Diffusion Tube Experiment
Introduction
This experiment is similar to that described by Lee and Wilke. The theory for the special
case of “species A” diffusing through stagnant “species B” is detailed in Geankoplis. In
our case we will be using acetone as our diffusing species “A”, and dry air as our
“stagnant” species “B”. Dry air is passed over an NMR tube with an inside diameter of
4.20+/-0.025 mm. A cathetometer is used to visually track liquid levels over time.
Constant air flow is from house air that is reduced in pressure by flowing through a 0-10
psig pressure regulator. The air flow is measured with a wet-test meter and then passed
through a drying tube. A 40 foot long copper coil immersed in the bath brings the air to
bath temperature before it enters the manifold. The manifold is constructed of copper to
further assure constant air temperature.
Figure 1- Diffusion apparatus. Flowrate is measured with the wet-test meter. Air is dried by passing
through a drying tube filled with DriRite absorbent. The tubing and manifold are made of copper to
heat the air and provide a uniform temperature. Liquid levels measured with a cathetometer. A
bundle of small tubes inside the manifold are used as flow straighteners. Not shown is a 40 ft x 1/4”
copper coil used to warm the flowing air to bath temperature.
Figure 2- This diagram shows the diffusion tube in the vertical position
such as you will observe it. In order that the tube be inserted the same
distance into the manifold each time, the tope edge of the "P" should just
bartouch the rubber mounting grommet. As a reference point, the
bottom leg (as shown in this orientation) of the “N” has been precisely
measured as 3.630 cm from the top (mouth) of the tube. By using the
cathetometer to first measure the height of the “N”, then the height of the
meniscus, a diffusion path can be determined +/- 0.005 cm.
Figure 2 should be consulted in order to understand how the path length for diffusion can
be obtained with cathetometer measurements of the reference (“N”) height and the
meniscus minima in the tube. The Wet test meter and drying tube are cathetometer is
shown below in figure 3. Note the color change of the drying tube packing (“Drierite”) as
moisture is absorbed. Blue indicates fresh absorbent, while pink indicates that the
packing is becoming fully reacted with water.
The flow rate through the manifold can be measured by means of the wet test meter (Fig
4). Each revolution of the meter corresponds to a volume of 3.00 L. The volume can be
corrected to standard conditions by noting the pressure difference between inlet and
outlet flow on the wet test meter manometer and thermometer, and applying the ideal gas
law.
The pressure regulator is located next to the top of the drying tube. When you come to
lab, the flow rate will be set. Use the regulator knob to very carefully adjust the flow rate
to approximately constant- it is possible to “blow out” the manometer and stop the
airflow if too course of a correction is made, so go slowly.
Figure 3- Wet-test meter and drying column. The pressure regulator adjustment knob is mounted
next to the drying tube.
The cathetometer base and scope will be leveled by the TA or instructor at the start of
the run. Avoid bumping the instrument! Leave the base adjustment alone, but check to
see that the scope level bubble is centered before taking readings. The level can be easily
and precisely adjusted using the knob under the scope.
Figure 4- top view of cathetometer sight. Note that the leveling bubble should always be centered to
avoid measurement error. The knob shown is for focusing. The knob for leveling the scope is under
the scope.
Figure 5- The height to the nearest 0.005 cm may be determined using the Vernier scale on the
cathetometer. The photo shows a reading of 84.670 cm.
Figure 5 shows a photo of the Vernier scale on the cathetometer. Check the references on
the “Lab Manuals” web page if you are still uncertain as to how to read the scale. It is
important that everyone have similar operating definitions and procedures for using the
scope. You should agree on a general procedure for taking measurements.
Standard Operating Procedure
1. Check the Lab Schedule and Excel Data Sheet (hard copy will be provided in lab
for each run) to see how the experiment is schedule and what data needs to be
recorded.
2. The TA or instructor will fill the tube to the desired level, set the constant
temperature bath and start the airflow. He will also level the manifold and align
the tube to be parallel with the plumb bob. This should assure that the air flow is
perpendicular to the direction of diffusion.
3. Take data according to the schedule you develop. For each reading, follow the
instructions below.
4. Check to make sure that the cathetometer scope is still level. The scope can be
leveled very, very precisely. Each division on the scope bubble corresponds to an
angle of 30 seconds. A second is 1/3600th of a degree in the same way that a
temporal second is 1/3600th of an hour.
5. Carefully focus the cathetometer if necessary. Bring the cross hair down to the
meniscus minima (the image will actually be inverted in the scope) until it just
touches. Read the cathetometer scale and record the height. Double check
yourself.
6. Time the wet test meter hand to see how long it takes for one full revolution (3.00
L) and record. Record the delta P on the manometer. If necessary, carefully
adjust the regulator knob to bring delta P and F back to the original value.
7. Record temperatures for the bath water, head space and ambient room
temperature.
8. Repeat at 2 other heights as given in the lab schedule. Each section will take data
at a different temperature so as to gauge the effect of temperature on diffusivity.
Analysis
1. Calculate the apparent diffusivity for each tube using eqn. 6.2-26. Plot your data by
modifying equation 6.26-26 in such a way that all of the time data is used and the
diffusion coefficient may be obtained from the slope. Is the data linear- are there
any patterns? Why or why not? How long would you expect it to take for the
system to come to steady state? What does scatter in the data represent? Use linear
regression and statistical output (Excel or Polymath) to estimate the uncertainty in
the value of diffusivity based solely on the assumption of random scatter in the data
(you may eliminate points thought to be inaccurate due to startup if they are early in
the run and clearly not in line with the set).
2. Plot the apparent diffusivity values of each tube as in eqn 11 in Lee and Wilke in
order to determine actual values of diffusivity. Use linear regression and statistical
output (Excel or Polymath) to estimate the uncertainty in the value of diffusivity
based solely on the assumption of random scatter in the data.
3. Calculate the expected value of diffusivity using the Chapman-Enskog equation
(eqn 6.2-45, table 6.2-2, Example 6.2-5 in Geankoplis).
4. Compare your experimental value of the diffusivity coefficient with the estimated
values from number 2 above, as well as with the literature value for air- or airacetone. Are the results consistent? Is the temperature dependence between T1.5
and T1.75?
5. What systematic uncertainties are present as a result of the methods and materials
you used to measure the diffusion coefficient?
6. What assumptions were made in the derivation of equation 6.2-26? How does the
method outlined in the Lee and Wilke paper correct for some of the “non-idealities”
of the system?
7. Show plots in items 1 and 2 in your “Results” section and discuss all items fully in
the “Discussion”. (You need only have Results, Discussion and Appendices in this
individual report).