Experiment 1 (Diffusion)

Experiment No. 1

DIFFUSION OF LIQUIDS THROUGH STAGNANT NON-DIFFUSING AIR

Submitted by:

JAMES LAURENCE D. RAVIZ Abstract – The experiment aims to determine

the diffusivity of vapor A through a stagnant non-diffusing B using several known methods specifically the Capillary Tube Method and Chapman-Enskog Method. We have defined diffusion as the movement under the influence of physical stimulus of an individual component through a mixture in which the driving force is concentration gradient of the diffusing component.

This experiment focuses also on the temperature dependence of diffusivity and thus the rate of diffusion of liquids through stagnant non-diffusing air.

I.INTRODUCTION

Diffusion involves the mass transfer of a volatile component A through a non-diffusing stagnant B. The most common cause diffusion is concentration gradient of the diffusing components. A concentration gradient tends to move the component in such a direction as to equalize concentration and destroy the gradient while the gradient is maintained by constantly supplying the diffusing component to the high concentration end of the gradient and removing it at low-concentration end. There is steady state reflux of the diffusing component. This is characteristics of many mass transfer operations.

Diffusion is not restricted to molecular transfer through stagnant layers of solid or fluid. It also takes place when fluids of different compositions are mixed. The first step in mixing is often mass transfer called by eddy motion characteristics of turbulent flow. This is called eddy diffusion. The second step is molecular diffusion between and inside the very small eddies. Sometimes the diffusion process is accompanied by bulk flow of the mixture in a direction parallel to the direction of diffusion.

Diffusivity is a proportionality constant between the mass flux due to molecular diffusion and the gradient in the concentration of the species. It should be apparent that the rate of molecular diffusion in liquids is considerably slower in gasses. The

molecules in liquid are very close toether compared to a gas. Hence, the molecules of the diffusing solute A will collide with molecules of liquid B more often and diffuse more slowly that in gases. In general, the diffusion coefficient in a gas will be in order of magnitude of about 105 _{times greater than in liquid.}

A number of different experimental methods have been used to determine the molecular diffusivity for binary gas mixtures. One method is through the capillary tube method. It is to evaporate a pure liquid in a narrow tube with a gas passed over the top. The fall in liquid level is measure with time and the diffusivity is calculated from:

DAB= ρAPBMRT tP M_A

(

P_{A 1}−P_{A 2}

)

(

zf2−z02 2

)

where:

ρA - density of liquid A at temperature T

PBM – logarithmic mean pressure

R – universal gas constant T – absolute temperature

t – time during which the meniscus fall from zo to zf

P – ambient atmospheric pressure MA – molecular weight of liquid

PA1 – vapor pressure of liquid A at temperature T

PA2 – partial pressure of vapor A at the mouth of

capillary

zf – distance from the mouth of the capillary to the

meniscus at t=t

zo – distance from the mouth of the capillary to the

meniscus at t=0

A more accurate and rigorous treatment must be considered which is the intermolecular forces of attraction and repulsion between molecules as well as the different sizes of molecules A and B. Chapman and Enskog solved the Boltzmann equation, which uses a distribution function instead of the mean free path.

The final relation for predicting the diffusivity of binary gas pair A and B molecule is:

Diffusion of Liquids Through Stagnant Non-Diffusing Air 1.8583 x 10−7 D_AB=¿(T1.5 ) ¿ P σ2ABΩ

(

1 M_A+ 1 M_B

)

0.5 where: DAB – diffusivity T – absolute temperature MA – molecular weight of gas A

MB – molecular weight of stagnant B

P – absolute pressure σ – average collision Ω – collision integral

II. EQUIPMENT AND APPARATUS

Apparatus: Constant Water Bath Thermometers Iron Stand Iron Clamp Cork Capillary Tube Vernier Caliper Portable Electric Fan Stopwatch

