Coeficientes de difusión

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Advances in Environmental Research 8 ( 2004 ) 667–678

1093-0191/04/$ - see front matter 2003 Elsevier Science Ltd. All rights reserved.doi:10.1016/S1093-0191(03)00039-X

Pseudo-binary molecular diffusion of vapors into air

K.C. Kwon*, T.H. Ibrahim, YoonKook Park, C.M. Simmons Department of Chemical Engineering, 517 Engineering Building, University Avenue, Tuskegee University, Tuskegee, AL 36088,

USA

Accepted 4 April 2003

Abstract

A novel open-tube evaporation method was developed to determine the experimental diffusion coefficients of thevapors of various liquids diffused into air. The mass losses of the volatile liquids chosen for this study were measuredwith a balance rather than changes in the level of the liquid in a diffusion tube for various evaporation durations andno fresh air was passed over the top end of the diffusion path by forced convection, as opposed to the conventionalopen-tube evaporation method. A diffusion equation was developed which is suitable for the novel open-tubeevaporation method. The experimental diffusion coefficient values obtained from the novel experimental diffusionmethods were in reasonable agreement with the diffusion coefficient values predicted with both the Wilke-and-Leemethod and the Fuller et al . method. The experimental diffusion coefficients of n-heptane diffused into air areindependent of the lengths and the evaporation areas of the diffusion paths chosen for this study. The experimentaldiffusion coefficients of normal alcohols and hydrocarbons in air decrease with increased number of carbon atoms in

their molecular formulas. The overall root mean squares of deviation of the diffusion values of this experimentalstudy from those predicted with the Wilke-and-Lee method and the Fuller et al . method are 5.8 and 6.0%, respectively. 2003 Elsevier Science Ltd. All rights reserved.

Keywords: Molecular diffusion coefficient; Diffusion equation; Open tube evaporation method; ‘Student’s’ t distribution

1. Introduction

Molecular mass transfer of toxic gases and vapors of industrial solvents into air is widely investigated tostudy air pollution control and environmental emissionsof volatile vapors. Rates of absorption, adsorption,drying, distillation and condensation occurring in vari-ous industrial processes within the chemical, petroleumand gas industries are dependent on diffusion of proc-essed gaseous chemicals (Berezhnoi and Semenov,1997 ) . The extensive use of the term diffusion in theliterature refers to the net transport of material within asingle phase in the absence of convective mixing. Binarydiffusion coefficients are dependent on temperature,pressure and the nature of the binary components. Bothexperiment and theory have shown that the driving

*Corresponding author. Tel.: q 1-334-727-8976; fax: q 1-334-724-4188.

E-mail address: [email protected] ( K.C. Kwon ) .

forces of diffusion are pressure gradients, temperaturegradients and concentration gradients (Reid et al.,1987 ) . Diffusion coefficients of vapors of various organ-ic chemicals utilized in industrial applications are impor-tant in understanding transport mechanisms in industrialprocesses ( Monfort and Pellegatta, 1991 ) .

Many experimental methods (Coulson and Richard-son, 1984; Berezhnoi and Semenov, 1997; Marrero andMason, 1972 ) have been employed in determiningdiffusion coefficients of both gases and vapors. Diffu-sion coefficients of the vapor of a volatile liquid diffusedinto air are most conveniently determined by the opentube evaporation method (Carmichael et al., 1955 ) . Inthis method, a volatile liquid is partially contained in avertical diffusion tube with a narrow diameter, main-tained at a constant temperature, and an air stream ispassed over the top end of the diffusion tube (Coulsonand Richardson, 1984 ) by forced convection. Thismethod is widely used to determine diffusion coeffi-


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668 K.C. Kwon et al. / Advances in Environmental Research 8 (2004) 667–678

cients of vapors of various liquids dispersed into astagnant gas, which fills the rest of the diffusion tube.A diffusion coefficient is determined from experimentaldata of slow losses of a liquid in the diffusion tube fora given evaporation duration at a constant temperature

and pressure. In the diffusion tube, mass transfer of thevapor of the liquid takes place from the surface of theliquid by molecular diffusion alone (Nirdosh et al.,2000 ) at constant temperature and pressure. Slow lossesof the liquid by evaporation are determinal from thechange in the liquid level in the diffusion tube (Nirdoshet al., 2000 ) .

The closed-tube method (Geankoplis, 1983; Marreroand Mason, 1972 ) is usually quite reliable in determin-ing diffusion coefficients of gases. The essential char-acteristics of this method are a variation of mixturecomposition with time and position throughout a longtube closed at both ends. Gas mixtures are initiallyseparated in the closed tube then interdiffused at con-stant temperature and pressure (Marrero and Mason,1972 ) . The diffusion time is controlled by an openingmechanism at the middle of the tube. The compositionchanges are measured as a function of time, eithercontinuously or after a definite period of diffusion.

