Technological Institute of the Philippines – Manila CHE – 502 Unit Operations Laboratory 2, 1st Semester SY 2016-2017
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 nondiffusing 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.
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:
This experiment focuses also on the temperature dependence of diffusivity and thus the rate of diffusion of liquids through stagnant nondiffusing 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.
ρ A PBM RT z 2f −z 20 D AB= 2 tP M A ( P A 1−P A 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 z o 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
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.
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.
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
The final relation for predicting the diffusivity of binary gas pair A and B molecule is: 1
Diffusion of Liquids Through Stagnant Non-Diffusing Air
1.8583 x 10−7 1 1 D AB=¿ (T 1.5 ) ¿2 + P σ AB Ω M A M B
(
0.5
X
)
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
Close the other end of the capillary tube and fill it with pure volatile liquid
Measure the initial height of the liquid
II. EQUIPMENT AND APPARATUS Provide gentle stream of air using a fan
Apparatus: Constant Water Bath Thermometers Iron Stand Iron Clamp Cork Capillary Tube Vernier Caliper Portable Electric Fan Stopwatch
Provide gentle stream of air using a fan
Materials: Ethanol Methanol Acetone
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
III. PROCEDURE/ METHODOLOGY START
Compare the result with those obtained using Chapmann-Enskog and other empirical formula Prepare the constant Water Bath and Set it to END X
2
Technological Institute of the Philippines – Manila CHE – 502 Unit Operations Laboratory 2, 1st Semester SY 2016-2017
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 Ethanol Methanol Acetone
59mm 58mm 53mm
-
58mm 57mm 52mm
30 30 30
Liquid
ho
Ethanol Methanol Acetone
59mm 55mm 55mm
-
57mm 53mm 54mm
T=58˚C 0.00045 0.000098 -
CALCULATIONS TRIAL 1
T,C
57mm 56mm 51mm
38 38 38
ETHANOL For 10 minutes:
Table 4.2 Height of liquid in the capillary Trial 2 T=65˚C T,C h10
T=48˚C 0.00027 0.00016 0.000022
Ethanol Methanol Acetone
PBM =
( P−P A 1 )−(P−P A 2) ln
T,C
h15
T,C
48 48 48
53mm 52.5 53mm
58 58 58
PBM =
(
P−P A 1 P−P A 2
)
( 101.325−19.53 )−(101.325) 101.325−19.53 ln 101.325
(
)
A. CAPILLARY TUBE METHOD
Table 4.3 Properties from Perry’s ChE Handbook Liquid Ethanol Methanol Acetone
Density, kg/m3 781.36 784.74 780.58
775.34 776.90 800.33
PBM =95.98 kPa
Vapor Pressure, kPa 10.53 16.23 21.76 32.18 37.95 52.30
Table 4.4 Diffusivities Computed for Trial 1 Liquid