Materials: Ethanol Methanol Acetone

III. PROCEDURE/ METHODOLOGY

START

Prepare the constant Water Bath and Set it to

X

X

Close the other end of the capillary tube and fill it with pure volatile liquid

Measure the initial height of the liquid

Provide gentle stream of air using a fan

Provide gentle stream of air using a fan

Measure the height of the remaining liquid in the capillary

tube after 10 and 15 minutes

Repeat procedure 2-4 for 2 trials having 65˚C and 80 ˚C as the

temperature respectively

Compare the result with those obtained using Chapmann-Enskog

and other empirical formula

IV. DATA AND RESULTS

Table 4.1 Height of liquid in the capillary

Trial 1 T=50˚C Liquid ho T,C h10 T,C h15 T,C Ethanol 59mm - 58mm 30 57mm 38 Methanol 58mm - 57mm 30 56mm 38 Acetone 53mm - 52mm 30 51mm 38

Table 4.2 Height of liquid in the capillary

Trial 2 T=65˚C Liquid ho T,C h10 T,C h15 T,C Ethanol 59mm - 57mm 48 53mm 58 Methanol 55mm - 53mm 48 52.5 58 Acetone 55mm - 54mm 48 53mm 58

A. CAPILLARY TUBE METHOD

Table 4.3 Properties from Perry’s ChE Handbook Liquid Density, kg/m3 _{Vapor Pressure,}

kPa Ethanol 781.36 775.34 10.53 16.23 Methanol 784.74 776.90 21.76 32.18 Acetone 780.58 800.33 37.95 52.30

Table 4.4 Diffusivities Computed for Trial 1

Liquid Diffusivity DAB, m2/s 10 minutes T=30˚C 15 minutesT=38˚C Ethanol 0.000367 0.000318 Methanol 0.000241 0.000205 Acetone 6.24X10-5 8.09 X10-5

Table 4.5 Properties from Perry’s ChE Handbook Liquid Density, kg/m3 _{Vapor Pressure,}

MPa Ethanol 763.68 754.69 26.871 42.793 Methanol 766.89 756.61 50.866 77.897 Acetone 759.74 747.53 76.11 107.945

Table 4.6 Diffusivities Computed for Trial 2

Liquid Diffusivity DAB, m2/s 10 minutes 15 minutes T=48˚C T=58˚C Ethanol 0.00027 0.00045 Methanol 0.00016 0.000098 Acetone 0.000022 -CALCULATIONS TRIAL 1 ETHANOL For 10 minutes: PBM=

(

P−P_{A 1}

)

−(P−P_{A 2}) ln

(

P−PA 1 P−PA 2

)

PBM= (101.325−19.53 )−(101.325) ln

(

101.325−19.53 101.325

)

P_BM=95.98 kPa DAB= ρABPBMRT tP M_A

(

P_{A 1}−P_{A 2}

)

(

zf 2 −zo 2 2

)

D_AB=(781.36) (95.98) (8.314) (303.15) (600 )(46)(101.325)(10.53)

(

0.0592−0.0582 2

)

D_AB=0. 000367m 2 s For 15 minutes P_BM=

(

P−PA 1

)

−(P−PA 2) ln

(

P−PA 1 P−PA 2

)

PBM= (101.325−16.22)−(101.325) ln

(

101.325−16.22 101.325

)

PBM=93.01kPa

Diffusion of Liquids Through Stagnant Non-Diffusing Air D_AB= ρABPBMRT tP M_A

(

P_{A 1}−P_{A 2}

)

(

zf 2 −zo 2 2

)

D_AB=(775.34) (93.01) (8.314) (311.15) (900 )(46)(101.325 )(16.22)

(

0.0592_−0.0572 2

)

D_AB=0.000318m 2 s METHANOL For 10 minutes P_BM=

(

P−PA 1

)

−(P−PA 2) ln

(

P−PA 1 P−PA 2

)

PBM= (101.325−21.76 )−(101.325) ln

(

101.325−21.76 101.325

)

P_BM=89.99 kPa D_AB= ρABPBMRT tP M_A

₍

P_{A 1}−P_{A 2}

₎

(

zf2−zo2 2

)