Gas chromatography (Monfort and Pellegatta, 1991;Tang and Hawkes, 1984 ) is a method in which a traceamount of a gas is injected as a pulse in a carrier gasflowing through a long hollow tube. The combinedaction of molecular diffusion and the parabolic velocityprofile of the carrier gas cause the dispersion of the

pulse. As the pulse emerges from the tube outlet,measurements of the dispersion lead to values of molec-ular diffusion (Marrero and Mason, 1972 )

The interferometric method (Berezhnoi and Semenov,1997 ) uses a barrier, which separates a liquid from agas prior to diffusion. At the instant of removing thebarrier between the liquid and the gas, unsteady-stateevaporation begins in an open cylinder. Shifts of inter-ference bands with time are photographed with a high-speed camera and a neon lamp.

The point source method ( Marrero and Mason, 1972 )was developed especially for the determination of dif-fusion coefficients at high temperatures. A trace amountof a gas is introduced through a fine hypodermic tubeinto a carrier gas flowing in the same direction. Thetracer spreads by diffusion through the carrier gas, whichhas characteristics of steady-state laminar flow with aflat velocity profile. The mixture composition is meas-ured by means of a sample probe located at variousdistances downstream of the tracer inlet. Electrical heatallows the temperature to increase to 1200 K.

Changes in the liquid level in a diffusion tube forshort evaporation duration are hardly measurable withthe conventional open-tube evaporation method.Amounts of volatile liquids evaporated in the diffusiontube in this study were measured with a balance ratherthan changes of the liquid level in the diffusion tube to

overcome this limitation of the conventional open-tubeevaporation method. No fresh air was passed over thetop end of the diffusion tube by forced convectionduring the diffusion experiments, but natural convectionat the top end of the diffusion path might cause air to

move slightly in laminar flow. The novel open-tubeevaporation method and a newly developed diffusionequation suitable for the novel open-tube evaporationmethod were employed to determine diffusion coeffi-cients of the vapors of various volatile liquids diffusedinto air. Surprisingly, our novel open-tube evaporationmethod has proven to be reliable and accurate inaddition to being easy and simple for experimentation.Nonetheless, this method is restricted to narrow rangesof temperatures, and strongly dependent on the volatilityof the liquid being tested (Marrero and Mason, 1972 ) .

2. Theory

Diffusion coefficients of vapors of volatile liquidscan be experimentally measured in a diffusion tube. Thediffusion tube is partially filled with a neat volatileliquid A at a constant temperature and atmosphericpressure. The inside and the outside of the diffusiontube, partially-filled with the neat volatile liquid A, aresurrounded with a gas B having a negligible solubilityin the liquid A. The liquid A vaporizes and diffusesthrough the stagnant gas phase B in the diffusion pathof the diffusion tube. The vaporization rate of the liquidA is described in Fick’s first law, in which diffusion of the vapor of the liquid A through the stagnant or non-diffusing B occurs at steady-state (Geankoplis, 1983 ) .The mole fraction of the vapor of the liquid A isassumed to be negligible at the top end of the diffusionpath of the diffusion tube in developing a diffusionequation. In this study, atmospheric air was chosen asstagnant gas phase. Air is considered as a single sub-stance, since the constituents of the air in the diffusionpath remain in fixed proportions and the air in thediffusion path is almost stagnant.

A pseudo-steady state diffusion of the vapor of liquidA through the stagnant gas B is assumed, since thelength of the diffusion path does not change significantlyover a short period of time. The molar flux of the vaporA in the diffusion path is also described in terms of theamount of the liquid A vaporized. The following diffu-sion equation (Geankoplis, 1983 ) is developed underthe above-mentioned assumptions.

r RT A 2 2ts z y z (1)Ž .o2PD M ln 1y 1y yŽ Ž .. AB A Ao

The amount of the liquid A vaporized for the vapor-


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669K.C. Kwon et al. / Advances in Environmental Research 8 (2004) 667–678

Fig. 1. Diffusion tube with moving liquid level.

Fig. 2. Schematic diagram of an experimental set-up.

Fig. 3. Loss amounts of liquids by evaporation at various evap-oration durations under atmospheric pressure.

ization duration t is obtained from the following equa-tion (see Fig. 1) .

m y mŽ .o zs z q (2)o

Sr A

Substituting Eq. (2) into Eq. ( 1) produces the followingequation.

r RT Ats 2PD M ln 1y 1y yŽ Ž .. AB A Ao

B EB Em y m m y mo oC FC F= 2z q (3)oD GD GSr Sr A A

Several models (Bird et al., 1960; Hines and Maddox,1985; Mason and Monchick, 1962 ) have been developedto predict diffusion coefficients of both gases and vaporsof volatile liquids. The Wilke and Lee method (Treybal,1980 ) as shown in Eq. (4) and the Fuller et al. method(Reid et al., 1987 ) were used to predict diffusioncoefficients of the systems chosen for this study. The

Wilke-and-Lee method is exclusively recommended formixtures of non-polar gases or a polar gas with a non-polar gas.

y 4 3 y2y y10 1.084 y 0.249 1 yM q 1yM T 1yM q 1yMŽ . A B A B D s AB 2P r f kT y´ Ž . Ž . AB AB

(4)

3. Experimental set-up and procedure

In the conventional open tube evaporation method, avolatile liquid is partially contained in a vertical diffu-sion tube with a narrow diameter, maintained at a

constant temperature, and an air stream is passed overthe top end of the diffusion tube by forced convection.Slow losses of a liquid by evaporation are determinedfrom changes in the liquid level in the diffusion tube.Our novel open-tube experimental method is differentfrom the conventional open-tube method. In this study,slow losses of the liquid by evaporation were determinedby measuring continuously losses of the liquid in theopen diffusion tube with a balance rather than measuringchanges in the liquid level in the diffusion tube. Nofresh air was passed over the top end of the diffusiontube during diffusion experiments by forced convection,as opposed to the conventional open-tube evaporationmethod.

