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Evaporation of solutes from water
Environment International Vol. 3, pp. 231-236. Pergamon Press Ltd. 1980. Printed in Great Britain
Evaporation of Solutes from Water*
Cary T. Chiou, Virgil H. Freed, Louis J. Peters and Rodger L. Kohnert Environmental Health Sciences Center, Department of Agricultural Chemistry, Oregon State University, Corvallis, OR 97331, U.S.A.
A model is developed to define the evaporation rates of solutes from water. The rate equation, similar in form to the Knudsen equation, takes into consideration the effect of air and subwater turbulences on the evaporation loss. At given system conditions, the factor accounting for the air turbulence appears to be essentially constant and independent of temperature (3.5-25 °C) for various organic chemicals and water. These characteristics allow one to study the rate of evaporation from water and the relative enhancement by subwater mixing for different solutes. This report shows that the volatilization loss of pure substances and solutes with low Henry's law constants is enhanced by air turbulence, not by subwater mixing. However, the loss of volatile solutes (high Henry's law constants) may be promoted both by air turbulence and by subwater mixing, in which the extent of enhancement by liquid mixing is determined primarily by the Henry's law constant. The present model provides a theoretical basis to explain these effects and others, which appear to be important for assessment of pollutant evaporative transport in the environment.
turbulence of the system, which may be expressed by a modified Knudsen equation:
Introduction and theory A proper understanding of the evaporative transport of components in water is necessary for better assessments of the environmental consequences of pollutants in aquatic systems. Although a significant amount of data on the evaporation rates of organics from water has been obtained, attempts to fit the data with existing models appear to be only qualitatively successful (Dilling, 1977). Of a particular interest to the study of evaporation mechanisms is a theoretical explanation of the effect of system turbulence and solute concentration on the evaporative behavior of different solutes. We have devised a model to account for the evaporation rate of a component from water as a function of solution properties and system conditions. The model employs the partial pressure difference between the interface (/~.) and the bulk air (PT) as the (thermodynamic) driving force for evaporation and assumes that on the two sides of the air-water interface the concentration C~ and the partial pressure/~, are in constant equilibrium, as imposed by others (Lewis and Whitman, 1924; Liss and Slater, 1974; Mackay and Leinonen, 1975), i.e., H~ = P;/CT, where H; is the Henry's law constant. The rate of loss is determined by the product of the partial pressure difference and the vapor diffusion efficiency (Hartley, 1969) under a given
Q , = d m , / A d t = B~,P~(M,/21cRT) 1/2
where B, (dimensionless) is the evaporation coefficient dependent on the atmospheric pressure and air turbulence, P, is the partial pressure corresponding to the bulk concentration C, at temperature T, or, (<_ 1), equal to C f f C , , determines the depletion of component i near the surface relative to that in the bulk-liquid phase during evaporation, and a,P, = P~. The relationship of ~, to subwater mixings and solution properties will be discussed later. In equation (1), P t h a s dropped for all organic compounds evaporating into ambient air since the existing vapor densities are negligible. For water, however, P, needs to be corrected for the humidity (P 7). For solutes in dilute aqueous solutions, Q, may be expressed as: Q, = ~ , B , H ~ ( M , / 2 x R T ) 1,2 C, = k,C,
(2)
where H,C, is used to replace P, (i.e., H , = I b / C ; = P , / C , ) , and k, is the transfer coefficient from water. Assuming that t~, is constant over a small concentration range, equation (2) leads to a first-order half-life for evaporation: 0.693 L tv=(,) = t~,~,H,(M,/21tRT)I/z -
*Received 12 September 1979; received in revised form 24 October 1979
(1)
0.693 L
(3)
k,
where L is the depth of the solution in a container of 231
C.T. Chiouetal.
232 uniform cross section. The present model treats the effects o f liquid mixing and air turbulence on the evaporative loss of component i separately by the corresponding ix, and/~, terms. In principle, Q, has a maximum for a given Ci when ix, = 1 and/~t = 1 (as a vacuum). In ambient air,/~ thus has a value less than 1 and depends on the extent of air turbulence which affects the movement o f the vapors from the interface to the bulkair phase. The magnitude of a, and its dependence on system conditions can be rationalized as follows. For pure substances, cts = 1 under all conditions since no gradient exists. In solution, if the relative loss of solute i in a given period is lower than or comparable to that of water (whose ot always approximates 1 since no significant gradient can arise for the major component), a, should be -=- 1 under all conditions (i.e., mixed and unmixed solutions). If the relative loss of the solute is substantially greater than that of water, the value o f ot~ will be small ( < 1) in an unmixed or poorly mixed solution since in this case the rapid depletion of solute near the surface cannot be effectively restored by diffusion or mixing. Consequently, more efficient subwater mixing will increase ~ by reducing the gradient for a highly volatile solute (high H,) and ultimately increase its evaporation. By contrast, one would expect to find little enhancement in evaporation by subwater mixing itself for poorly volatile solutes (low H,) since or,. -- 1 in both mixed and unmixed solutions. For a volatile component under poor mixing (in which ot~ < 1), t~, may decrease as C, is greatly reduced since at a lower concentration (where solute molecules are farther apart) transport of solute molecules to the surface through solute-water mutual diffusion will be more difficult. Experiments were conducted to test these hypotheses.