Ethanol
Diffusivity DAB, m2/s 10 minutes 15 minutes T=30˚C T=38˚C 0.000367 0.000318
Methanol
0.000241
0.000205
Acetone
6.24X10-5
8.09 X10-5
Ethanol Methanol Acetone
Density, kg/m3 763.68 766.89 759.74
754.69 756.61 747.53
D AB=
( 781.36 ) ( 95.98 ) ( 8.314 ) ( 303.15 ) 0.0592 −0.0582 ( 600 )(46) ( 101.325 )( 10.53 ) 2
(
) (
For 15 minutes
PBM =
( P−P A 1 )−(P−P A 2) ln
Vapor Pressure, MPa 26.871 42.793 50.866 77.897 76.11 107.945
PBM =
Table 4.6 Diffusivities Computed for Trial 2 Liquid
ρ AB PBM RT z 2f −z 2o 2 tP M A ( P A 1−P A 2 )
m2 D AB=0. 000367 s
Table 4.5 Properties from Perry’s ChE Handbook Liquid
D AB=
Diffusivity DAB, m2/s 10 minutes 15 minutes
(
P−P A 1 P−P A 2
( 101.325−16.22 ) −(101.325) 101.325−16.22 ln 101.325
(
PBM =93.01kPa 3
) )
)
Diffusion of Liquids Through Stagnant Non-Diffusing Air
PBM = ρ AB PBM RT z 2f −z 2o D AB= 2 tP M A ( P A 1−P A 2 )
(
D AB=
)
( 101.325−32.18 )−(101.325) 101.325−32.18 ln 101.325
(
)
PBM =84.21kPa
2 2 ( 775.34 ) ( 93.01 ) ( 8.314 ) ( 311.15 ) 0.0592−0.057 2 ρ AB PBM RT z f −z o D = AB ( 900 )(46) (101.325 )( 16.22 ) 2 2 tP M A ( P A 1−P A 2 )
(
D AB=0.000318
m s
)
(
2
D AB=
( 776.90 ) ( 84.21 )( 8.314 )( 311.15 ) 0.0582 −0.0562 ( 900 )( 32) ( 101.325 )( 32.18 ) 2
(
METHANOL
D AB=0. 000205
For 10 minutes
PBM =
PBM =
( P−P A 1 )−( P−P A 2) P−P A 1 ln P−P A 2
(
)
m2 s
For 10 minutes
PBM =
( 101.325−21.76 )−(101.325) 101.325−21.76 ln 101.325
(
PBM =
ρ AB PBM RT z 2f −z 2o 2 tP M A ( P A 1−P A 2 )
(
( P−P A 1 )−(P−P A 2) ln
)
)
(
P−P A 1 P−P A 2
)
( 101.325−37.95 )−(101.325) 101.325−37.95 ln 101.325
(
)
PBM =80.87 kPa
( 784.74 ) ( 89.99 ) ( 8.314 ) ( 303.15 ) 0.058 2−0.0572 ρ AB PBM RT z 2f −z 2o D AB= D AB= ( 600 ) (32) ( 101.325 ) ( 21.76 ) 2 2 tP M A ( P A 1−P A 2 )
(
D AB=0. 000241
)
m2 s
(
D AB=
D AB=6.24 X 1 0−5
( P−P A 1 )−( P−P A 2) ln
(
P−P A 1 P−P A 2
)
For 15 minutes:
4
)
( 780.58 ) ( 80.87 ) ( 8.314 ) ( 303.15 ) 0.0532 −0.0522 ( 600 ) (58.08) ( 101.325 ) ( 37.95 ) 2
For 15 minutes:
PBM =
)
ACETONE
PBM =89.99 kPa
D AB=
)
(
m2 s
)
Technological Institute of the Philippines – Manila CHE – 502 Unit Operations Laboratory 2, 1st Semester SY 2016-2017
PBM =
( P−P A 1 )−( P−P A 2) ln
PBM =
(
P−P A 1 P−P A 2
( 753.09 )( 77.87 )( 8.314 )( 33 1.15 ) 0.0592−0.05 32 D AB= ( 9 00 ) ( 46) ( 101.325 ) ( 42.97 ) 2
(
)
D AB=0.0004
( 101.325−52.3 )−(101.325) 101.325−52.3 ln 101.325
(
)
PBM =72.04 kPa ρ AB PBM RT z 2f −z 2o D AB= 2 tP M A ( P A 1−P A 2 )
(
METHANOL
)
For 10 minutes
( 800.33 ) ( 72.04 ) ( 8.314 ) ( 311.15 ) 0.0532−0.0512 D AB= ( 900 ) (58.08) ( 101.325 ) ( 52.3 ) 2
(
D AB=
ρ AB PBM RT z 2f −z 2o 2 tP M A ( P A 1−P A 2 )
D AB=
( 766.89 )( 72.96 4 ) ( 8.314 )( 3 21.15 ) 0.05 82−0.05 ( 6 00 ) (32) ( 101.325 ) ( 50.87 ) 2