The experimental set-up (see Fig. 2) of the novelopen-tube evaporation method consists of a diffusiontube, a balance (Gardner and Preston, 1992 ) , a barom-eter and a thermometer. The following glass test tubesof various diameters and lengths were utilized to obtainexperimental data of losses of a liquid by evaporationfor various evaporation durations. ( 1) 1.38-cm diameter


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Table 1Calculations of the mole fraction of the vapor of a liquid at the surface of the liquid in a diffusion tube with Antoine equation and experimental

Vapor z (cm)o S ( cm )2 T ( 8C) SV = 10 cm ymin4 2 M A r (gycm )

3 A P ( mmHg ) Antoine parameter

A B

Acetic acid 6.07 1.4957 24.7 5.627 60.05 1.049 763.0 7.80307 1651.2 Acetic acid 2.4 1.4957 25 6.036 60.05 1.049 763.3 7.80307 1651.2 Acetone 1.5 1.4957 24.3 125.0 58.08 0.792 766.6 7.02447 1161 Acetone 6.43 1.4957 26.1 152.2 58.08 0.792 762.3 7.02447 1161 n-Butanol 0.95 1.4957 24.8 2.928 74.12 0.81 763.8 7.4768 1362.39 n-Propanol 1.95 1.4957 24.8 10.54 60.09 0.804 763.3 7.84767 1499.21 Ethanol 1.15 1.4957 24.9 29.91 46.07 0.789 766.6 8.04494 1554.3 Methanol 1.3 1.4957 25 60.81 32.04 0.792 762.3 7.87863 1473.11 Carbon disulfide 2.65 1.4957 25.2 206.3 76.13 1.261 763.3 6.94279 1169.11 Diethylamine 2.75 1.4957 25.2 166.0 73.14 0.712 763.3 5.8016 583.3 Benzene 2.05 1.4957 23.7 51.05 78.11 0.879 766.3 6.90565 1211.033Ethyl acetate 2.15 1.4957 25.3 57.46 88.1 0.901 762.5 7.09808 1238.71 n-heptane 1.83 1.4957 24.7 30.38 100.2 0.684 761.7 6.9024 1268.115n-heptane 2.45 1.4957 24.8 31.92 100.2 0.684 761.7 6.9024 1268.115n-heptane 3.97 1.4957 25 32.44 100.2 0.684 761.7 6.9024 1268.115n-heptane 5.45 1.4957 25.7 35.72 100.2 0.684 762.3 6.9024 1268.115n-heptane 4.1 11.2221 24.6 31.89 100.2 0.684 765 6.9024 1268.115n-heptane 4.1 4.2638 26 33.67 100.2 0.684 765.6 6.9024 1268.115n-heptane 4.1 1.4957 25.7 33.49 100.2 0.684 760.7 6.9024 1268.115n-heptane 4.1 0.9677 25.5 33.95 100.2 0.684 760.7 6.9024 1268.115n-heptane 4.1 0.5217 25.6 35.25 100.2 0.684 760.7 6.9024 1268.115n-hexane 5.84 1.4957 26 123.8 86.17 0.659 762.3 6.87776 1171.53 Methylene chloride 1.35 1.4957 25 227.7 84.94 1.336 762.5 7.4092 1325.9

Methylene chloride 6.1 1.4957 26.2 303.7 84.94 1.336 762.3 7.4092 1325.9 Isooctane 5.63 1.4957 24.2 35.36 114.22 0.692 763 6.81189 1257.84 Isooctane 4.1 1.4957 25.1 35.62 114.22 0.692 760.7 6.81189 1257.84 Toluene 2.55 1.4957 24 16.16 92.13 0.866 765 6.95334 1343.943


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Table 2Experimental diffusion coefficients and their deviations of various vapors, using the Student’s t distribution with the 95% confidenceinterval and the ( ny 1) degrees of freedom

Vapor z (cm)o S (cm )2 T ( 8C) Experimental D AB Experimental D AB

(cm ys) and its2 (cm ys) and its2

deviation ( cm ys)2 deviation ( %)