Experimental Rates of evaporation of pure chemicals were measured gravimetrically (by a Mettler H54 balance). A stopwatch was used to record the time for weight loss. Stainless-steel planchcts (4.6 cm 2) with a wall height of 6 mm were used as the sample containers. Sufficient chemicals were added to the planchet resulting in a liquid level of about 4 mm height, thus minimizing the wall height effect (Hartley, 1969). During sample evaporation, the balance doors were kept open to avoid vapor saturation. The balance was located at the corner of the room (24 4I°C and R.H. ---- 30) where air flow was minimal. To correct for a small cooling effect (_<2°C during the experimental time span) noted for the evaporation of highly volatile compounds (e.g., chloroform and benzene), rates of loss were extrapolated to time zero. Low temperature evaporation studies were carried out for chloroform, benzene, 1,2-dichloropropane, tetrachloroethene, and water at 3-4°C with R.H. = 8590°7o. The actual temperature and relative humidity fluctuated rapidly between the above specified ranges. Because of turbulent air circulation in the room, the experiments were conducted with the balance doors closed. Measurements were taken within short time intervals such that the vaporized materials inside the balance chamber would not reach appreciable concen-
trations to affect the evaporation rates significantly. Evaporation rates were then computed based on the weight loss over a short time period following the outset of the experiments. To test the reliability of data obtained by this method, similar runs (with the balance doors closed) were conducted for these four organic compounds at 'x,24°C (R.H. = 30). The resulting rates showed only a small reduction (_< 3°70) compared to the values obtained with open balance doors. For the evaporation of the volatile solutes (Table 2) from water, samples were contained by glass dishes with a wall height of 1.7 cm and a diameter of 5.2 cm. The mechanical stirring was carried out by a Teflon magnetic stirring bar (5.0 cm length and 0.7 cm diameter) at a controlled speed of 100 4- 10 rpm. The runs for 2chlorophenol and 4-chlorophenol from water were conducted in small planchets previously described. The solutions were maintained at a depth L = 0.38 cm by adding water to replenish the amounts lost every 25-30 min, and a magnetic bar (1 cm length and 0.3 cm diameter) at a speed of about 100 rpm was used for stirring. The runs for PCBs, lindane, DDT and parathion from water were carried out in glass dishes with a wall height of 4.8 cm and a diameter of 6.5 cm. The stirring was carried out by a magnetic bar (5.0 cm length; 0.7 cm diameter) at a speed of 130 4- 15 rpm. Solution levels were kept constant by adding water for prolonged experiments. Under these specified stirrings, liquid surfaces were fairly placid, showing no visible vortex. Aqueous samples were taken with a microsyringe at different time intervals and analyzed directly, or through extraction, by a Varian 3700 gas chromatograph equipped with Ni s3 EC detector. A glass column packed with a porous polymer Chromosorb 101 was used for separation of volalite organics. When dilution of aqueous samples with water was needed, it was carried out inside a septum-capped volumetric flask to prevent evaporative loss. The septum of the flask cap was lined with a layer of Teflon to avoid its contact with the sample solution. A small hole was drilled in the center of the cap so that aqueous samples could be taken by a syringe. The air/water partition coefficients of the halogenated hydrocarbons were determined by analyzing the respective vapor and water concentrations at equilibrium in a septum-capped test tube which had the same capping device as described. Both liquid and vapor samples were withdrawn by syringe through the septum (a gas-tight syringe equipped with a Teflon tipped plunger was used for sampling vapors). The vapor pressure data of the selected organic chemicals and water were obtained from the Handbook o f Chemistry and Physics (49th Edition) unless otherwise specified. Extrapolation or interpolation was made based on the Clausius-Clapeyron equation to obtain the vapor pressures at desired temperatures. All test chemicals were of reagent grade and used without further purification. The purities of the chemicals ranged from 96 to 99 + o70.
Results and discussion Equation (1) may be simplified for pure substances since or, = 1 and P; = p,.o (saturation), and/3, can be
233
Evaporation of solutes from water
determined from the measured Q , Figure l shows the rates of evaporation for a number of organic chemicals and water in still air and with minimal container wall height. The determined values of /5 appear to have nearly constant value (Table 1) for these chemicals (~ = 1.98 × l0 s ± 907o S.D.) despite a wide variation in molecular weight and vapor pressure at different temperatures. The observed constancy of ~/, facilitates assessment of the evaporative loss for other compounds by use of j3 for/~, in the reported temperature range. The rates of evaporation for some highly volatile organics from water solution (L = 1.6 cm; ~,24°C) are given in Table 2. The data consist of measured half-lives for the solutes at two drastically different initial concentrations (C°); the high C,.° corresponds to 75-95070 solubility limits and the low C,.° is in the 0.1-2 ppm range. The solutions were moderately stirred (with a magnetic bar) at approximately the same controlled speeds. For a correction of the air turbulence resulting from stirring, j~ = 2.50 × 10-s (13070 S.D.) was found based on the/Ts of pure chemicals (including water) studied under similar stirrings. Substitution of B for ~, allowed or, to be determined by comparing the experiment half-life with the or,t1/2value from equation (3). For the high-concentration data set, or, -_- 1 is observed for compounds which have relatively low H,, as for 1,2-dibromoethane and 1,1,2,2-tetrachloroethane, under the applied stirring; for compounds which have high H , a, is < 1 and decreases as Hi increases from, for instance, 0.68 as for 1,2-dichloroethane to 0.14 as for carbon tetrachloride. A representative first-order
0.020
o o,5 .." ~ ~ o.o~o ~'
0.005
o.ooo 0
2
4
6
8
Table 1. Evaporation rates of organic chemicals and water into still air. t(°C)
P(mm)
Qexp x l 0 s
F
/~xlOs
Chloroform
23.4 3.5 23.5 23.8 23.7 24.0 23.7 23.9 25.0 3.5 24.5 23.6 3.5 23.4 23.2 3.5 25.0 24.0 23.5 23.7 3.5 23.4 23.2
185 71.0 208 104 120 118 78.0 71.8 94.0 33.1 88.2 48.4 17.4 34.5¶ 16.7 5.40 28. l 13.5 7.68 22.0 5.89 4.70§ 1.25
13.2 (5.23)* 9.86 9.23 9.04 5.23 5.20 5.07 5.72 (1.89) 3.69 3.15 (1.10) 1,80 1.36 (0.477) 1.88 1.24 0.501 0.504 (0.0214) 0.448 0.118
6.84 (2.72) 4.77 4.41 4.68 2.22 2.63 2.78 2.80 (1.02) 1.90 1.74 (0.646) 1.09 0.727 (0.243) 0.907 0.625 0.269 0.221 t" ('x,0.0110)~ 0.206 0.0510
1.93 (1.92) 2.07 2.09 1.93 2.36 1.98 1.83 2.04 (1.85) 1.94 1.8 l (1.70) 1.65 1.87 (1.96) 2.07 1.98 1.86 2.28 ('x,1.95) 2.17 2.31
1,1, l-Tlichloroethane Methanol 1,2-Dichloroethane Trichloroethene Benzene Acetonitrile
1,2-Dichloropropane p-Dioxane Tetrachloroethene Toluene
1,2-Dibromoethane m-Xylene Water 1,1,2,2-Tetrachloroethane 1,2-Dichlorobenzene
12
14
Fig. 1. Evaporation of the selected organic chemicals and water into still air at 23-25°C.
Compound
Acetone Carbon tetrachloride
I0
Time ( m i n )
Q . , = experimental rate (g/cm ~- s); F = I)(M/2TRT) 1'' (g/cm2-s);/~ = Q , , / F *Numbers in parentheses refer to 3.5 ± 0.5°C. 1"Corrected for 30% relative humidity. ~:Corrected for 87.5% relative humidity. §Value obtained from Nelson (1930). ¶Value obtained from Crenshaw et al. (1938).
234
C.T. Chiou et aL Table 2. Evaporation half-lives of volatile organics from water (L = 1.6 cm) under stirring.
