Department of Chemical & Biomolecular Engineering
THE NATIONAL UNIVERSITY of SINGAPORE
Chemical Engineering Process Laboratory II
Experiment M2
Determination of Liquid Diffusion Coefficient
Name : Erick Hadinata A0169493M
Tay Hong Wei A018
Muhammad Daniaal A018
Group : 4
Date of Expt. : 1st April 2019
GRADE :
Objective
The objective of the experiment is to determine the diffusion coefficient of
acetone vapour at different temperature.
Theory
In this experiment, Winklemann’s method will be used to determine the
diffusivity of volatile liquid which we used acetone in this case. Liquid is
contained in a narrow diameter vertical tube, maintained at a constant
temperature and an air stream is passed over the top of the tube to ensure
that the partial pressure of the vapor is transferred from the surface of the
liquid to the air stream by molecular diffusion.
The rate of mass transfer if given by
C C
N ' A D A T (Equation 1)
L C BM
Where
CA Saturation concentration at interface ( kmol / m 3 )
3
C BM Log mean molecular concentration of vapor ( kmol / m )
C B1 C B 2
C BM
C
ln B1
CB2
CT Total molar concentration
L Effective distance of mass transfer (mm)
D Diffusivity ( m 2 / s )
Considering the evaporation of the liquid,
dL
N A' L (Equation 2)
M dt
From Equation 1 & 2 for mass balance, we have
L dL C A C T
D
M dt L C BM
Integrating and putting L=L0 at t=0
2 MD C A CT
L2 L20 t
L C BM
Plotting
C L C BM
L BM L L0
t
L0
L L0 2 MD C A CT MD C A CT
The slope can be found as
L C BM
S
2 MD C A CT
L C BM
D
2 MS C A CT
Therefore, the diffusivity can be calculated.
Apparatus
Gas dispersion or gaseous coefficient apparatus
Water bath
Microscope
Capillary tube
Thermometer
Acetone
Experiment Procedure
Temperature controller
Capillary tube
Air pump switch
Vernier scale
Microscope Heater switch
A capillary tube was filled with acetone by using syringe.
The air pump and water bath temperature was switched on.
The air pump was tested and adjusted.
The water temperature was set up to 40oC and wait until the steady
temperature was reached.
The capillary tube was then put inside the water bath and the air pump
tube was placed on other side of the capillary tube.
The height of the microscope was adjusted until the capillary tube is
visible. If the capillary tube is visible, the distance from the object lens to
the tank is adjusted.
The position of sight microscope lens was adjusted in or out of the
microscope body in order to get clear view of the meniscus inside the
capillary tube.
When viewing the meniscus. Take note that the image seen is inverted
The level inside the capillary tube (L) was recorded at t = 0 min and every
30 minutes and take minimum four reading which is at 30,60,90 and 120
minutes
The experiment is repeated at temperature of 50oC.
Tabulation & Calculation
Table 1: Experimental Data – operational temperature 40oC
Height of
Liquid Height of
Liquid t
Time (t) Time (t) Meniscus Liquid ( L Lo)
Evaporated
min sec Reading x Evaporated
[(L – Lo) x sec/m
0.75 (mm) (m)
0.75] (mm)
0 0 1.05 0 0 0
30 1800 2.14 1.09 0.00109 1651376
60 3600 3.08 2.03 0.00203 1773399
90 5400 3.98 2.93 0.00293 1843003
120 7200 4.88 3.83 0.00383 1879896
Table 2: Experimental Data – operational temperature 50oC
Height of
Liquid Height of
Liquid t
Time (t) Time (t) Meniscus Liquid ( L Lo)
Evaporated
min sec Reading x Evaporated
[(L – Lo) x sec/m
0.75 (mm) (m)
0.75] mm
0 0 0.75 0 0 0
30 1800 2.29 1.54 0.00154 1168831
60 3600 3.60 2.85 0.00285 1263158
90 5400 4.80 4.05 0.00405 1333333
120 7200 6.00 5.25 0.00525 1371429
Given Acetone Physical Properties at 40oC
Determination of molar mass at 40oC
1 Tabs
CT
Kmol Vol Ta
1 273.313
=
22.4 40 273.313
kmol
= 0.0389
m3
CB1 CT
kmol
= 0.0389
m3
P
C A v CT
Pa
56
= 0.0389
101.3
kmol
= 0.0215
m3
P Pv
C B 2 a CT
Pa
101.3 56
= 0.0389
101 .3
kmol
= 0.0174
m3
C A 2 CT CB 2
= (0.0389 – 0.0174)
kmol
= 0.0215
m3
CB1 CB 2
CBM
C
In B1
CB 2
0.0389 0.0174
= 0.0389
ln
0.0174
kmol
= 0.0267
m3
Determination of slope s of resultant curve at 40oC
(L – Lo) m 0.00109 0.00203 0.00293 0.00383
t
( L Lo) 1651376 1773399 1843003 1879896
sec/m
𝑡/(𝐿−𝐿𝑜) vs (L-Lo)
1950000
1900000
1850000
1800000
t/(L-Lo)
𝑡/(𝐿−𝐿𝑜) vs (L-Lo)
1750000
y = 8E+07x + 2E+06
1700000 R² = 0.9444
1650000
1600000
0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 0.0045
(𝐿−𝐿𝑜)
L C BM L C BM
Slope S = 8 x 107 = or D =
2 MD C A CT 2sM C A CT
760×0.0267
D =( )
2×(8×107 )×58.08×0.0215×0.0389
= 2.61 × 10−6 m2/s
Given Acetone Physical Properties at 50oC
*Note: The vapour pressure given above is incorrect so we can determine the
vapour pressure by using Antoine Equation
Antoine Equation: ln P = A –
B
T C
For Acetone,
A = 14.3145
B = 2756.22
C = 228.060
At 50oC
2756.22
ln P = 14.3145 –
50 228.060
P = 81.6 kN / m2
Determination of molar mass at 50˚C
1 Tabs
CT
Kmol Vol Ta
1 273.303
=
22.4 50 273.303
kmol
= 0.0377
m3
CB1 CT
kmol
= 0.0377
m3
P
C A v CT
Pa
81.6
= 0.0377
101.3
kmol
= 0.0304
m3
P Pv
C B 2 a CT
Pa
101.3−81.6
=( ) (0.0377)
101.3
𝑘𝑚𝑜𝑙
= 0.00733