)
m2 D AB=8.09 X 1 0 s
(
) (
−5
D AB=0.00016 TRIAL 2 ETHANOL
For 15 minutes
For 10 minutes
ρ AB PBM RT z 2f −z 2o D AB= 2 tP M A ( P A 1−P A 2 )
(
)
ρ AB PBM RT z 2f −z 2o D AB= 2 tP M A ( P A 1−P A 2 )
(
( 763.68 ) ( 87.2 )( 8.314 )( 321.15 ) 0.05 92−0.05 7 2 D AB= ( 6 00 ) ( 46) ( 101.325 ) ( 26.87 ) 2
(
) D AB=
D AB=0.00027
D AB=
( 756.61 )( 72.964 )( 8.314 )( 3 3 1.15 ) 0.0582−0.05 6 ( 9 00 ) (32) ( 101.325 ) (77.897 ) 2
D AB=0.000098
For 15 minutes
(
2
2
ρ AB PBM RT z f −z o 2 tP M A ( P A 1−P A 2 )
)
ACETONE For 10 minutes
5
) (
Diffusion of Liquids Through Stagnant Non-Diffusing Air
(
2
2
ρ AB PBM RT z f −z o D AB= 2 tP M A ( P A 1−P A 2 )
D AB=
Methanol Acetone
)
1.22 x 10−5 4.16 x 10−6
2 ( 7 59.74 ) ( 72.965 )( 8.314 ) ( 321.15 ) 0.0582−0.056TRIAL 1 ( 6 00 ) (58.08) ( 101.325 )( 76.11 ) 2 METHANOL
(
)
For 10 minutes
D AB=0.000022
D AB=
( 1.8583 x 10−7 ) ( 303.151.5 ) (1)(4.40)(1.65)
B. CHAPMAN-ENSKOG METHOD
−6
D AB=7.86 x 10
Table 4.7 Properties of Volatile Liquid from Perry’s Chemical Engineer’s Handbook 8th Ed. Propert Methanol Ethanol Acetone y Tb,K 336.71 351.52 329.05 387.22 404.25 387.22 /k σAB, Ǻ 4.40 3.36 5.70 MW, 32.08 46 58.08 kg/kmol
D AB=
o−4.909
+1.91T
D AB=
o−1.575 0.1
)
1.5
( 1.8583 x 10 ) ( T ) 1 1 + 2 P σ AB Ω
(M
A
MB
)
0.5
)
m2 s
15 min 0.80 1.63
10 min 0.75 1.69
15 min 0.77 1.67
10 min 0.78 1.65
15 min 0.80 1.63
2
m s
(1)(3.36)(1.6 7)
0.5
( 46 29 )
m2 s
ACETONE For 10 minutes
Diffusivities for Trial 1 Liquid
Diffusivity DAB, m2/s 10 minutes 15 minutes T=48˚C T=58˚C −6
( 46 29 )
( 1.8583 x 10−7 ) ( 3 11.151.5 ) 1 1 +
D AB=1.29 x 10−5
D AB=
7.86 x 10
(1)(3.36)(1.6 9)
0.5
For 15 minutes
Acetone
Ethanol
Methanol
Property
(
( 1.8583 x 10−7 ) ( 3 03.151.5 ) 1 1 +
D AB=1.22 x 10−5
0.5
D AB=
Ethanol
(1)( 4.40)(1.6 3)
1 1 + 32.08 29
For 10 minutes
−7
To Ω
)
ETHANOL
Ω=( 44.54 T
10 min 0.78 1.65
0.5
2
( 1.8583 x 10−7 ) ( 3 11 .151.5 )
D AB=8.28 x 10−6
kT T = ❑
D AB=
m s
(
1 1 + 32.08 29
For 15 minutes
o
Time
1.29 x 10−5 4.38 x 10−6
( 1.8583 x 10−7 ) ( 3 03.151.5 ) (1)(5.70)(1.6 5)
D AB=4.16 x 10−6
−6
8 . 28 x 10
D AB= 6
(
1 1 + 58.08 29
(
1 1 + 58.08 29
)
0.5
2
m s
( 1.8583 x 10−7 ) ( 3 11.151.5 ) (1)(5.70)(1.6 3)
0.5
)
Technological Institute of the Philippines – Manila CHE – 502 Unit Operations Laboratory 2, 1st Semester SY 2016-2017
D AB=4.38 x 10−6
2
m 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.
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.
VI. DOCUMENTATION
The experimental setup wherein a portable fan is used to force air in the system The reagents used in the experiment namely (from left to right) Ethanol, Acetone and Methanol
7
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]).
8
