Diffusion of Acetone in Air
Bryan John (50%)
Jeremy Alley (50%)
Alley, John 2
Table of Contents(check short report format)
I. Abstract(usually put abstract before TC, no page #s, etc. also)
1
II. Background
4
III. Experimental Methods
4
IV. Discussion of Results
5
V. Conclusions and Recommendations
12
Figures and Tables
Figure 1
6
Figure 2
6
Figure 3
7
Table 1
9
Appendices
Appendix A (Nomenclature and Sample Calculations)
Appendix B (Excel Spread Sheets)
Bibliography
Alley, John 3
Abstract (3 C’s: Clear, Concise , Complete)
A molecular diffusion experiment (redundant w/ last sentence. . concise)was
conducted with the goal of determining the diffusion coefficient of acetone into air. For
this experiment, acetone was placed in a 3mm OD, 2mm ID . . (is that correct?) NMR
tube? e and was allowed to diffuse into non-diffusing air that was passed over the test
tube. The air that passed over the tube was from natural circulation in the room and no
air was forced over the top of the test tube. The diffusion occurred over a period of
approximately eight hours, with readings taken each hour. The diffusion coefficient was
calculated to be 0.098 + 0.02 cm2/s at T = ? Our results were compared using the
Chapman-Enskog equation as well as the Fuller, Schettler, and Giddings method. The
diffusion coefficient calculated by the Chapman-Enskog was 0.990 + 0.001 cm2/s and the
result of the Fuller, Schettler, and Giddings method was 0.104 + .002 cm2/s. The
literature value found in Perry’s Chemical Engineer’s Handbook was 0.125 + 0.00 cm2/s.
(at T = ?. . .or extrapolated from?) The agreement of our method with the other methods
available for calculating the diffusion coefficient was very good (how good is “very”
good. ..significant discrepencies or not?), and also agreed well with the literature value
found. This led to a conclusion that this method of determining the diffusion coefficient
of acetone into air can be aconsidered a reasonably reliable method.
Alley, John 4
BACKGROUND
Molecular diffusion is the transfer or movement of individual molecules through a
fluid by random molecular movements (Geankoplis, year of publication). In the diffusion
process, the molecules of interest flow from regions of high concentration to low
concentration. Molecular diffusion can occur in both directions with the system. In the
case of the diffusion tube experiment, however, acetone diffuses through non-diffusing
air, which is passed over the top of the test tube containing the acetone. The air is
allowed into the test tube, but does not diffuse into the acetone.
Molecular diffusion of gases has been studied for many years. Molecular
diffusion is a mass transport process Motivation for its study comes from the fact that
chemical separation processes such as distillation, drying, ion exchange systems as well
as many other processes depend on molecular diffusion (Kirk-Othmer Vol 8, p 149(check
format)
EXPERIMENTAL METHODS
For the performance of this experiment, aBe specific. . how small, starting height,
diam, etc. This test tube was then vertically placed in a 10mL graduated cylinder which
contained small beads. The purpose of the beads was to ensure that the test tube
remained vertical. This assembly was then placed on a digital scale. The amount of air
movement provided by the ventilation system was assumed to be adequate so as to ensure
that the concentration of the acetone at the top of the tube was zero. An initial acetone
level in the test tube was taken, as well as the mass of the assembly and the temperature
of the area surrounding the assembly. After this initial data was taken, the area
Alley, John 5
temperature and mass of the assembly were taken approximately every hour for the next
eight hours. The final level of the acetone in the test tube was taken when the final
temperature and mass reading were taken.
DISCUSSION OF RESULTS
From the data collected from the experiment, the diffusion coefficient was calculated
using equation 6.2-26 from Geankoplis:
t
 A ( z 2 f  z 2 0 ) RTp BM
2M A D AB P( p A1  p A2 )
(Equation 1)
As the z value was only recorded at the beginning and the end of the experiment, the
intermediate values of z had to be calculated. The following equation was used for the
calculation of the intermediate z values:
zt 
(m0  mt )
 z0
AA
(Equation 2)
Thus, all values but DAB were known and could be plotted versus time to obtain a linear
plot. By rearranging equation 1, it can be seen that the slope of this plot will be equal to
1/ DAB :
t (
1  A ( z 2 f  z 2 0 ) RTp BM
)(
)
DAB
2M A P( p A1  p A2 )
(Equation 1.1)
The initial plot of data which includes all points is shown below in Figure 1. This
plot contains all points and has an R2 value of 0.9478. From this plot the molecular
diffusivity coefficient was determined to be 0.108 + 0.022 cm2/s.
Alley, John 6
t vs x
30000.00
25000.00
20000.00
t
15000.00
10000.00
5000.00
0.00
-5000.00 0
0.05
0.1
0.15
0.2
0.25
0.3
x
Figure 1: First plot of data in Equation 1
The second point in the data (t=2700s) showed no diffusion occurred in the first
45 minutes, which seems unlikely (yes, good- sensitivity of balance, etc) If this point is
taken as erroneous, the R2 value goes up to 0.9639 (more important here will be the
confidence interval on the slop. . .get that from Tools- Data Analyis-Regression menu in
Excel or else in Polymath or TableCureve, etc) and the molecular diffusivity calculates
out to be 0.098 + 0.021 cm2/s. The plot of the experimental data excluding the second
point is presented below in Figure 2.
t vx x
30000
25000
20000
t
15000
10000
5000
0
-5000 0
0.05
0.1
0.15
x
0.2
0.25
0.3
Alley, John 7
Figure 2: Second plot of data in Equation 1. . forcing through zero point is good. . .looks to me
like first FOUR points would give a lower Dab then the last 4. Problems with next 3 that lie below line?
Anytihing suspicious happening here?
To determine the time it takes for the system to reach steady state, the following
equation can be used to calculate the fraction of steady state the system is at:

( N A )t
 1  2e
( N A ) t 
Dzt2t
zo2
 2e

4 Dzt2t
zo2
 2e

9 Dzt2t
zo2
 2e

16 Dzt2t
zo2
 2e

25 Dzt2t
zo2
(Equation 3)
By plotting the value of ((NA)t/(NA)t=∞) versus time, the curve in Figure 3 was generated
which demonstrates the systems approach to steady state. Wow, great! Cite source. (still
wonder about SST conditions of 1st 4 pts though. . .
((NA)t/(NA)t=∞) vs t
((NA)t/(NA)t=∞)
1.20E+00
1.00E+00
8.00E-01
6.00E-01
4.00E-01
2.00E-01
0.00E+00
0
100
200
300
400
500
t (min)
Figure 3: Fraction of steady state versus time
From this plot, it could be said that the system achieves steady state in 115
minutes; however, there is strong evidence this may not be accurate. As mentioned
earlier, the second point may be erroneous. This would change the path of the curve. In
addition, data was not collected at a high enough frequency for this curve to be highly
accurate at predicting the time to steady state. If in fact the second point is erroneous, the
Alley, John 8
system could have come to steady state well before 115 minutes. This time of 115
minutes at best, could be the upper bound (or lower bound according to Whitaker’s
criteria in his article (handout). . .not sure!!for the time it takes for the system to come to
steady state.
The scatter in the data can be attributed to various factors in the experiment. The
scatter could be attributed to the changes in temperature, as the temperature did fluctuate
slightly through the duration of the experiment – Good!. At what time did it stabilize?
The change in temperature would cause a change in the partial pressure of the acetone
leading to further deviations. In addition, there was no measure of airflow past the tube.
Changes in the airflow could also have contributed to the scatter as it could effect the
concentration of the acetone at the top of the test tube (Good!)
The diffusion coefficient was also calculated using the Chapman Enskog
equation,
DAB 
1.8583 *10 7 T 3 / 2 1
1 1/ 2
(