𝑚3
C A 2 CT CB 2
= (0.0377 − 0.00733)
𝑘𝑚𝑜𝑙
= 0.0304
𝑚3
CB1 CB 2
CBM
C
In B1
CB 2
0.0377−0.00733
=( 0.0377 )
𝑙𝑛( )
0.00733
𝑘𝑚𝑜𝑙
= 0.0497
𝑚3
Determination of slope s of resultant curve at 50oC
(L – Lo) m 0.00154 0.00285 0.00405 0.00525
t
( L Lo) 1168831 1263158 1333333 1371429
sec/m
𝑡/(𝐿−𝐿𝑜) vs (L – Lo)
1400000
1350000
1300000
𝑡/((𝐿−𝐿𝑜))
1250000 y = 6E+07x + 1E+06 𝑡/(𝐿−𝐿𝑜) vs (L – Lo)
R² = 0.9731 Linear (𝑡/(𝐿−𝐿𝑜) vs (L – Lo) )
1200000
1150000
1100000
0.001 0.002 0.003 0.004 0.005 0.006
(𝐿−𝐿𝑜)
L C BM L C BM
Slope S = 6 x 107 = or D =
2 MD C A CT 2sM C A CT
775×0.0497
D =( )
2×(6×107 )×58.08×0.0304×0.0377
= 4.82× 10−6 m2/s
Discussion
Vapor pressure, PV 56 ( kN / m ) at T=40˚C is given, when the temperature
2
of the acetone, vapor pressure should increase with the increasing
temperature. However, according to appendix in the reference book (Refer to
the Reference part of the report), vapor pressure at T=50˚C was given as
PV 40 ( kN / m 2 ), which is wrong according to the correlation between
vapour pressure and temperature. In this case, Antoine Equation
B
ln P A is then used to calculate PV at T=50˚C.
T C
From the experimental data obtained, the diffusivity of acetone vapour were
calculated for 40˚C and 50˚C:
Temperature Diffusivity
40˚C 2.61 × 10−6 m2/s
50˚C 4.82× 10−6 m2/s
From the table above, it can be observed that the value of diffusivity is directly
proportional to the temperature. The higher the temperature is, the diffusivity
of the acetone vapour will also increase. Diffusion is the motion of molecules
that moves from a region of higher liquid concentration to a region of lower
liquid concentration and the motion is also further increased by the increase in
temperature due to a higher temperature, the kinetic energy generated by
molecules is also higher which also will excite the molecules more, increasing
the overall diffusivity of the acetone vapour.
The temperature range used in this experiment is between 40 to 50 degree
Celsius which is sufficient and suitable temperature test condition. As we
know, the boiling point of acetone is 56.5˚C and if we did the experiment at
the temperature above the boiling point of acetone then the diffusivity that we
obtained by calculation might not be feasible. This is because of the physical
properties and nature of the acetone which is considered volatile. An increase
in pressure will have a significant effect on the overall volatility of the acetone
solution. Since increase in temperature also means that the increase in
pressure, then increase in temperature also effects the overall volatility of the
solution. Therefore, the temperature value selected for the conduct of the
experiment must not exceed the boiling point of the acetone because it will
increase the volatility properties of acetone which will affect the accuracy of
the meniscus reading.
Error Analysis
The scale of the microscope is very small and the line marking scale of
every 1mm (0.75mm for the vernier scale) were close to each other and
also the eye position of the person reading the scale is important. The
eyesight should be parallel to the scale which might contribute to
parallax error.
The liquid in the narrow tube was moving at a speed that is very difficult
to measure even by using the microscope to observe the liquid level in
the tube and by the time the meniscus height values were taken, they
were not the actual values that corresponded to the time as there were
delays in taking the reading (phone camera focus adjustment contribute
to the time lapses) which contributed to the inaccuracy in calculating
t
as the time taken were not exactly at 30, 60, 90 and 120
( L Lo)
minutes which in this case we assumed that the time taken were exactly
at every 30 minutes to ease calculations
Two different instruments were used for T= 40˚C and 50˚C, which might
have some deviations in terms of thermostat calibration curve which
definitely is different from one to another
Conclusion
It can be concluded that temperature directly affects the rate of diffusion of
the acetone vapour. Diffusion will happen at a faster rate when the
surrounding temperature is higher. Increase in temperature explains that there
is more kinetic energy generated by the molecules, causing molecules to move
at a faster rate and faster spreading of molecules over to the air, which also
means higher diffusion rate Therefore, the higher the temperature, the higher
the diffusivity of the vapour. The conclusion made is correct as supported by
the calculations that the diffusivity of the acetone at 40 degree is lower as
compared to at 50 degree which values are 2.61 × 10−6 m2/s and 4.82× 10−6
m2/s.
Reference
Welty, J.R., Wicks, C.E., Wilson, R.E., Fundamentals of Momentum, Heat
and Mass Transfer, John Wiley and Sons, New York, NY (1984).
Christie John Geankoplis (University of Minnesota), Transport Processes
and Separation Process Principles (Includes Unit Operations) – fourth
edition, Pearson Education International.