Acetic acid 6.07 1.4957 24.7 0.0975 " 0.0096 0.0975 " 9.9Acetic acid 2.4 1.4957 25 0.0968 " 0.0082 0.0968 " 8.5Acetone 1.5 1.4957 24.3 0.1008 " 0.0004 0.1008 " 0.4Acetone 6.43 1.4957 26.1 0.1117 " 0.0005 0.1117 " 0.4n-butanol 0.95 1.4957 24.8 0.0815 " 0.0023 0.0815 " 2.8n-propanol 1.95 1.4957 24.8 0.1051 " 0.0030 0.1051 " 2.9Ethanol 1.15 1.4957 24.9 0.1318 " 0.0045 0.1318 " 3.4Methanol 1.3 1.4957 25 0.1690 " 0.0012 0.1690 " 0.7Carbon disulfide 2.65 1.4957 25.2 0.1078 " 0.0013 0.1078 " 1.2Diethylamine 2.75 1.4957 25.2 0.0934 " 0.0013 0.0934 " 1.4Benzene 2.05 1.4957 23.7 0.0938 " 0.0005 0.0938 " 0.5Ethyl acetate 2.15 1.4957 25.3 0.0884 " 0.0016 0.0884 " 1.8n-heptane 1.83 1.4957 24.7 0.0693 " 0.0009 0.0693 " 1.4n-heptane 2.45 1.4957 24.8 0.0725 " 0.0009 0.0725 " 1.4n-heptane 3.97 1.4957 25 0.0730 " 0.0006 0.0730 " 0.9n-heptane 5.45 1.4957 25.7 0.0777 " 0.0009 0.0777 " 1.2n-heptane 4.1 11.2221 24.6 0.0734 " 0.0009 0.0734 " 1.3n-heptane 4.1 4.2638 26 0.0725 " 0.0005 0.0725 " 0.6n-heptane 4.1 1.4957 25.7 0.0727 " 0.0007 0.0727 " 0.9n-heptane 4.1 0.9677 25.5 0.0744 " 0.0009 0.0744 " 1.3n-heptane 4.1 0.5217 25.6 0.0769 " 0.0015 0.0769 " 1.9n-hexane 5.84 1.4957 26 0.0834 " 0.0005 0.0834 " 0.6Methylene chloride 1.35 1.4957 25 0.0881 " 0.0002 0.0881 " 0.3Methylene chloride 6.1 1.4957 26.2 0.1095 " 0.0011 0.1095 " 1.0Isooctane 5.63 1.4957 24.2 0.0678 " 0.0009 0.0678 " 1.5Isooctane 4.1 1.4957 25.1 0.0653 " 0.0005 0.0653 " 0.8Toluene 2.55 1.4957 24 0.0859 " 0.0044 0.0859 " 5.2

tube with a cross-sectional area of 1.4957 cm and a2

length of 12.6 cm, (2) tube with a cross-sectional areaof 11.2221 cm and a length of 4.9 cm, (3) tube with2

a cross-sectional area of 4.2638 cm and a length of 4.92

cm, (4) a tube with a cross-sectional area of 0.9677cm and a length of 9.8 cm, and (5) a tube with a2

cross-sectional area of 0.5217 cm and a length of 7.32

cm.The tube was partially filled with a liquid. The initial

length of the diffusion path, the initial distance fromthe top end of the diffusion tube to the liquid level inthe diffusion tube was measured. The top window of the balance remained open for air to be passed over bynatural convection. The tube, partially filled with aknown amount of the liquid to a known level in thetube was placed on the balance. The balance was resetand a stopwatch started, after the inside wall of the tubewas dried for 5 min. The temperature of the liquid andatmospheric pressure were measured with a thermometerand a barometer. Loss amounts of the liquid by evapo-ration were measured with the balance at random timeintervals for 10–45 min.

4. Calculations

Eq. (3) is rearranged to obtain Eq. (5) with evapo-ration durations as an independent variable and left-sidevalues of Eq. (5) containing loss amounts of liquid Aas a dependent variable.

B Em y moC FD GSr A

2PD M ln 1y 1y yB E Ž Ž .. AB A Aom y moC F= 2z q s t (5)oD GSr r RT A A

Loss amounts of liquid A by evaporation were meas-ured at random evaporation durations. These experimen-tal data were applied to both sides of Eq. (5) , and then

independent variablesB EB E B Em y m m y mo oC F C FC F= 2z qo

D G D GSr SrD G A Aagainst dependent variables (t ) were plotted on a graphto obtain the value of the slope

through the linear leastB E2PD M ln 1y 1y yŽ Ž .. AB A AoC FD Gr RT A


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Table 3Estimation of the binary diffusion coefficients for the various vapors using Wilke and Lee method *

Vapor T BP P Vapor Vapor r AB ´ yk AB kT y´ AB f (kT y´ ) AB Predicted D AB(8C) ( 8C) ( mmHg ) ´ yk A r A (cm ys)