Compound
/'/* atl/z(cal)t (dyne-cm/g) (min)
Carbon tetrachloride
5.9 x 107
0.40
l,l,l-Trichloroethan¢
4.8 x 107
0.52
Tetrachloroethene
2.1 x 107
1.I
1,2-Dichloropropane
1.5 x 107
1.9
1,2-Dichlorobenzene
1.1 x 107
2.3
1,2-Dichloroethane
8.3 x 106
3.6
1,2-Dibromoethane
3.0 × I0 e
7.1
l,l,2,2-Tetrachloroethane
2.0 x l0 e
II
tt,= (exp):~
C°§ (ppm)
t(°C)
2.8
742
24.6
(8.0)
(%1)
%24
2.0 (7.2) 3.2 (7.0) 4.4 (8.0) 4.8 (8.1) 5.3 (8.0) 6.4 (6.8) 9.2 (8.6)
1350 (~). 1) 180 (%0.1) 2900 (%1) 137 (%2) 4510 (%2) 2750 (,xA).1) 2270 (%0.1)
23.9 %24 24.5 %24 24.0 %24 24.0 %24 23.1 %24 23.7 %24 24.8 %24
(min)
*Henry's law constant at %24°C with 5-17°70 uncertainty. 1"Calculated with B = 2.50 x 10-s. :~Value obtained from a plot of log C vs time. § Initial solute concentration.
plot o f log Cl vs time is shown in Fig. 2. With initial solute concentrations reduced to the 0.1-2 ppm range, at~ is practically unchanged for 1,2-dibromoethane and 1,1,2,2-tetrachloroethane, but decreases to 0.45 for 1,2dichloroethane and to 0.049 for carbon tetrachloride as Hi increases. When compared to the high-concentration data set, the relative reduction in at, is practically proportional to H,. Similar experiments were conducted for these solutes in the absence o f stirring to determine the effect o f subwater mixing on their rates of loss. The observed halflives for carbon tetrachloridc (C ° = ,x, 1 ppm), 1,1,1trichloroethane (,x,0.1 ppm), tetrachloroethene (,x~).l ppm), and 1,1,2,2-tetrachloroethane ('~,0.1 ppm) were found to be 81, 78, 69 and 78 min, respectively. Using = 1.98 x 10-5, at is calculated to be 0.0062, 0.0084, 0.020, and 0.18 for these four compounds in static water. Clearly, these values are considerably lower than those under similar conditions except with stirring. Likewise, the relative reduction in at (or k) is proportional to H. I00
i
I
I
I
2
3
I
I
I
I
I
4
5
6
7
8
Time
(rain)
~ 90 8o
~ 70 c
g,
~ 60 5o
0
Fig. 2. A first-order plot for the evaporative loss from water (L = 1.6 cm; %24°C) of 1,2-dichioroethane (X), 1,2-dichloropropane ( e ) , tetrachloroethene ((I)), 1,2-dichlorobenzene (111) 1,1,1-trichloroethane ((]p), l,l,2,2-tetrachloroethane ([~), carbon tetrachloride ([:]), and 1,2-dibromoethane (A). The initial solute concentrations are in the range of 75-95°/0 solubility limits. Stirring conditions were described in the text.
Turning to poorly volatile solutes, one should expect at to be = 1 irrespective of mixing and solute concentration. This may be illustrated by the evaporation from water (L = 0.38 cm; ~,24°C) of 2-chlorophenol and 4chlorophenol which have notably low H values. Since the relative loss was greater for water than for the solute, the solution depth has been kept constant by adding water to replenish water loss. Half-lives were determined under static conditions (/3 = 1.98 x 10-5) for both compounds at C ° = 2 ppm and under stirring (fl _= 2.50 x 10-5) for 2-chlorophenol at 2 ppm and 4000 ppm and 4-chlorophenol at 2 ppm. In all cases, the results summarized in Table 3 show good agreement between the measured half-lives and those calculated by using at = 1. A t 2 5 ° C , D D T h a s H = 1.07 - 1.42 x l0 s (dynecm/g), as estimated from the ratio o f its vapor pressure P° = 3.2 x 10-7 mm Hg (Balson, 1947) to aqueous solubility S = 3-4 ppb (Biggar et al., 1967). According to the estimated H , DDT is expected to escape rapidly from a shallow water. As shown in Fig. 3, DDT has a half-life o f 8.8 h in unstirred and 5.2 h in stirred (fl = 2.97 x 10-s ± 4% S.D.) solutions o f C ° = ,x,3 ppb and L = 4.5 cm at 25°C. The value of/~ in stirred case was obtained based on the loss rate of pure water (with correction o f relative humidity) under a similar stirring. According to the magnitude of H for DDT and the previously noted enhancement o f at by stirring, c~ = 1 may be assumed for DDT in the present stirred water. The predicted half-life using/3 = 2.97 x 10-5 and ct = 1 is 4.3-5.6 h, which is very close to the observed value o f 5.2 h. The experimental half-li/'e o f 8.8 h in the unstirred solution gives o~ = 0.89 for DDT in static water (/~ = 1.98 x 10-s). The rapid loss of DDT from water was attributed by other investigators to codistillation with water (Acree et al., 1963). Our present model, by contrast, accounts quantitatively for the loss o f DDT in terms o f its H a n d at. Based on the results of above studies, a plot of at vs H for the selected organics in stirred (/~ = 2.50 × 10-s) and unstirred dilute aqueous solutions (_< 2 ppm for high-H
Evaporation of solutes from water
235
Table 3. Evaporation half-lives of chlorophenols from water (L = 0.38 cm). tv2 (h) H* Compound t(°C) (ppm) (dyne-craig)Experimental Estimated§ 2-Chlorophenol~" 23.8 2 7.54 x 104 1.60 1.70 2-Chlorophenol :~ 23.8 2 7.54 x 104 1.35 1.36 2-Chlorophenol :~ 23.0 4000 7.54 × 104 1.45 1.36 4-Chlorophenol~" 23.6 2 7.07 × 10s 17.4 18.2 4-Chlorophenol :~ 23.6 2 7.07 × l0s 12.8 14.5 *Henry's law constants at 25°C calculated from the data of Tsonopoulosand Prausnitz (1971). t In static water. :~In stirred water. §Assuming c~, = 1 and using B = 1.98 × 10-s for static solutions and ~ = 2.50 x 10-s for stirred solutions.
I00
,
,
i
,
0.8
\',\\\\\
~
~ (1.6
.02 c 00
I
o, ° ' , o ~"t0.2 I Ill
o
5 xlO4
o I--
105
I
I
I
I
I
I I II
I
I
I
i
I
n i I ~
t0 6 tO7 Henry's Low Constont H ( d y n e - c m / g ) , Log Scole
:
,
--
~
i i
tO8
Fig. 4. The relationship between c~and H for solutes in dilute aqueous solutions. 40
0
I
I
!
I
2
4
6
8
I0
Time (hours)
Fig. 3. The evaporative loss of DDT from water (L = 4.5 cm) with stirring ( @) and without stirring (©). solutes) may be constructed as shown in Fig. 4. Since ct = 1 sets the theoretical limit for enhancement by subwater mixing, an estimate o f this limit (i.e., l / a in static water) may be obtained for different solutes by reference to the c~-H relationship in static water. Thus, compounds with large H would, in principle, be able to give a greater enhancement by appropriate subwater mixings than those with low H in the region where c~ < 1. In the present study with moderate stirring, the relative enhancement, o~(stirred)/o~(static), is seen to be greater for solutes in the high-H region than those in the l o w - H region although o~ (stirred) has not reached 1 for most volatile solutes. With H lower than ,x,1 × l0 s, subwater mixing itself (i.e., discounting the resulting air turbulance) produces essentially no enhancement for solute evaporation since a = 1 under all conditions. As such, a l o w - H solute evaporates as though it were a pure substance (o~ = 1) but had vapor pressure reduced to its partial pressure, and consequently, t:/2 is merely a function of H, (MI2~rRT) l/z and air turbulence (fl) at a given solution depth as previously shown for the two phenols. As the (M/21rRT) l/z term makes relatively small contribution, the half-lives for l o w - H solutes under similar system conditions are primarily determined by their H values. This also becomes true for high-H solutes in "well mixed" aqueous solutions when c~ approaches 1.
