvent attractive
potential energy in water and a-seawater – may cause deviation from the
Sechenov relationship (see the Supplement).
In Eq. (22), KH(T) is represented by Eq. (13), as described in Sect. 3.1.
Therefore, KeqS(T) is represented by Eq. (23):
lnKeqS(T)=-49.71+77.70-0.134×S0.5×100T+19.14×lnT100.
The values calculated with Eq. (23) are indicated by the solid curves in
Fig. 4 and are listed in Table 3. Table 3 lists errors at the 95 %
confidence level for the regression. These errors (error23) are
calculated using Eq. (24):
error23=KeqS×error13KH2+error22KeqS2,
where error13 represents errors at the 95 % confidence level for the
regression by Eq. (12); error22 represents errors at the 95 % confidence
level for the regression by Eq. (21). Table 3 also lists errors due to errors at the 95 % confidence
level for the regression plus potential systematic bias (±2 %). Equation (23) reproduced the experimentally
determined values of KH(T) and KeqS(T) within the uncertainty of
these experimental runs.
Dissolution of CH2F2 in the ocean mixed layer and its influence on estimates of CH2F2 emissions
The solubility of CH2F2 in a-seawater can be represented as a
function of temperature and salinity relevant to the ocean (Eq. 23).
Monthly averaged equilibrium fractionation values of CH2F2 between
the atmosphere and the ocean (Rm in Gg patm-1, where patm is
10-12 atm) in which the ocean mixed layer is at solubility equilibrium
with the atmosphere are estimated as follows. If we divide the global ocean
into 0.25∘ × 0.25∘ grids, Rm can be
estimated from the sum of the equilibrium fractionation values from the gridded cells:
Rm=md,mPa=Q∑i=-360i=360∑j=-720j=720KeqS(T)di,j,mAi,j,m,
where md,m, in gigagrams, is the amount of CH2F2
dissolved in the ocean mixed layer; pa, in 10-12 atm, is
the CH2F2 partial pressure in the air; di,j,m is the monthly
mean depth, in meters, of the ocean mixed layer in each grid cell;
Ai,j,m is the oceanic area, in square meters, in each grid cell; Q is
a conversion factor (with a value of 52); m is the month index; and i and
j are the latitude and longitude indices. We obtained monthly
0.25∘ × 0.25∘ gridded sea surface temperatures and
sea surface salinities from WOA V2 2013 data collected at 10 m depth
from 2005 to 2012 (https://www.nodc.noaa.gov/OC5/woa13/woa13data.html;
Boyer et al., 2013) and monthly 2∘ × 2∘ gridded mean
depths of the ocean mixed layer from mixed layer depth climatology and other
related ocean variables in temperature with a fixed threshold criterion
(0.2 ∘C)
(http://www.ifremer.fr/cerweb/;
de Boyer Montégut et al., 2004). Values of Ai,j,m were estimated to
be equal to the area of each grid cell in which both gridded data were
unmasked.
Plots of monthly averaged equilibrium fractionation of
CH2F2 between atmosphere and ocean, Rm (Gg patm-1) in the
global and the semi-hemispheric atmosphere. Right vertical axis represents
the residence ratio of CH2F2 in the ocean, instead of Rm, for
each lower-tropospheric semi-hemisphere of the AGAGE 12-box model.
Figure 6 shows the Rm values for the global and the semi-hemispheric
atmosphere. Values of Rm for the global atmosphere are between 0.057 and
0.096 Gg patm-1. Because 10-12 atm of CH2F2 in the
global atmosphere corresponds to 9.4 Gg of atmospheric burden of
CH2F2, 0.6 to 1.0 % of the atmospheric burden resides in the
ocean mixed layer when that layer is at solubility equilibrium with the
atmosphere. The magnitude of “buffering” of the atmospheric burden of
CH2F2 by the additional CH2F2 in ocean surface waters
is therefore realistically limited to only about 1 % globally. However,
such buffering would be more effective in each lower-tropospheric semi-hemisphere of the AGAGE 12-box model, which has been used for a
top–down estimate of CH2F2 emissions. The right vertical axis of
Fig. 6 represents the residence ratios of CH2F2 dissolved in the
ocean mixed layer for each lower-tropospheric semi-hemispheric atmosphere of
the AGAGE 12-box model. The residence ratios were calculated on the
assumption that 10-12 atm of CH2F2 corresponds to 1.2 Gg of
atmospheric burden of CH2F2 in each lower-tropospheric semi-hemisphere. As seen in Fig. 6, in the southern semi-hemispheric lower
troposphere (30–90∘ S), at least 5 % of the
atmospheric burden of CH2F2 would reside in the ocean mixed layer
in the winter, and the annual variance of the CH2F2 residence
ratio would be 4 %. These ratios are, in fact, upper limits because
CH2F2 in the ocean mixed layer may be undersaturated. It takes
days to a few weeks after a change in temperature or salinity for oceanic
surface mixed layers to come to equilibrium with the present atmosphere, and
equilibration time increases with the depth of the surface mixed layer (Fine,
2011). In the estimation using the gridded data here, > 90 %
of CH2F2 in the ocean mixed layer would reside in less than 300 m
depth (Tables S4–S7).
Haine and Richards (1995) demonstrated that seasonal variation in ocean
mixed layer depth was the key process which affected undersaturation and
supersaturation of chlorofluorocarbon 11 (CFC-11), CFC-12, and CFC-113 by the use of a one-dimensional slab mixed model. As described above, > 90 %
of CH2F2 in the ocean mixed layer is expected to reside in
less than 300 m depth. According to the model calculation results by Haine
and Richards (1995), saturation of CH2F2 would be > 0.9
for the ocean mixed layer with less than 300 m depth. The saturation of
CH2F2 in the ocean mixed layer is thus estimated to be at least 0.8.
In the southern semi-hemispheric lower troposphere (30–90∘ S), therefore,
at least 4 % of the atmospheric burden of
CH2F2 would reside in the ocean mixed layer in the winter, and the
annual variance of the CH2F2 residence ratio would be 3 %.
In the Southern Hemisphere, CH2F2 emission rates are much lower
than in the Northern Hemisphere. Hence, dissolution of CH2F2 in
the ocean, even if dissolution is reversible, may influence estimates of
CH2F2 emissions derived from long-term observational data on
atmospheric concentrations of CH2F2; in particular, consideration
of dissolution of CH2F2 in the ocean may affect estimates of
CH2F2 emissions in the Southern Hemisphere and their seasonal
variability because of slow rates of inter-hemispheric transport and a small
portion of the CH2F2 emissions in the Southern Hemisphere compared to the
total emissions.