Experiment 9

KKEK2171 Laboratory and Communication I Semester 2, 2013/14
E9. Gas Diffusion
1. Objective
To measure and determine the value vapour diffusion coefficient of

a volatile liquid (e.g. acetone or ethanol) in air at atmospheric pressure and
specific temperature.
2. Introduction
Diffusion is a natural phenomenon where molecules move randomly from

area of high concentration to area of low concentration. Concentration
difference is the main driving force promoting this phenomenon. Diffusion
in gases, liquids and solids occurs naturally or could be induced
artificially. A binary system is the absolute minimum condition required
for diffusion to occur. For example, a freshly open durian fruit would release the
typical durian odour through the air by diffusion.
Diffusion is an important phenomenon for many chemical engineering

processes such as in mass transport and chemical reaction. For
example, diffusion is important in catalytic based chemical reaction where
the rate of diffusion is the rate limiting step for the overall reaction. In
this case, the ability to predict and calculate the diffusion
phenomenon is critical to overall productivity of the process.
2.1 Theory
Diffusion phenomenon can be explained through Ficks Law.

However,
in this experiment only First Ficks Law will be used. First Ficks
Law
states that molar diffusion flux of A into B in a certain direction
(e.g.
horizontally, z) is proportional to negative concentration gradient of A
in that
direction.
J AB,Z - dCA
dz
JAB,Z = molar flux in the z direction

dCA
= concentration gradient in the z-direction
dz
Introduction of a proportional coefficient will transform First Ficks Law

into an equation. The proportionality is known as diffusion coefficient of A into
B, DAB:
1
dCA
J AB,Z = - DAB
dz
If cA = xAc, where xA is the mole fraction of A and c is total molar concentration

of the mixture. Assuming conditions of constant pressure and temperature, the
First Ficks Law can be rewritten as:
2
dCA
J AB,Z = - c DAB
dz
The diffusion coefficient of A into B is not constant. The value of

the diffusion coefficient is dependent of A and B mixture characteristics,
temperature and pressure where diffusion occurs and concentration of A.
The value of DAB is needed for calculations involving mass transfer. If the
diffusion coefficient cannot be predicted it must be measured.
2.2 Bulk Flow and Unimolecular Diffusion.
The theory from previous section assumes that there is no bulk flow of
mixture A and B. Generally, the mixture flow due to pumping energy or
gravity force. In such cases, the flux of A is contributed by diffusion and bulk
flow.
NA,Z = molar flux of A in z-direction
= bulk flow + diffusion
= xANz + JA,Z
Where
xA = mole fraction if A in the mixture
Nz = total molar flux for all component due to bulk flow in z-direction
Moreover, a special case exist where A is moving and B is stationary. This

condition is called unimolecular diffusion. This condition is very useful to
determine the value of diffusion coefficient of molecule A into B.
For unimolecular diffusion, NZ = NZ,A

dx A
(1-x A )NA,Z = - c DAB
dz
c DABdx A
NA,Z = -
(1-x A )dz
3
3 Experimental Procedure
The experiment is based on Winkleman method(Fig. 1).
Materials:
1. Volatile liquid (e.g. acetone)

2. Capillary tube
3. Syringe & beaker
4. Water bath
5. Thermometer
Fig. 1 Winkleman apparatus
The liquid which the diffusion coefficient is to be determined is placed in a

capillary tube. An air flow is passed above the T-junction at constant flow rate.
The air flow at the T-junction causes the concentration of the vapour to low
(almost zero) at the capillary mouth. As a result, a concentration gradient of
the vapour exists and induced diffusion. Since only the vapour diffuses vertically,
unimolecular diffusion exists where the vapour diffuses through a stationary air.
The temperature surrounding the capillary could be kept constant by immersion in