Since ot is mainly a function of H and mixing, One may estimate the values o f o~ (thus t:/2) for other solutes from their values of H according to the c~-H relationship under given system conditions. The experimental and calculated half-lives of evaporation from water (L -4.5 cm; 24°C) for three PCBs, lindane, and parathion are summarized in Table 4. The observed tl/2 values in static water ranging from about 4 h for 2 , 2 ' - P C B to 14 days for parathion are in close agreement with the corresponding calculated values. The data indicate that the improved evaporation in stirred solutions for lindane and parathion (for which ot = 1 in static water) occurs mainly as a result of the air turbulence caused by mixing (i.e., from/~ factor), not by mixing itself; more enhancement is observed for others (for which ct < 1 in static water) due to an additional promotion in o~ by subwater mixing. In the latter, the relative enhancement is greater, for instance, for 2 , 2 ' - P C B than for 4 , 4 ' - P C B because of the difference in their ct values in static water. The fact that 2 , 2 ' - P C B and 4 , 4 ' - P C B have about the same half-lives in static water is a result of the inverse relationship between ~ and H that makes their product terms otH close to each other. As stirring minimizes their difference in c~, the observed half-lives in stirred solutions become more distinctively a function o f their H values. Our estimated H for 2 , 2 ' - P C B could be too high; using H = 8 x l0 s, the predicted values (3.6 and 1 h in static and stirred solutions, respectively) are in better agreement with the observed data. For 2,5,2',5 ' - P C B whose H is not known, an assumed H = --9 x l0 s gives a reasonable fit to the observed halflives. In conclusion, the observed rates o f evaporation under various system conditions and for various solutes
236
C.T. Chiou et al. Table 4. Evaporation half-lives of some solutes from water (L = 4.5 cm) at "~,24°C.
Compound
/-/*(dyne-cm/g)
~
tvs (est):~
tl/s(exp)§
2,2'-PCB
1.7 x 106
4,4'-PCB
4.5 x 10s
0.22 1 0.57
3.1 h (0.46 h) 4.5 h
3.9h (0.90 h) 4.0h
]
(1.7 h)
2,5,2',5
'-PCB
--
--
--
Lindane
1.1 x l0 t
Parathion
3.3 x lot
1 1 1 1
---
3.4days (2.3 days) 13 days (8.7 days)
(1.5
h)
2.8 h
(0.68 h)
3.2days (1.5 days) 14 days (9.3 days)
*Estimated from vapor pressure (po) and aqueous solubility (S) values at 25°C as H -- P°/S. The po values for 2,2'-PCB and 4,4'-PCB are from Smith et al. (1974), lindane from Spencer and Cliath (1970), and parthion from Bright et al. (1950). The S value for parathion is from Williams (1951), and the remainder from Weil et al. (1974). "~Obtained from c~-Hrelationships. ~tv= = 0.693L/(ct~Hx/M/2TRT); B = 1.98 x 10-s in static water; B = 2.97 x 10-s in stirred water. Numbers in parentheses refer to stirred solutions. §The C ° values for the solutes (from top to bottom) are approximately 0.1, 0.03, 0.005, 5 and 2 ppm, respectively.
are consistent with the proposed model. For volatile solutes, subwater mixing enhances the rate of loss by reducing the liquid-layer gradient as measured by or; the effect of the solute concentration on the relative evaporative loss may be similarly explained in terms of oe. For poorly volatile solutes, ot is shown to be = 1, independent of mixings and solute concentrations. The functional relationship between tx and H facilitates assessment of the rates of evaporation of solutes in water and gives a basis of explaining the differences in the effect of subwater mixing on different solutes. Acknowledgement ~ We thank Dr. M. Manes and Dr. I.J. Tinsley for helpful comments. This work was published with the approval of the Oregon State Agricultural Experiment Station as Technical Paper No. 4634. Research was supported by NSF/RANN AEN-76-17700 and NIH ES-00210 and ES-00040 grants.
References Acree, F., Jr., Beroza, M. and Bowman, M.C. (1963) Codistillation of DDT with water. J. agric. Food Chem. 11, 278. Baison, E.W. (1947) Studies in vapor pressure measurement, Part III. An effusion manometer sensitive to 5 x 10-6 mm Hg: Vapor pressure of DDT and other slightly volatile substances, Trans. Faraday Soc. 43, 54. Biggar, J.W., Dutt, G.R. and Riggs, R.L. 0967) Predicting and measuring the solubility of p,p '-DDT in water. Bull. Environ. Contam. ToxicoL 2, 90. Bright, N.F.H., Cuthill, J.C. and Woodbury, N.H. (1950) The vapor
pressure of parathion and related compounds. J. Sci. Fd Agric. 1, 344. Crenshaw, J.L., Cope, A.C., Finkelstein, N. and Rogan, R. (1938) The dioxanates of the mercuric halides. J. Am. Chem. Soc. 60, 2308. Dilling, W.L. (1977) Interphase transfer processes. II. Evaporation rates of chloromethane, ethanes, ethylenes, propanes, and propylene from dilute aqueous solutions. Comparisons with theoretical predictions. Environ. Sci. Technol. 11,405. Hartley, G.S. (1969) Evaporation of pesticides. Adv. Chem. Ser. 86, 115. Lewis, W.K. and Whitman, W.G. (1924) Principles of gas absorption. Ind. Eng. Chem. 16, 1215. Liss, P.S. and Slater, P.G. (1974) Flux of gases across the air-sea interface. Nature 247, 181. Mackay, D. and Leinonen, P.J. (1975) Rate of evaporation of lowsolubility contaminants from water bodies to atmosphere. Environ. ScL Technol. 9, 1178. Nelson, O.A. (1930) Vapor pressures of fumigants. IV. 1,1,2,2-tetra, penta and hexachloroethanes. Ind. Eng. Chem. 22, 971. Smith, N.K., Gorin, G., Good, W.D. and McCullough, J.P. (1964) The heats of combustion, sublimation, and formation of four dihalobiphenyls. J. phys. Chem. 68, 940. Spencer, W.F. and Cliath, M.M. (1970) Vapor density and apparent vapor pressure of lindane. J. agric. Food Chem. 18, 529. Tsonopoulos, G. and Prausnitz, J.M. (1971) Activity coefficients of aromatic solutes in dilute aqueous solutions. Ind. Eng. Chem. Fundam. 10, 593. Weil, L., Dur~, G. and Quentin, K. (1974) WasserlOslichkeit yon insektiziden chlorierten Kohlenwasserstoffen und polychlorierten Biphenylen im Hinblick auf eine Gew~sserbelastung mit diesen Stoffen. Z. Wass. Abwass. Forsch. 7, 169. Williams, E.F. (1951) Properties of 0,0-diethyl 0-p-Nitrophenyl thiophosphate and 0,0-diethyl 0-p-nitrophenyl phosphate. Ind. Eng. Chem. 43, 950.