2

Acetic acid 24.7 118.1 763.0 473.4 0.4826 0.4268 192.9 1.544 0.5980 0.1078Acetic acid 25.0 118.1 763.3 473.4 0.4826 0.4268 192.9 1.546 0.5977 0.1080Acetone 24.3 56.5 766.6 398.9 0.4954 0.4333 177.1 1.680 0.5741 0.1088Acetone 26.1 56.5 762.3 398.9 0.4954 0.4333 177.1 1.690 0.5725 0.1108n-butanol 24.8 117 763.8 472.1 0.5542 0.4627 192.6 1.547 0.5975 0.0891n-propanol 24.8 97.8 763.3 448.9 0.5114 0.4412 187.8 1.586 0.5902 0.1022Ethanol 24.9 78.4 766.6 425.4 0.4599 0.4155 182.9 1.630 0.5825 0.1217Methanol 25.0 64.7 762.3 408.8 0.3932 0.3822 179.3 1.662 0.5771 0.1571Carbon disulfide 25.2 46.3 763.3 386.5 0.4769 0.4240 174.3 1.712 0.5690 0.1113Diethylamine 25.2 55.5 763.3 397.7 0.5686 0.4699 176.8 1.688 0.5729 0.0905Benzene 23.7 80.1 766.3 427.4 0.5403 0.4557 183.3 1.620 0.5844 0.0924Ethyl acetate 25.3 77.1 762.5 423.8 0.5668 0.4689 182.5 1.635 0.5817 0.0875n-heptane 24.7 98.4 761.7 449.6 0.6443 0.5077 188.0 1.585 0.5906 0.0724n-heptane 24.8 98.4 761.7 449.6 0.6443 0.5077 188.0 1.585 0.5905 0.0724n-heptane 25.0 98.4 761.7 449.6 0.6443 0.5077 188.0 1.586 0.5903 0.0725n-heptane 25.7 98.4 762.3 449.6 0.6443 0.5077 188.0 1.590 0.5896 0.0728n-heptane 24.6 98.4 765.0 449.6 0.6443 0.5077 188.0 1.584 0.5907 0.0720n-heptane 26.0 98.4 765.6 449.6 0.6443 0.5077 188.0 1.591 0.5893 0.0726n-heptane 25.7 98.4 760.7 449.6 0.6443 0.5077 188.0 1.590 0.5896 0.0729n-heptane 25.5 98.4 760.7 449.6 0.6443 0.5077 188.0 1.589 0.5898 0.0728n-heptane 25.6 98.4 760.7 449.6 0.6443 0.5077 188.0 1.589 0.5897 0.0729n-hexane 26.0 69 762.3 414.0 0.6136 0.4923 180.4 1.658 0.5777 0.0805Methylene chloride 25.0 40 762.5 378.9 0.4895 0.4303 172.6 1.728 0.5664 0.1070Methylene chloride 26.2 40 762.3 378.9 0.4895 0.4303 172.6 1.735 0.5653 0.1079Isooctane 24.2 99.3 763.0 450.7 0.6724 0.5217 188.2 1.580 0.5914 0.0672Isooctane 25.1 99.3 760.7 450.7 0.6724 0.5217 188.2 1.585 0.5905 0.0678Toluene 24.0 110.8 765.0 464.6 0.5791 0.4751 191.1 1.555 0.5959 0.0820

The values of ´ yk and r for air used are 78.6 K and 0.3711 nm, respectively.*

B B

squares method (Johnson and Leone, 1964 ) , as shownin Fig. 3. The density r and the molecular weight M A A(Perry and Chilton, 1973 ) of the liquid A, and the molefraction y of the vapor of the liquid A at the surface Aoof the liquid A in a diffusion tube, the diffusiontemperature, and atmospheric pressure were substituted

into the slope value toB E2PD M ln 1y 1y yŽ Ž .. AB A AoC FD Gr RT A

calculate the experimental pseudo-binary diffusion coef-

ficient of the liquid A diffused into the stagnant air inthe diffusion path. The diffusion coefficients obtainedby Eq. (5) are shown in Tables 1 and 2.

The saturated vapor pressure at the surface of liquidA in a diffusion tube was obtained with the temperatureof the liquid A and the Antoine equation (Dean, 1992;Felder and Rousseau, 1986 ) . Saturated vapor pressuresof liquids are dependent on their temperatures alone,and independent of humidity of air according to theAntoine equation ( see Eq. ( 6)) . The mole fraction ( y ) Aoof the vapor of the liquid A at the surface of the liquidA in the diffusion tube can be obtained by dividing thesaturated vapor pressure of the liquid A with atmos-pheric pressure, as shown in Table 1. Fluctuations of both temperature and atmospheric pressure are consid-

ered to be almost negligible during relatively shortexperimental durations in comparison with the conven-tional open tube evaporation method.

A y B y C q TŽ Ž ..P s 10 (6)S

The Wilke-and-Lee method (see Eq. (4)) and itsparameter equations, as shown in Eq. (7) through Eq.(11) , were used to predict the diffusion values of thevapors of the volatile liquids chosen for this study. Eq.(7) and Eq. (8) were used to calculate the value of r

Aand the value of ´ yk of the vapor of liquid A, Arespectively. Air is considered as a single substance,since the constituents of the air in a diffusion pathremain in fixed proportions and the air in the diffusionpath is almost stagnant. The value of r and the value Bof ´ yk of air were not calculated for this study, but Bwere obtained from the literature (Treybal, 1980 ) . Thevalue of r and the value of ´ yk of air are 0.3711 nm B Band 78.6 K, respectively.