a constant temperature bath. Pressure is assumed to be constant as the system is
open to atmosphere.
When the system reaches steady state, all volatile liquid will diffuse out. By
measuring the rate of fall of liquid level, the diffusion coefficient can be calculated.
4 Experimental Procedure
1) Using a clean syringe, spray the capillary tube with detergent

followed by distilled water. Finally rinse the capillary tube with a
little acetone.
2) Using another syringe, spray slowly liquid acetone into the capillary
tube until liquid level reached almost 40mm of height.
4
3) Slowly insert the capillary tube into the metal nut. Continue until the
top of the tube is seated right above the nut.
4) Slowly, the screw the capillary tube at the plate, with the tail of the
T-shape of the capillary tube submerged in the water bath. The
capillary tube should be perpendicular to the microscope. Switch on
the stirrer ensure the even heating of the water bath. Set the
temperature at 50oC.
5) Adjust the position of the microscope until the capillary tube could be
seen through the microscope.
6) Next, determine the position of liquid acetone meniscus. Adjust the

vernier scale to allow convenient measurements.
7) Connect A tube from an air pump to one of the ends of the capillary T tube.
Switch on the air pump to allow air flow through the capillary tube above the
acetone.
8) Record the initial level of the acetone as z0.
9) After 15 minutes, switch off the air and record the new level of the acetone.
10) Step 9 was repeated for 10 times.
t
11) Plot a graph of vs z - z0 . Calculate the gradient of the graphs and
z + z0
calculate the diffusion coefficient, based on derivations from Ficks First Law.
5. Data Analysis
t
1. Plot a graph of vs z - z0 .
z + z0
5
2. Derive the equation that relate DAB to the slope of the graph.
3. Find the gradient of the graph and calculate the coefficient of

diffusion.
DAB. Explain how the values of other quantities (such as mole
fraction)
were derived.
4. Discuss the experimental results. Compare with published

literature values. What are the sources of errors in this experiment?
6. References
1. Brodkey, R. S. & Hershey, H. C. (1998), Transport Phenomena A

Unified Approach, McGraw-Hill, pp 3340,172.
2. Welty, J. R. & Wicks, C. E. (1984), Fundamentals Of Momentum,
Heat and Mass Transfer, Wiley, pp 483, 780 782.
3. Jos Coca , Julio L. Bueno , Ricardo Alvarez. Gaseous Diffusion
Coefficients by the Stefan-Winkelmann Method Using a Polymer-
Solvent Mixture as Evaporation Source. Ind. Eng. Chem. Fundamen.,
1980, 19 (2), pp 219221.

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KKEK2171 Laboratory and Communication I Semester 2, 2013/14

E9. Gas Diffusion

To measure and determine the value vapour diffusion coefficient of

Diffusion is a natural phenomenon where molecules move randomly from

Diffusion is an important phenomenon for many chemical engineering

Diffusion phenomenon can be explained through Ficks Law.

JAB,Z = molar flux in the z direction

Introduction of a proportional coefficient will transform First Ficks Law

If cA = xAc, where xA is the mole fraction of A and c is total molar concentration

The diffusion coefficient of A into B is not constant. The value of

2.2 Bulk Flow and Unimolecular Diffusion.

Moreover, a special case exist where A is moving and B is stationary. This

For unimolecular diffusion, NZ = NZ,A

The experiment is based on Winkleman method(Fig. 1).

1. Volatile liquid (e.g. acetone)

Fig. 1 Winkleman apparatus

The liquid which the diffusion coefficient is to be determined is placed in a

The temperature surrounding the capillary could be kept constant by immersion in

1) Using a clean syringe, spray the capillary tube with detergent

6) Next, determine the position of liquid acetone meniscus. Adjust the

8) Record the initial level of the acetone as z0.

10) Step 9 was repeated for 10 times.

3. Find the gradient of the graph and calculate the coefficient of

4. Discuss the experimental results. Compare with published

1. Brodkey, R. S. & Hershey, H. C. (1998), Transport Phenomena A

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