Evaporation of Solutes from Water*
Cary T. Chiou, Virgil H. Freed, Louis J. Peters and Rodger L. Kohnert Environmental Health Sciences Center, Department of Agricultural Chemistry, Oregon State University, Corvallis, OR 97331, U.S.A.
A model is developed to define the evaporation rates of solutes from water. The rate equation, similar in form to the Knudsen equation, takes into consideration the effect of air and subwater turbulences on the evaporation loss. At given system conditions, the factor accounting for the air turbulence appears to be essentially constant and independent of temperature (3.5-25 °C) for various organic chemicals and water. These characteristics allow one to study the rate of evaporation from water and the relative enhancement by subwater mixing for different solutes. This report shows that the volatilization loss of pure substances and solutes with low Henry's law constants is enhanced by air turbulence, not by subwater mixing. However, the loss of volatile solutes (high Henry's law constants) may be promoted both by air turbulence and by subwater mixing, in which the extent of enhancement by liquid mixing is determined primarily by the Henry's law constant. The present model provides a theoretical basis to explain these effects and others, which appear to be important for assessment of pollutant evaporative transport in the environment.
turbulence of the system, which may be expressed by a modified Knudsen equation:
Introduction and theory A proper understanding of the evaporative transport of components in water is necessary for better assessments of the environmental consequences of pollutants in aquatic systems. Although a significant amount of data on the evaporation rates of organics from water has been obtained, attempts to fit the data with existing models appear to be only qualitatively successful (Dilling, 1977). Of a particular interest to the study of evaporation mechanisms is a theoretical explanation of the effect of system turbulence and solute concentration on the evaporative behavior of different solutes. We have devised a model to account for the evaporation rate of a component from water as a function of solution properties and system conditions. The model employs the partial pressure difference between the interface (/~.) and the bulk air (PT) as the (thermodynamic) driving force for evaporation and assumes that on the two sides of the air-water interface the concentration C~ and the partial pressure/~, are in constant equilibrium, as imposed by others (Lewis and Whitman, 1924; Liss and Slater, 1974; Mackay and Leinonen, 1975), i.e., H~ = P;/CT, where H; is the Henry's law constant. The rate of loss is determined by the product of the partial pressure difference and the vapor diffusion efficiency (Hartley, 1969) under a given
Q , = d m , / A d t = B~,P~(M,/21cRT) 1/2
where B, (dimensionless) is the evaporation coefficient dependent on the atmospheric pressure and air turbulence, P, is the partial pressure corresponding to the bulk concentration C, at temperature T, or, (<_ 1), equal to C f f C , , determines the depletion of component i near the surface relative to that in the bulk-liquid phase during evaporation, and a,P, = P~. The relationship of ~, to subwater mixings and solution properties will be discussed later. In equation (1), P t h a s dropped for all organic compounds evaporating into ambient air since the existing vapor densities are negligible. For water, however, P, needs to be corrected for the humidity (P 7). For solutes in dilute aqueous solutions, Q, may be expressed as: Q, = ~ , B , H ~ ( M , / 2 x R T ) 1,2 C, = k,C,
(2)
where H,C, is used to replace P, (i.e., H , = I b / C ; = P , / C , ) , and k, is the transfer coefficient from water. Assuming that t~, is constant over a small concentration range, equation (2) leads to a first-order half-life for evaporation: 0.693 L tv=(,) = t~,~,H,(M,/21tRT)I/z -
*Received 12 September 1979; received in revised form 24 October 1979
(1)
0.693 L
(3)
k,
where L is the depth of the solution in a container of 231
C.T. Chiouetal.
232 uniform cross section. The present model treats the effects o f liquid mixing and air turbulence on the evaporative loss of component i separately by the corresponding ix, and/~, terms. In principle, Q, has a maximum for a given Ci when ix, = 1 and/~t = 1 (as a vacuum). In ambient air,/~ thus has a value less than 1 and depends on the extent of air turbulence which affects the movement o f the vapors from the interface to the bulkair phase. The magnitude of a, and its dependence on system conditions can be rationalized as follows. For pure substances, cts = 1 under all conditions since no gradient exists. In solution, if the relative loss of solute i in a given period is lower than or comparable to that of water (whose ot always approximates 1 since no significant gradient can arise for the major component), a, should be -=- 1 under all conditions (i.e., mixed and unmixed solutions). If the relative loss of the solute is substantially greater than that of water, the value o f ot~ will be small ( < 1) in an unmixed or poorly mixed solution since in this case the rapid depletion of solute near the surface cannot be effectively restored by diffusion or mixing. Consequently, more efficient subwater mixing will increase ~ by reducing the gradient for a highly volatile solute (high H,) and ultimately increase its evaporation. By contrast, one would expect to find little enhancement in evaporation by subwater mixing itself for poorly volatile solutes (low H,) since or,. -- 1 in both mixed and unmixed solutions. For a volatile component under poor mixing (in which ot~ < 1), t~, may decrease as C, is greatly reduced since at a lower concentration (where solute molecules are farther apart) transport of solute molecules to the surface through solute-water mutual diffusion will be more difficult. Experiments were conducted to test these hypotheses.
Experimental Rates of evaporation of pure chemicals were measured gravimetrically (by a Mettler H54 balance). A stopwatch was used to record the time for weight loss. Stainless-steel planchcts (4.6 cm 2) with a wall height of 6 mm were used as the sample containers. Sufficient chemicals were added to the planchet resulting in a liquid level of about 4 mm height, thus minimizing the wall height effect (Hartley, 1969). During sample evaporation, the balance doors were kept open to avoid vapor saturation. The balance was located at the corner of the room (24 4I°C and R.H. ---- 30) where air flow was minimal. To correct for a small cooling effect (_<2°C during the experimental time span) noted for the evaporation of highly volatile compounds (e.g., chloroform and benzene), rates of loss were extrapolated to time zero. Low temperature evaporation studies were carried out for chloroform, benzene, 1,2-dichloropropane, tetrachloroethene, and water at 3-4°C with R.H. = 8590°7o. The actual temperature and relative humidity fluctuated rapidly between the above specified ranges. Because of turbulent air circulation in the room, the experiments were conducted with the balance doors closed. Measurements were taken within short time intervals such that the vaporized materials inside the balance chamber would not reach appreciable concen-
trations to affect the evaporation rates significantly. Evaporation rates were then computed based on the weight loss over a short time period following the outset of the experiments. To test the reliability of data obtained by this method, similar runs (with the balance doors closed) were conducted for these four organic compounds at 'x,24°C (R.H. = 30). The resulting rates showed only a small reduction (_< 3°70) compared to the values obtained with open balance doors. For the evaporation of the volatile solutes (Table 2) from water, samples were contained by glass dishes with a wall height of 1.7 cm and a diameter of 5.2 cm. The mechanical stirring was carried out by a Teflon magnetic stirring bar (5.0 cm length and 0.7 cm diameter) at a controlled speed of 100 4- 10 rpm. The runs for 2chlorophenol and 4-chlorophenol from water were conducted in small planchets previously described. The solutions were maintained at a depth L = 0.38 cm by adding water to replenish the amounts lost every 25-30 min, and a magnetic bar (1 cm length and 0.3 cm diameter) at a speed of about 100 rpm was used for stirring. The runs for PCBs, lindane, DDT and parathion from water were carried out in glass dishes with a wall height of 4.8 cm and a diameter of 6.5 cm. The stirring was carried out by a magnetic bar (5.0 cm length; 0.7 cm diameter) at a speed of 130 4- 15 rpm. Solution levels were kept constant by adding water for prolonged experiments. Under these specified stirrings, liquid surfaces were fairly placid, showing no visible vortex. Aqueous samples were taken with a microsyringe at different time intervals and analyzed directly, or through extraction, by a Varian 3700 gas chromatograph equipped with Ni s3 EC detector. A glass column packed with a porous polymer Chromosorb 101 was used for separation of volalite organics. When dilution of aqueous samples with water was needed, it was carried out inside a septum-capped volumetric flask to prevent evaporative loss. The septum of the flask cap was lined with a layer of Teflon to avoid its contact with the sample solution. A small hole was drilled in the center of the cap so that aqueous samples could be taken by a syringe. The air/water partition coefficients of the halogenated hydrocarbons were determined by analyzing the respective vapor and water concentrations at equilibrium in a septum-capped test tube which had the same capping device as described. Both liquid and vapor samples were withdrawn by syringe through the septum (a gas-tight syringe equipped with a Teflon tipped plunger was used for sampling vapors). The vapor pressure data of the selected organic chemicals and water were obtained from the Handbook o f Chemistry and Physics (49th Edition) unless otherwise specified. Extrapolation or interpolation was made based on the Clausius-Clapeyron equation to obtain the vapor pressures at desired temperatures. All test chemicals were of reagent grade and used without further purification. The purities of the chemicals ranged from 96 to 99 + o70.