D_AB=(784.74) (89.99) (8.314) (303.15) (600)(32)(101.325) (21.76)

(

0.0582−0.0572 2

)

D_AB=0. 000241m2 s For 15 minutes: P_BM=

(

P−PA 1

)

−(P−PA 2) ln

(

P−PA 1 P−PA 2

)

PBM= (101.325−32.18 )−(101.325) ln

(

101.325−32.18 101.325

)

P_BM=84.21kPa D_AB= ρABPBMRT tP M_A

₍

P_{A 1}−P_{A 2}

₎

(

zf2−zo2 2

)

D_AB=(776.90) (84.21)(8.314 )(311.15) (900 )(32)(101.325)(32.18 )

(

0.0582_−0.0562 2

)

D_AB=0. 000205m 2 s ACETONE For 10 minutes P_BM=

(

P−PA 1

)

−(P−PA 2) ln

(

P−PA 1 P−PA 2

)

PBM= (101.325−37.95 )−(101.325) ln

(

101.325−37.95 101.325

)

PBM=80.87 kPa D_AB= ρABPBMRT tP M_A

(

P_{A 1}−P_{A 2}

)

(

zf 2 −zo 2 2

)

D_AB=(780.58) (80.87) (8.314) (303.15) (600)(58.08)(101.325) (37.95)

(

0.0532_−0.0522 2

)

D_AB=6.24 X 1 0−5m 2 s For 15 minutes:

PBM=

(

P−P_{A 1}

)

−(P−P_{A 2}) ln

(

P−PA 1 P−PA 2

)

PBM= (101.325−52.3 )−(101.325) ln

(

101.325−52.3 101.325

)

P_BM=72.04 kPa DAB= ρABPBMRT tP M_A

(

P_{A 1}−P_{A 2}

)

(

zf2−zo2 2

)

D_AB=(800.33) (72.04) (8.314) (311.15) (900)(58.08)(101.325) (52.3)

(

0.0532_−0.0512 2

)

D_AB=8.09 X 1 0−5m 2 s TRIAL 2 ETHANOL For 10 minutes D_AB= ρABPBMRT tP M_A

(

P_{A 1}−P_{A 2}

)

(

zf 2 −zo 2 2

)

D_AB=(763.68) (87.2)(8.314 )(321.15) (6 00)(46)(101.325) (26.87)

(

0.05 92_{−0.05 7}2 2

)

D_AB=0.00027 For 15 minutes D_AB= ρABPBMRT tP M_A

₍

P_{A 1}−P_{A 2}

₎

(

zf2−zo2 2

)

DAB= (753.09)(77.87 )(8.314 )(33 1.15) (9 00)(46)(101.325) (42.97)

(

0.0592_{−0.05 3}2 2

)

DAB=0.0004 METHANOL For 10 minutes D_AB= ρABPBMRT tP M_A

₍

P_{A 1}−P_{A 2}

₎

(

zf2−zo2 2

)

D_AB=(766.89)(72.96 4) (8.314 )(3 21.15 ) (6 00)(32)(101.325) (50.87)

(

0.05 82−0.0572 2

)

D_AB=0.00016 For 15 minutes D_AB= ρABPBMRT tP M_A

(

P_{A 1}−P_{A 2}

)

(

zf 2 −zo 2 2

)

D_AB=(756.61)(72.964 )(8.314 )(3 3 1.15) (9 00 )(32)(101.325) (77.897 )

(

0.0582_{−0.05 6}2 2

)

D_AB=0.000098 ACETONE For 10 minutes

Diffusion of Liquids Through Stagnant Non-Diffusing Air D_AB= ρABPBMRT tP M_A

(

P_{A 1}−P_{A 2}

)

(

zf 2 −zo 2 2

)

DAB= (7 59.74) (72.965)(8.314 ) (321.15) (6 00)(58.08)(101.325)(76.11)

(

0.0582 −0.0562 2

)

D_AB=0.000022 B. CHAPMAN-ENSKOG METHOD

Table 4.7 Properties of Volatile Liquid from Perry’s Chemical Engineer’s Handbook 8th _Ed.