1 y3r s 1.18v (7) A

´ yks 1.21T (8) A b

r s ( r q r )y2 (9) AB A B


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Table 4Literature diffusion coefficients of various vapors diffused into air from the references

Vapor Temperature Literature value Ref.(8C) D (cm ys)2 AB

Acetic acid 24.7 0.1207 Geankoplis, 1983Acetic acid 25 0.1209 Geankoplis, 1983Acetone 24.3 0.1110 Berezhnoi and Semenov, 1997Acetone 26.1 0.1120 Berezhnoi and Semenov, 1997n-butanol 24.8 0.0865 Geankoplis, 1983; Treybal, 1980n-propanol 24.8 0.1000 Coulson and Richardson, 1984Ethanol 24.9 0.1347 Reid et al., 1987; Hines and Maddox, 1985Methanol 25 0.1591 Coulson and Richardson, 1984Carbon disulfide 25.2 0.1046 Berezhnoi and Semenov, 1997Diethylamine 25.2 0.0000 Not availableBenzene 23.7 0.0956 Geankoplis, 1983; Bennett and Myers, 1962Ethyl acetate 25.3 0.0867 Treybal, 1980n-heptane 24.7 0.0724 Reid et al., 1987n-heptane 24.8 0.0724 Reid et al., 1987n-heptane 25 0.0725 Reid et al., 1987n-heptane 25.7 0.0728 Reid et al., 1987n-heptane 24.6 0.0724 Reid et al., 1987n-heptane 26 0.0729 Reid et al., 1987n-heptane 25.7 0.0728 Reid et al., 1987n-heptane 25.5 0.0727 Reid et al., 1987n-heptane 25.6 0.0727 Reid et al., 1987n-hexane 26 0.0820 Geankoplis, 1983; Reid et al., 1987Methylene chloride 25 0.1037 Berezhnoi and Semenov, 1997Methylene chloride 26.2 0.1043 Berezhnoi and Semenov, 1997Isooctane 24.2 0.0530 Berezhnoi and Semenov, 1997Isooctane 25.1 0.0532 Berezhnoi and Semenov, 1997Toluene 24 0.8518 Geankoplis, 1983

1 y2w x´ yks ( ´ yk)( ´ yk) ( 10) AB A By 0.4857 f (kT y´ )s 0.7375 (kT y´ ) ( 11) AB AB

The value of r and the value of ´ yk were AB ABcalculated with Eq. (9) and Eq. (10) , respectively. Thevalue of f (kT y´ ) was obtained with Eq. (11) , which ABwas developed from the collision function figure ( Trey-bal, 1980 ) . Table 3 shows the calculated parametervalues of the Wilke-and-Lee method and its predicteddiffusion coefficients of the various vapors chosen forthis study.

The literature diffusion coefficients (see Table 4)were obtained from the publications (Geankoplis, 1983;Berezhnoi and Semenov, 1997; Treybal, 1980; Coulsonand Richardson, 1984; Reid et al., 1987; Hines andMaddox, 1985; Bennett and Myers, 1962 ) . The predict-ed diffusion coefficients and the literature diffusioncoefficients of the vapors of the volatile liquids werecompared with the experimental diffusion coefficientsobtained from the novel open-tube evaporation method,as shown in Table 5.

5. Results and discussion

The experimental and predicted pseudo-binary diffu-sion coefficients of the vapor–air systems chosen for

this study at atmospheric pressure are shown in Tables1, 3 and 5. Table 4 shows the literature diffusion valuesof the vapors of the liquids obtained from thepublications. The experimental pseudo-binary diffusionvalues from this study were compared with the literaturediffusion values as well as the predicted diffusionvalues, as shown in Table 5 and Figs. 4, 5 and 9.

The experimental pseudo-binary diffusion coefficientsof the normal alcohols in air were plotted against thenumber of carbon atoms in their molecular formulas, asshown in Fig. 5. The result indicates that the experi-

mental pseudo-binary diffusion coefficients of the nor-mal alcohols in air decrease with increased number of carbon atoms in their molecular formulas. This result isin good agreement with the fact that heavier moleculeshave larger collision diameters and larger energy of molecular attractions, as shown in Eq. (4) .

A series of experiments with liquid n-heptane wereconducted to find out effects of initial lengths of adiffusion path on its pseudo-binary diffusion coefficientsinto air, as shown in Figs. 6 and 7. These results indicatethat the pseudo-binary diffusion coefficients of n-hep-tane diffused into air are almost independent of theinitial length of the diffusion path. This fact may justifythe assumption that mole fractions of vapors of liquidsat the top end of the diffusion path are negligible.


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Table 5Experimental, predicted, and literature value of diffusion coefficients

Vapo ra Diffusion Temperature Experimental Predicted D (cm ys)2 AB Literature path ( cm) ( 8C) D (cm ys) and2 AB Wilke and Lee Fuller et al.