Results and discussion Equation (1) may be simplified for pure substances since or, = 1 and P; = p,.o (saturation), and/3, can be
233
Evaporation of solutes from water
determined from the measured Q , Figure l shows the rates of evaporation for a number of organic chemicals and water in still air and with minimal container wall height. The determined values of /5 appear to have nearly constant value (Table 1) for these chemicals (~ = 1.98 × l0 s ± 907o S.D.) despite a wide variation in molecular weight and vapor pressure at different temperatures. The observed constancy of ~/, facilitates assessment of the evaporative loss for other compounds by use of j3 for/~, in the reported temperature range. The rates of evaporation for some highly volatile organics from water solution (L = 1.6 cm; ~,24°C) are given in Table 2. The data consist of measured half-lives for the solutes at two drastically different initial concentrations (C°); the high C,.° corresponds to 75-95070 solubility limits and the low C,.° is in the 0.1-2 ppm range. The solutions were moderately stirred (with a magnetic bar) at approximately the same controlled speeds. For a correction of the air turbulence resulting from stirring, j~ = 2.50 × 10-s (13070 S.D.) was found based on the/Ts of pure chemicals (including water) studied under similar stirrings. Substitution of B for ~, allowed or, to be determined by comparing the experiment half-life with the or,t1/2value from equation (3). For the high-concentration data set, or, -_- 1 is observed for compounds which have relatively low H,, as for 1,2-dibromoethane and 1,1,2,2-tetrachloroethane, under the applied stirring; for compounds which have high H , a, is < 1 and decreases as Hi increases from, for instance, 0.68 as for 1,2-dichloroethane to 0.14 as for carbon tetrachloride. A representative first-order
0.020
o o,5 .." ~ ~ o.o~o ~'
0.005
o.ooo 0
2
4
6
8
Table 1. Evaporation rates of organic chemicals and water into still air. t(°C)
P(mm)
Qexp x l 0 s
F
/~xlOs
Chloroform
23.4 3.5 23.5 23.8 23.7 24.0 23.7 23.9 25.0 3.5 24.5 23.6 3.5 23.4 23.2 3.5 25.0 24.0 23.5 23.7 3.5 23.4 23.2
185 71.0 208 104 120 118 78.0 71.8 94.0 33.1 88.2 48.4 17.4 34.5¶ 16.7 5.40 28. l 13.5 7.68 22.0 5.89 4.70§ 1.25
13.2 (5.23)* 9.86 9.23 9.04 5.23 5.20 5.07 5.72 (1.89) 3.69 3.15 (1.10) 1,80 1.36 (0.477) 1.88 1.24 0.501 0.504 (0.0214) 0.448 0.118
6.84 (2.72) 4.77 4.41 4.68 2.22 2.63 2.78 2.80 (1.02) 1.90 1.74 (0.646) 1.09 0.727 (0.243) 0.907 0.625 0.269 0.221 t" ('x,0.0110)~ 0.206 0.0510
1.93 (1.92) 2.07 2.09 1.93 2.36 1.98 1.83 2.04 (1.85) 1.94 1.8 l (1.70) 1.65 1.87 (1.96) 2.07 1.98 1.86 2.28 ('x,1.95) 2.17 2.31
1,1, l-Tlichloroethane Methanol 1,2-Dichloroethane Trichloroethene Benzene Acetonitrile
1,2-Dichloropropane p-Dioxane Tetrachloroethene Toluene
1,2-Dibromoethane m-Xylene Water 1,1,2,2-Tetrachloroethane 1,2-Dichlorobenzene
12
14
Fig. 1. Evaporation of the selected organic chemicals and water into still air at 23-25°C.
Compound
Acetone Carbon tetrachloride
I0
Time ( m i n )
Q . , = experimental rate (g/cm ~- s); F = I)(M/2TRT) 1'' (g/cm2-s);/~ = Q , , / F *Numbers in parentheses refer to 3.5 ± 0.5°C. 1"Corrected for 30% relative humidity. ~:Corrected for 87.5% relative humidity. §Value obtained from Nelson (1930). ¶Value obtained from Crenshaw et al. (1938).
234
C.T. Chiou et aL Table 2. Evaporation half-lives of volatile organics from water (L = 1.6 cm) under stirring.