Propert

y Methanol Ethanol Acetone

Tb,K 336.71 351.52 329.05 /k 387.22 404.25 387.22 σAB, Ǻ 4.40 3.36 5.70 MW, kg/kmol 32.08 46 58.08 To=kT ❑ Ω=

(

44.54 To−4.909+1.91To−1.575

)

0.1 DAB=

(

1.8583 x 10−7

_{) (}

_T1.5

₎

P σ2_ABΩ

(

1 MA + 1 MB

)

0.5 Pr op er ty M et ha no l Et ha no l A ce to ne Time 10

min min15 min10 min15 min10 min15

To _{0.78 0.80 0.75 0.77 0.78 0.80}

Ω 1.65 1.63 1.69 1.67 1.65 1.63

Diffusivities for Trial 1

Liquid Diffusivity DAB, m2/s 10 minutes T=48˚C 15 minutesT=58˚C Ethanol _{7.86 x 10}−6 _{8 . 28 x 10}−6 Methanol _{1.22 x 10}−5 1.29 x 10−5 Acetone _{4.16 x 10}−6 4.38 x 10−6 TRIAL 1 METHANOL For 10 minutes D_AB=

(

1.8583 x 10 −7

_{) (}

303.151.5

)

(1)(4.40)(1.65)

(

1 32.08+ 1 29

)

0.5 DAB=7.86 x 10 −6m2 s For 15 minutes D_AB=

(

1.8583 x 10 −7

_{) (}

_{3 11.15}1.5

₎

(1)(4.40)(1.6 3)

(

1 32.08+ 1 29

)

0.5 D_AB=8.28 x 10−6m2 s ETHANOL For 10 minutes D_AB=

(

1.8583 x 10 −7

_{) (}

3 03.151.5

)

(1)(3.36)(1.6 9)

(

1 46+ 1 29

)

0.5 D_AB=1.22 x 10−5m2 s For 15 minutes D_AB=

(

1.8583 x 10 −7

_{) (}

_{3 11.15}1.5

₎

(1)(3.36)(1.6 7)

(

1 46+ 1 29

)

0.5 D_AB=1.29 x 10−5m2 s ACETONE For 10 minutes D_AB=

(

1.8583 x 10 −7

_{) (}

_{3 03.15}1.5

₎

(1)(5.70)(1.6 5)

(

1 58.08+ 1 29

)

0.5 D_AB=4.16 x 10−6m2 s D_AB=

(

1.8583 x 10 −7

_{) (}

3 11.151.5

)

(1)(5.70)(1.6 3)

(

1 58.08+ 1 29

)

0.5

DAB=4.38 x 10 −6m2

s

HAZARDS

Among numerous hazards posed by the conduct of this experiment, is minor chemical reagent irritation, scalding acquired from the hot water in the constant water bath and lacerations and wound that can be acquired if the glass apparatuses breaks and is mishandled.

WASTE DISPOSAL

Hot water from the constant temperature water bath needs to be cooled first before discharging it to the drainage system. Organic solvents used must be disposed in the organic waste bottle.

V. CONCLUSION

From this experiment it can be concluded that diffusivity of volatile liquids can be determined using different known methods. However poses slight discrepancies in the results because of certain parameters. In addition, from this experiment it can be learned that the driving force of diffusion is the concentration gradient between the two interfaces.

VI. DOCUMENTATION

The reagents used in the experiment namely (from left to right) Ethanol, Acetone and Methanol

A few of the apparatuses used in this experiment. The iron stand and iron clamp that is used to hold the capillary

tube and thermometer in place just above the constant temperature water bath.

The experimental setup wherein a portable fan is used to force air in the system

Diffusion of Liquids Through Stagnant Non-Diffusing Air

Raviz, James Laurence, Chemical Engineering Department, Technological Institute of the Philippines, Manila, Philippines, 09179744486, (e-mail: [email protected]).