D (cm ys)2 AB

its deviation ( %) method method

Acetic acid 6.07 24.7 0.0975 " 9.9 0.1078 0.1041 0.1207 Acetic acid 2.4 25 0.0968 " 8.5 0.1080 0.1043 0.1209 Acetone 1.5 24.3 0.1008 " 0.4 0.1088 0.1053 0.1110 Acetone 6.43 26.1 0.1117 " 0.4 0.1108 0.1064 0.1120 n-butanol 0.95 24.8 0.0815 " 2.8 0.0891 0.0894 0.0865 n-propanol 1.95 24.8 0.1051 " 2.9 0.1022 0.1023 0.1000 Ethanol 1.15 24.9 0.1318 " 3.4 0.1217 0.1224 0.1347 Methanol 1.3 25 0.1690 " 0.7 0.1571 0.1597 0.1591 Carbon disulfide 2.65 25.2 0.1078 " 1.2 0.1113 0.1054 0.1046 Diethylamine 2.75 25.2 0.0934 " 1.4 0.0905 0.0895 0.0000 Benzene 2.05 23.7 0.0938 " 0.5 0.0924 0.0889 0.0956 Ethyl acetate 2.15 25.3 0.0884 " 1.8 0.0875 0.0871 0.0867 n-heptane 1.83 24.7 0.0693 " 1.4 0.0724 0.0704 0.0724 n-heptane 2.45 24.8 0.0725 " 1.4 0.0724 0.0704 0.0724 n-heptane 3.97 25 0.0728 " 0.9 0.0725 0.0705 0.0725 n-heptane 5.45 25.7 0.0775 " 1.2 0.0728 0.0708 0.0728 n-heptane e 4.1 24.6 0.0734 " 1.3 0.0720 0.0703 0.0724 n-heptane f 4.1 26 0.0725 " 0.6 0.0726 0.0709 0.0729 n-heptane 4.1 25.7 0.0727 " 0.9 0.0729 0.0708 0.0728 n-heptane g 4.1 25.5 0.0744 " 1.3 0.0728 0.0707 0.0727 n-heptane h 4.1 25.6 0.0769 " 1.9 0.0729 0.0707 0.0727 n-hexane 5.84 26 0.0834 " 0.6 0.0805 0.0770 0.0820 Methylene chloride 1.35 25 0.0881 " 0.3 0.1070 0.1033 0.1037 Methylene chloride 6.1 26.2 0.1095 " 1.0 0.1079 0.1040 0.1043 Isooctane 5.63 24.2 0.0678 " 1.5 0.0672 0.0653 0.0530

Isooctane 4.1 25.1 0.0653 " 0.8 0.0678 0.0656 0.0532 Toluene 2.55 24 0.0859 " 5.2 0.0820 0.0801 0.8518

The evaporation area was 1.4957 cm in all runs except es 11.2221 cm , f s 4.2638 cm , gs 0.9677 cm , and hs 0.5217 cm .a 2 2 2 2 2

(experimental value–predicted value ) yexperimental value = 100%.b

The overall root mean square of deviation percentage of the experimental diffusion values from those predicted with Wilke and Lee methc

method ( Reid et al., 1987 ) .


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Fig. 4. Comparison of experimental pseudo-binary diffusion coefficient values of vapors of various liquids with literature valuesand predicted values at atmospheric pressure.

Fig. 5. Comparison of experimental pseudo-binary diffusion coefficient values of normal alcohols with literature values and predictedvalues at atmospheric pressure.

The experimental pseudo-binary diffusion coefficientsof n-heptane in air obtained from this study were plottedagainst evaporation temperatures as shown in Fig. 8.This observation shows that the pseudo-binary diffusioncoefficients of n-heptane diffused into air increase withincreased evaporation temperatures inspite of the narrowevaporation temperature range of 24–26 8C at atmos-

pheric pressure. These observations also agree with theWilke-and-Lee method.The experimental pseudo-binary diffusion coefficients

of the normal hydrocarbons in air were plotted against

the number of carbon atoms in their molecular formulasas shown in Fig. 9. This fact suggests that experimentalpseudo-binary diffusion coefficients of normal hydro-carbons in air decrease with increased number of carbonatoms in their molecular formulas. This result is alsowell known and follows directly the fact that heaviermolecules have larger collision diameters and larger

energy of molecular attractions, as shown in Eq. (

4).A series of diffusion experiments with liquid n-

heptane were conducted to find out effects of evapora-tion areas on its pseudo-binary diffusion coefficients


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Fig. 6. Loss amounts of liquid n-heptane by evaporation atvarious evaporation durations and various initial lengths of dif-fusion path ( zo) under atmospheric pressure.

Fig. 7. Effects of diffusion-path length on diffusion of n-hep-tane vapor into stagnant air in the temperature range of 24.7–25.7 8C.

Fig. 9. Comparison of experimental pseudo-binary diffusioncoefficient values of normal hydrocarbon with literature valuesand predicted values at atmospheric pressure.

Fig. 10. Loss amounts of liquid n-heptane by evaporation withvarious evaporation areas ( S) and the initial 4.1 cm diffusion-path length ( zo) at atmospheric pressure.