Compound
/'/* atl/z(cal)t (dyne-cm/g) (min)
Carbon tetrachloride
5.9 x 107
0.40
l,l,l-Trichloroethan¢
4.8 x 107
0.52
Tetrachloroethene
2.1 x 107
1.I
1,2-Dichloropropane
1.5 x 107
1.9
1,2-Dichlorobenzene
1.1 x 107
2.3
1,2-Dichloroethane
8.3 x 106
3.6
1,2-Dibromoethane
3.0 × I0 e
7.1
l,l,2,2-Tetrachloroethane
2.0 x l0 e
II
tt,= (exp):~
C°§ (ppm)
t(°C)
2.8
742
24.6
(8.0)
(%1)
%24
2.0 (7.2) 3.2 (7.0) 4.4 (8.0) 4.8 (8.1) 5.3 (8.0) 6.4 (6.8) 9.2 (8.6)
1350 (~). 1) 180 (%0.1) 2900 (%1) 137 (%2) 4510 (%2) 2750 (,xA).1) 2270 (%0.1)
23.9 %24 24.5 %24 24.0 %24 24.0 %24 23.1 %24 23.7 %24 24.8 %24
(min)
*Henry's law constant at %24°C with 5-17°70 uncertainty. 1"Calculated with B = 2.50 x 10-s. :~Value obtained from a plot of log C vs time. § Initial solute concentration.
plot o f log Cl vs time is shown in Fig. 2. With initial solute concentrations reduced to the 0.1-2 ppm range, at~ is practically unchanged for 1,2-dibromoethane and 1,1,2,2-tetrachloroethane, but decreases to 0.45 for 1,2dichloroethane and to 0.049 for carbon tetrachloride as Hi increases. When compared to the high-concentration data set, the relative reduction in at, is practically proportional to H,. Similar experiments were conducted for these solutes in the absence o f stirring to determine the effect o f subwater mixing on their rates of loss. The observed halflives for carbon tetrachloridc (C ° = ,x, 1 ppm), 1,1,1trichloroethane (,x,0.1 ppm), tetrachloroethene (,x~).l ppm), and 1,1,2,2-tetrachloroethane ('~,0.1 ppm) were found to be 81, 78, 69 and 78 min, respectively. Using = 1.98 x 10-5, at is calculated to be 0.0062, 0.0084, 0.020, and 0.18 for these four compounds in static water. Clearly, these values are considerably lower than those under similar conditions except with stirring. Likewise, the relative reduction in at (or k) is proportional to H. I00
i
I
I
I
2
3
I
I
I
I
I
4
5
6
7
8
Time
(rain)
~ 90 8o
~ 70 c
g,
~ 60 5o
0
Fig. 2. A first-order plot for the evaporative loss from water (L = 1.6 cm; %24°C) of 1,2-dichioroethane (X), 1,2-dichloropropane ( e ) , tetrachloroethene ((I)), 1,2-dichlorobenzene (111) 1,1,1-trichloroethane ((]p), l,l,2,2-tetrachloroethane ([~), carbon tetrachloride ([:]), and 1,2-dibromoethane (A). The initial solute concentrations are in the range of 75-95°/0 solubility limits. Stirring conditions were described in the text.
Turning to poorly volatile solutes, one should expect at to be = 1 irrespective of mixing and solute concentration. This may be illustrated by the evaporation from water (L = 0.38 cm; ~,24°C) of 2-chlorophenol and 4chlorophenol which have notably low H values. Since the relative loss was greater for water than for the solute, the solution depth has been kept constant by adding water to replenish water loss. Half-lives were determined under static conditions (/3 = 1.98 x 10-5) for both compounds at C ° = 2 ppm and under stirring (fl _= 2.50 x 10-5) for 2-chlorophenol at 2 ppm and 4000 ppm and 4-chlorophenol at 2 ppm. In all cases, the results summarized in Table 3 show good agreement between the measured half-lives and those calculated by using at = 1. A t 2 5 ° C , D D T h a s H = 1.07 - 1.42 x l0 s (dynecm/g), as estimated from the ratio o f its vapor pressure P° = 3.2 x 10-7 mm Hg (Balson, 1947) to aqueous solubility S = 3-4 ppb (Biggar et al., 1967). According to the estimated H , DDT is expected to escape rapidly from a shallow water. As shown in Fig. 3, DDT has a half-life o f 8.8 h in unstirred and 5.2 h in stirred (fl = 2.97 x 10-s ± 4% S.D.) solutions o f C ° = ,x,3 ppb and L = 4.5 cm at 25°C. The value of/~ in stirred case was obtained based on the loss rate of pure water (with correction o f relative humidity) under a similar stirring. According to the magnitude of H for DDT and the previously noted enhancement o f at by stirring, c~ = 1 may be assumed for DDT in the present stirred water. The predicted half-life using/3 = 2.97 x 10-5 and ct = 1 is 4.3-5.6 h, which is very close to the observed value o f 5.2 h. The experimental half-li/'e o f 8.8 h in the unstirred solution gives o~ = 0.89 for DDT in static water (/~ = 1.98 x 10-s). The rapid loss of DDT from water was attributed by other investigators to codistillation with water (Acree et al., 1963). Our present model, by contrast, accounts quantitatively for the loss o f DDT in terms o f its H a n d at. Based on the results of above studies, a plot of at vs H for the selected organics in stirred (/~ = 2.50 × 10-s) and unstirred dilute aqueous solutions (_< 2 ppm for high-H
Evaporation of solutes from water
235
Table 3. Evaporation half-lives of chlorophenols from water (L = 0.38 cm). tv2 (h) H* Compound t(°C) (ppm) (dyne-craig)Experimental Estimated§ 2-Chlorophenol~" 23.8 2 7.54 x 104 1.60 1.70 2-Chlorophenol :~ 23.8 2 7.54 x 104 1.35 1.36 2-Chlorophenol :~ 23.0 4000 7.54 × 104 1.45 1.36 4-Chlorophenol~" 23.6 2 7.07 × 10s 17.4 18.2 4-Chlorophenol :~ 23.6 2 7.07 × l0s 12.8 14.5 *Henry's law constants at 25°C calculated from the data of Tsonopoulosand Prausnitz (1971). t In static water. :~In stirred water. §Assuming c~, = 1 and using B = 1.98 × 10-s for static solutions and ~ = 2.50 x 10-s for stirred solutions.
I00
,
,
i
,
0.8
\',\\\\\
~
~ (1.6
.02 c 00
I
o, ° ' , o ~"t0.2 I Ill
o
5 xlO4
o I--
105
I
I
I
I
I
I I II
I
I
I
i
I
n i I ~
t0 6 tO7 Henry's Low Constont H ( d y n e - c m / g ) , Log Scole
:
,
--
~
i i
tO8
Fig. 4. The relationship between c~and H for solutes in dilute aqueous solutions. 40
0
I
I
!
I
2
4
6
8
I0
Time (hours)
Fig. 3. The evaporative loss of DDT from water (L = 4.5 cm) with stirring ( @) and without stirring (©). solutes) may be constructed as shown in Fig. 4. Since ct = 1 sets the theoretical limit for enhancement by subwater mixing, an estimate o f this limit (i.e., l / a in static water) may be obtained for different solutes by reference to the c~-H relationship in static water. Thus, compounds with large H would, in principle, be able to give a greater enhancement by appropriate subwater mixings than those with low H in the region where c~ < 1. In the present study with moderate stirring, the relative enhancement, o~(stirred)/o~(static), is seen to be greater for solutes in the high-H region than those in the l o w - H region although o~ (stirred) has not reached 1 for most volatile solutes. With H lower than ,x,1 × l0 s, subwater mixing itself (i.e., discounting the resulting air turbulance) produces essentially no enhancement for solute evaporation since a = 1 under all conditions. As such, a l o w - H solute evaporates as though it were a pure substance (o~ = 1) but had vapor pressure reduced to its partial pressure, and consequently, t:/2 is merely a function of H, (MI2~rRT) l/z and air turbulence (fl) at a given solution depth as previously shown for the two phenols. As the (M/21rRT) l/z term makes relatively small contribution, the half-lives for l o w - H solutes under similar system conditions are primarily determined by their H values. This also becomes true for high-H solutes in "well mixed" aqueous solutions when c~ approaches 1.