)
P AB D , AB
MA MB
(Equation 4)
and the Fuller, Schettler and Giddings method.
DAB 
1.00 *10 7 T 1.75 (1 / M A  1 / M B )1/ 2
P[(v A )1/ 3  (vB )1/ 3 ]2
(Equation 5)
A literature value was also found for acetone at ?? K(check Perrys), which was corrected
to our experimental temperature using the correlation
DAB 2  DAB1
T21.75
T11.75
(Equation 6)
Alley, John 9
The values obtained with these methods as well as those from the experimental data are
presented in Table 2.
+ (cm2/s)
0.0213
0.0017
should
prob. Use
your given
Fuller Schettler and
(approx. 8%
Table 1: Values of molecular diffusivity0.1044
coefficients found.**
Giddings
and ?%
Chapman Enskog
0.0989
0.0015
Literature
0.125 ?
Experimental Plot
Value(cm2/s)
0.0981
** A very good way to show this graphically in Excel would be to use a bar graph showing the values of
Dab as height of a bar by method used, and error bars to easily demonstrate any overlap of uncertainty,
discrepancy, etc. Example:
Calculated Diffusivity
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
Data
Fuller Schettler and Chapman Enskog
Giddings
Literature
Method
The Chapman Enskog method is accurate within 8% and the Fuller Schettler and
Giddings value has a lower accuracy than the Chapman Enskog (Geankoplis 425). The
Chapman Enskog value is less than 1% different than the experimental value and the
Fuller Schettler and Giddings value only about 6% different. From this analysis, it seems
Alley, John 10
these equations predicted the experimental value very well. These calculated values are
about 20% lower than the literature value. This variance may come from the inconsistent
temperature in the room or from pressure fluctuations in the room caused perhaps by the
starting and stopping of the HVAC systems.
For the derivation of Equation 1, several assumptions are made. Beginning with
the general equation (Geankoplis 6.2-14):
N A  cD AB
dx A c A
 N A  N B 
dz
c
(Equation 7)
One assumption was that because the case examined was a diffusing A (acetone) into
non-diffusing B (air), the diffusion flux of air into the acetone (NB) was equal to zero.
Another assumption made was that since the total pressure was low, the acetone gas
diffusing into air was an ideal gas. This allowed for the term c to be replaced with its
ideal gas equivalent, P/RT. Additionally, the air passing over the test tube was assumed
to contain no water vapor. An average air velocity that was uniform was passing over the
acetone containing test tube was also assumed.
There are non-idealities that exist in the molecular diffusion of acetone into air.
Some of these non-idealities are corrected for in the journal from Lee and Wilke.
Acetone displays surface tension effects which, instead of having a perfectly horizontal
liquid surface, give the liquid acetone a slightly downward curved liquid level. Because
of this curvature, the actual diffusion path length that the acetone travels is smaller than
what the diffusion length would appear to be based on center liquid level or calculated
liquid volume (Lee 2384).
Alley, John 11
Along with a non ideal liquid surface, the air passing over the open end of the tube may
cause some turbulence to exist in the top portion of the tube. With its existence, the
turbulent area of the tube will cause a length to exist inside the tube where the
concentration of acetone is zero. With the presence of this acetone vapor-free region, the
diffusion length is again shorter than it would appear to be.
To account for the non-idealities in the diffusion process, Lee and Wilke do not
use the apparent diffusion path. Instead, they use an effective average diffusion path
which they give by:
x  xa  xs  xe  xa  x
(Equation 8)
Where x is the effective average diffusion path, Δxs is the length of the curvature of the
non-ideal liquid to account for the surface tension forces, Δxe is the length of the tube
where the acetone vapor-free region exists due to turbulence that exists from the passage
of the air, and Δx is the sum of Δxs and Δxe (Lee 2384). When this is substituted back
into the diffusion equation, it becomes the following:
NA 
Da Pp
DPp

RTp a 2 x a RTp f x a  x 
(Equation 9)
Where Da is the apparent diffusion coefficient and D is the true diffusion coefficient
based on the true diffusion path (Lee 2384). The way our experiment was setup, the
driving force for the air across the test tube was natural air flow and did not employ
forced air flow. Because of this, the length of the tube where the turbulence existed in
the Lee and Wilke journal would most likely not have been present in our experiment.
Alley, John 12
Also, the initial liquid acetone level selected in our experiment was such that the length
of the curvature due to the surface tension forces on the acetone would have been
negligible when compared to the apparent diffusion length of the tube.
The initial height of the liquid in the tube for this experiment was chosen wisely.
The reason for this is that with the initial level that was chosen, a sufficiently long
diffusion path existed such that the non-idealities that were accounted for in the Lee and
Wilke journal entry would have had a very insignificant impact on the results of our
experiment.
CONCLUSIONS AND RECOMMENDATIONS
From the data collected an analyzed, it has been determined that the experimental
procedure used here can determine the molecular diffusivity coefficient with some level
of accuracy. For future experiments, some form of air flow regulation should be
investigated. Something as simple as a room fan could be placed next to the scale to
ensure a more constant air flow. Another increase in accuracy could be achieved by
regulating the temperature with more consistency. If the experiment could be performed
in a large insulated room, the temperature may not vary as much.
Good job on Discussion, Conclusions, etc. . .to improve maybe expand to relate what
YOU think are the main ‘uncertaintys’ that caused problems in YOUR PARTICULAR
CASE and show eVIDENCE TO SUPPORT.
-DM
Alley, John 13
Alley, John 14
NOMENCLATURE & CALCULATIONS