Measurement of Gaseous Diffusivities
Inert
Gas
Z=0
Miniscus
L
Z=Z
Volatile
Liquid A
Z=L
The figure above depicts a volatile liquid A inside a capillary. An inert gas is blowing across the
Top of the capillary. The gas rate is just fast enough so that the partial pressure of the volatile
liquid at the top tip of the capillary is zero. If the gas rate is too high it is possible that the inert gas
might cause eddies and therefore convective mass transfer effects in the vapor space inside the
capillary. This is undesirable because we want pure molecular diffusion occurring inside the
capillary. It is suggested that you analyze a liquid that has a known diffusivity in air and adjust the
air rate until the experimental diffusivity agrees with the published diffusivity. Don’t forget to a
record both ambient pressure & temperature & make adjustments to exptl.values based on these
measurements..
A cathetometer is used to sight on the location of Z (height of meniscus above bottom of capillary)
as a function of time t. Use these measurements to approximate the diffusivity of A in the inert gas.
Zi,ti
Model
DAB
Model Development
Start with a pseudo steady state model for rate of diffusion of A up the capillary based on a
UUD model for molecular diffusion. Note the partial pressure of A at Z=Z is the vapor pressure
of A and the partial pressure of A at just outside the capillary at Z=0.0 is zero.
D AB dPA PA

NA
RT dZ
P
Z
PA 2
D
dPA
N A  dZ   AB 
0
RT PA1 (1  PA / P)
NA  
NA 
 P  PA 2 
D AB P
Log e 

RT ( Z )
 P  PA1 
PA1  PA* @ T  Vapor. Pr essure.of . A @ Z  Z ; PA 2  0.0
NA 
D AB P
( PA*  0.0)
RT ( Z ) PBm
1
Now address the unsteady State portion of the model
Observe that the diffusion flux causes the liquid level to decrease in the capillary that has
a cross sectional area Ar. Therefore,
N AAr  

Z
Zo
(Z )
dZ
A
MA

Ar
dZ D AB PAr ( PA* @ T  0.0)

dt
RTPBm ( Z )
D AB PPA* M A
(t  0.0)
RTPBm  A
2 D AB PPA* M A
(Z  Z ) 
t
RTPBm  A
Now measure Z as function of time & plot (Z2-Zo2) vs time, i.e.,
2
2
o
Z2-Zo2
Slope=
2 D AB PPA* M A
RTPBm  A
t=Time
Report Format
1) Title Page + Table of Contents(10%)
2) Research binary gaseous diffusivity. Summarize this research with
proper referencing. (10%)
3) Diffusivity measurement: Research & summarize methods for
measuring the diffusivity of gases in binary systems. Use proper referencing.
(15%)
4) Experimental Plan: Make an appropriate drawing and describe the
procedure that you used to determine the diffusivity of a pure gaseous component
in air. Your experimental plan must include studying the following: different
pure component using the Arnold Cell. Don’t forget the effect of temperature?
What was the ambient pressure and temperature during this experiment? Is it
2
important to know how this pressure & temperature varied during the experiment?
Explain how you assured that temperature was held constant or you accounted for
the variation in temperature during an experiment in your data analysis. (15%)
5) Tabulate your experimental data (an appropriate linear measurement &
temperature & ambient pressure vs time) in a spreadsheet & apply appropriate
regression analysis . Based on this statistical analysis what is the +/-%
uncertainty in your reported diffusivity of a pure component in air. (35%)
6) Recommendation: Describe how you could improve your experimental
procedure. Also describe another type experiment you might perform (including
required equipment) that involves gaseous diffusivity of binary systems. (15%)
Notes on Measurement of Gaseous Diffusivities with an Arnold Cell
Ulus has set up the Arnold Cell with a capillary mounted inside a test tube with a side
arm in the 17-1123 lab. Regulated air flows into the side arm of the test tube. A camera
has been mounted in front of the Arnold cell to facilitate viewing the location of the
vapor liquid interface inside the capillary. You must adjust the air rate so that it is not
excessive. If you have too much air flowing, mass transfer will be occurring by a
combination of molecular diffusion and convection. This is not desired for an experiment
that is attempting to measure a gaseous molecular diffusion coefficient. Please also note
that you need to have sufficient air flowing so that concentration at the top of the
capillary of the species diffusing up the capillary is zero.
Here is a potential list of chemical you may select from for this experiment. Remember
you should measure the diffusivity of a pure component in air. You are required to look
up & read carefully the MSDS sheet for the chemicals you are using. Select the
chemicals that are least hazardous. It may be necessary to locate the apparatus in a hood
if the chemicals are volatile & the MSDS indicates potential problems with exposure.
Don’t forget to make multiple temperature measurements and ambient pressure
measurements during an experiment.
n-propanol
Iso-propanol
Ethyl Acetate
Ethanol
Acetone
methanol
3
Title Page
California State Polytechnic University, Pomona
Chemical and Materials Engineering
CHE 313- MASS TRANSPORT SPRING QUARTER, 2012
EXPERIMENT #1
Measurement of Gaseous Diffusivities
INSTRUCTOR:
T. K. Nguyen
SECTION 01
GROUP #1
MEMBERS: Lau, Lee
McCaffrey, Charles
DUE DATE: May 10 2013
Title Page
(10) ______
Research binary gaseous diffusivity
(10) ______
Diffusivity measurement
(15) ______
Experimental Plan
(15) ______
Tabulated Data & Analysis
(35) ______
Recommendation
(15) ______
TOTAL
(100) ______
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