Since ot is mainly a function of H and mixing, One may estimate the values o f o~ (thus t:/2) for other solutes from their values of H according to the c~-H relationship under given system conditions. The experimental and calculated half-lives of evaporation from water (L -4.5 cm; 24°C) for three PCBs, lindane, and parathion are summarized in Table 4. The observed tl/2 values in static water ranging from about 4 h for 2 , 2 ' - P C B to 14 days for parathion are in close agreement with the corresponding calculated values. The data indicate that the improved evaporation in stirred solutions for lindane and parathion (for which ot = 1 in static water) occurs mainly as a result of the air turbulence caused by mixing (i.e., from/~ factor), not by mixing itself; more enhancement is observed for others (for which ct < 1 in static water) due to an additional promotion in o~ by subwater mixing. In the latter, the relative enhancement is greater, for instance, for 2 , 2 ' - P C B than for 4 , 4 ' - P C B because of the difference in their ct values in static water. The fact that 2 , 2 ' - P C B and 4 , 4 ' - P C B have about the same half-lives in static water is a result of the inverse relationship between ~ and H that makes their product terms otH close to each other. As stirring minimizes their difference in c~, the observed half-lives in stirred solutions become more distinctively a function o f their H values. Our estimated H for 2 , 2 ' - P C B could be too high; using H = 8 x l0 s, the predicted values (3.6 and 1 h in static and stirred solutions, respectively) are in better agreement with the observed data. For 2,5,2',5 ' - P C B whose H is not known, an assumed H = --9 x l0 s gives a reasonable fit to the observed halflives. In conclusion, the observed rates o f evaporation under various system conditions and for various solutes
236
C.T. Chiou et al. Table 4. Evaporation half-lives of some solutes from water (L = 4.5 cm) at "~,24°C.
Compound
/-/*(dyne-cm/g)
~
tvs (est):~
tl/s(exp)§
2,2'-PCB
1.7 x 106
4,4'-PCB
4.5 x 10s
0.22 1 0.57
3.1 h (0.46 h) 4.5 h
3.9h (0.90 h) 4.0h
]
(1.7 h)
2,5,2',5
'-PCB
--
--
--
Lindane
1.1 x l0 t
Parathion
3.3 x lot
1 1 1 1
---
3.4days (2.3 days) 13 days (8.7 days)
(1.5
h)
2.8 h
(0.68 h)
3.2days (1.5 days) 14 days (9.3 days)
*Estimated from vapor pressure (po) and aqueous solubility (S) values at 25°C as H -- P°/S. The po values for 2,2'-PCB and 4,4'-PCB are from Smith et al. (1974), lindane from Spencer and Cliath (1970), and parthion from Bright et al. (1950). The S value for parathion is from Williams (1951), and the remainder from Weil et al. (1974). "~Obtained from c~-Hrelationships. ~tv= = 0.693L/(ct~Hx/M/2TRT); B = 1.98 x 10-s in static water; B = 2.97 x 10-s in stirred water. Numbers in parentheses refer to stirred solutions. §The C ° values for the solutes (from top to bottom) are approximately 0.1, 0.03, 0.005, 5 and 2 ppm, respectively.
are consistent with the proposed model. For volatile solutes, subwater mixing enhances the rate of loss by reducing the liquid-layer gradient as measured by or; the effect of the solute concentration on the relative evaporative loss may be similarly explained in terms of oe. For poorly volatile solutes, ot is shown to be = 1, independent of mixings and solute concentrations. The functional relationship between tx and H facilitates assessment of the rates of evaporation of solutes in water and gives a basis of explaining the differences in the effect of subwater mixing on different solutes. Acknowledgement ~ We thank Dr. M. Manes and Dr. I.J. Tinsley for helpful comments. This work was published with the approval of the Oregon State Agricultural Experiment Station as Technical Paper No. 4634. Research was supported by NSF/RANN AEN-76-17700 and NIH ES-00210 and ES-00040 grants.
References Acree, F., Jr., Beroza, M. and Bowman, M.C. (1963) Codistillation of DDT with water. J. agric. Food Chem. 11, 278. Baison, E.W. (1947) Studies in vapor pressure measurement, Part III. An effusion manometer sensitive to 5 x 10-6 mm Hg: Vapor pressure of DDT and other slightly volatile substances, Trans. Faraday Soc. 43, 54. Biggar, J.W., Dutt, G.R. and Riggs, R.L. 0967) Predicting and measuring the solubility of p,p '-DDT in water. Bull. Environ. Contam. ToxicoL 2, 90. Bright, N.F.H., Cuthill, J.C. and Woodbury, N.H. (1950) The vapor
pressure of parathion and related compounds. J. Sci. Fd Agric. 1, 344. Crenshaw, J.L., Cope, A.C., Finkelstein, N. and Rogan, R. (1938) The dioxanates of the mercuric halides. J. Am. Chem. Soc. 60, 2308. Dilling, W.L. (1977) Interphase transfer processes. II. Evaporation rates of chloromethane, ethanes, ethylenes, propanes, and propylene from dilute aqueous solutions. Comparisons with theoretical predictions. Environ. Sci. Technol. 11,405. Hartley, G.S. (1969) Evaporation of pesticides. Adv. Chem. Ser. 86, 115. Lewis, W.K. and Whitman, W.G. (1924) Principles of gas absorption. Ind. Eng. Chem. 16, 1215. Liss, P.S. and Slater, P.G. (1974) Flux of gases across the air-sea interface. Nature 247, 181. Mackay, D. and Leinonen, P.J. (1975) Rate of evaporation of lowsolubility contaminants from water bodies to atmosphere. Environ. ScL Technol. 9, 1178. Nelson, O.A. (1930) Vapor pressures of fumigants. IV. 1,1,2,2-tetra, penta and hexachloroethanes. Ind. Eng. Chem. 22, 971. Smith, N.K., Gorin, G., Good, W.D. and McCullough, J.P. (1964) The heats of combustion, sublimation, and formation of four dihalobiphenyls. J. phys. Chem. 68, 940. Spencer, W.F. and Cliath, M.M. (1970) Vapor density and apparent vapor pressure of lindane. J. agric. Food Chem. 18, 529. Tsonopoulos, G. and Prausnitz, J.M. (1971) Activity coefficients of aromatic solutes in dilute aqueous solutions. Ind. Eng. Chem. Fundam. 10, 593. Weil, L., Dur~, G. and Quentin, K. (1974) WasserlOslichkeit yon insektiziden chlorierten Kohlenwasserstoffen und polychlorierten Biphenylen im Hinblick auf eine Gew~sserbelastung mit diesen Stoffen. Z. Wass. Abwass. Forsch. 7, 169. Williams, E.F. (1951) Properties of 0,0-diethyl 0-p-Nitrophenyl thiophosphate and 0,0-diethyl 0-p-nitrophenyl phosphate. Ind. Eng. Chem. 43, 950.