Fig. 8. Pseudo-binary diffusion coefficients of n-heptane at var-ious evaporation temperatures.

Fig. 11. Pseudo-binary diffusion coefficients of n-heptane withvarious evaporation areas at room temperature and atmosphericpressure.


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into air, as shown in Figs. 10 and 11. These resultsindicate that the pseudo-binary diffusion coefficients of n-heptane diffused into air are independent of theevaporation areas chosen for this study. These observa-tions may suggest that changes in concentrations of

vapors in the radial direction in a diffusion path do notoccur.The predicted diffusion coefficients of the various

vapors into air were also calculated with the Fuller etal. method (Reid et al., 1987 ) , as shown in Table 5.The overall root mean square (Spiegel, 1961 ) of devi-ation of the diffusion values obtained with the novelopen-tube evaporation method from those predicted withthe Wilke-and-Lee method (Treybal, 1980 ) is 6.0%,whereas it is 5.8% with the Fuller et al. method. Bothmethods seem to predict very closely the pseudo-binarydiffusion coefficients of the vapors of the various liquidschosen for this study.

The overall results suggest that the experimentaldiffusion values obtained from the novel open-tubeevaporation method are in reasonable agreement withthe diffusion values predicted with both methods.Although air contains some moisture and moisturecontents in air vary, the value of r and the value of B´ yk of air were obtained from the literature (Treybal, B1980 ) in order to calculate the predicted pseudo-binarydiffusion coefficients of the vapors into air with theWilke and Lee method. The value of r and the value Bof ´ yk of air from the literature (Treybal, 1980 ) are B0.3711 nm and 78.6 K, respectively. Although the results

from the novel open-tube evaporation method are ratherprecise, it is also important to notice the limitations of the novel open-tube evaporation method. It is recom-mended that disturbance of air surrounding the evapo-ration apparatus be minimized to obtain a goodagreement between experimental diffusion coefficientsand predicted diffusion coefficients. The novel open-tube evaporation method is restricted to narrow rangesof temperatures, and strongly dependent on the volatilityof a liquid being tested (Marrero and Mason, 1972 ) .

6. Conclusions

The experimental diffusion coefficients of the vaporsof the liquids into air in this study were obtained fromthe evaporated amounts of the liquids measured with abalance rather than changes in the liquid level in adiffusion tube for various evaporation durations. Nofresh air was passed over the top end of the diffusiontube by forced convection during diffusion experiments,as opposed to the conventional open-tube evaporationmethod. The experimental diffusion coefficient valuesobtained with the novel open-tube evaporation methodand the newly developed diffusion equation are reason-ably agreeable with the predicted diffusion coefficient

values. This novel open-tube evaporation method turnedout to be simple and convenient in determining experi-mental diffusion coefficients of vapors of liquids intoair at atmospheric pressure.

The pseudo-binary diffusion coefficients of n-heptane

diffused into air are almost independent of the initiallengths of the diffusion paths chosen for this study. Thisobservation indicates that mole fractions of vapors of liquids at the top end of the diffusion paths are negli-gible. The pseudo-binary diffusion coefficients of n-heptane diffused into air were also independent of theevaporation areas chosen for this study, suggesting thatchanges in concentrations of vapors in the radial direc-tion in the diffusion paths do not occur. The pseudo-binary diffusion coefficients of n-heptane diffused intoair increase with increased evaporation temperatures inspite of the narrow temperature range of 24–26 8C atatmospheric pressure. These results agree with the Wilkeand Lee method.

The experimental pseudo-binary diffusion coefficientsof the normal alcohols in air decrease with increasednumber of carbon atoms in their molecular formulas.The experimental pseudo-binary diffusion coefficientsof the normal hydrocarbons in air decrease withincreased number of carbon atoms in their molecularformulas. This result agrees with the fact that heaviermolecules have larger collision diameters and largerenergy of molecular attractions, as shown in Wilke-and-Lee method.

The overall root mean square (Spiegel, 1961 ) of

deviation of the diffusion values of this experimentalstudy from those predicted with the Wilke-and-Leemethod (Treybal, 1980 ) is 6.0%, whereas with the Fulleret al. method it is 5.8%. Both methods predict veryclosely the pseudo-binary diffusion values of the vaporsof various liquids chosen for this study.

7. Nomenclature

A, B, C : Parameters of Antonie equation BP: Boiling temperature of a liquid at

atmospheric pressure D : AB Diffusion coefficient of a vapor A diffused

into air, m ys for Eq. (4) and cm ys for Eq.2 2

(5) M : A Molecular weight of A, kg ykmol M : B Molecular weight of B, kg ykmolP : Atmospheirc pressure, atm for Eq. (5) , Nym2

for Eq. (4)P :S Saturated vapor pressure of a liquid at T 8C,

mmHg R: Ideal gas constant, 82.0545 atm-cm yg-mle-K3

for Eq. (5)S : Cross-sectional area of a diffusion tube, cm 2

SV : Slope value of the diffusion equation


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