GEOEE 404W:
SURFACE
AND INTERFACIAL PHENOMENA IN GEO-ENVIRONMENTAL SYSTEMS
Grade scale:
A >93
A-
90-93
B+ 85-89
B 80-84
B- 75-79
C+ 70-74
C 60-69
D 50-59
F <50
Lab
Schedule (updated!):
Note 1: Lab sessions will start during the week of 9/12 (Mark Klima and
Tom Motel, supervisors).
Note 2: During class between 9/1 and 9/22 we shall cover the basics
of each one of the lab experiments, so that you can ‘digest’ them with more
‘gusto’!
Lab Content:
Important
note:
Before you begin each experiment, you should prepare a
spreadsheet with tables that clearly identify the independent variables to be
measured and the parameters to be used. Devote special care to the analysis of
consistency of units for both the measured and the calculated quantities. You
should also know which graph(s) you will need to construct on the basis of
these tables; the best way to do this is to enter hypothetical (and hopefully
realistic!) values into the relevant tables and construct representative
graphs. If you need help in developing such a spreadsheet, be sure to contact
me 24/7.
Here
is an example for the RO experiment.
EXPRERIMENT
#1: Adsorption in packed columns
(basic phenomena: L/S equilibrium and mass transport)
-Analysis of breakthrough time:
Use one of your experimental results (say, tB at C/Co=0.5) to back-calculate
the MTC, and then confirm (?) the validity of the Wheeler equation by using
this MTC to obtain the correct tB values at your other two C/Co levels (see In-lieu-of-class
activity #4).
-Do you agree (see relevant class
handout) that a = (We D2 p)/(4 Co
Q) and b = (We rad Q)/(Co
Q Ka) ln(Ce/Co)? Do you also agree that, if a=129 h/m
(see HW2-5), the actual amount adsorbed (We) is only about 23% of what
one would expect from the isotherm constructed in HW1-4?
-Can you confirm, from the intercept of the ax+b line (see Table 1 in the Lab manual), that the MTC should
indeed be of the order of 10-5 m/s. (Remember the class handout
“Transport phenomena (2)”?) What does that say about the relationship between
adsorbent particle size and thickness of boundary layer that surrounds the
particle? Perhaps the diffusivity of MB, which is a relatively large molecule,
is LESS than the ‘typical’ liquid-phase diffusivity of ca. 10-9 m2/s…
-Key graph
and its message: Should the C/Co vs. t
graph be a straight line? (When might it be?)
EXPERIMENT
#2: Reverse osmosis or
‘ultrafiltration’ (basic
phenomena: mass and momentum transport)
-osmotic
pressure (see relevant class handouts): equal volumes of solutions showing
the same osmotic pressure contain equal numbers of molecules of solute
(“extended Avogadro’s law”)
-mass/mole balance of solutions: a rudimentary
example.
-solutions of electrolytes: why
does, say, a 0.1N solution of NaCl produce an effect (say, on vapor pressure
suppression) that is 10% less than expected on the basis of complete
ionization? Debye-Hückel theory provides a simple and elegant explanation (see
below).
-The key fundamental issues in this
experiment are to understand (i) whether indeed a “typical value [of parameter
A] is 0.255 gal/day/ft2/psi”, and (ii) whether a reasonable value of parameter
B can be ‘extracted’ from the results.
-key graph
and its message?
EXPERIMENT
#3: Soil washing (basic phenomena:
L/L equilibrium and ‘detergent’ effect of the surfactant)
-presumably the concentration of the
added surfactant is close to CMC…
-key graph
and its message?
EXPERIMENT
#4: Pressure filtration (basic
phenomenon: momentum transport)
-basic momentum transport equation
-Hagen-Poiseuille equation
-key graph
and its message?
EXPERIMENT
#5: Surface charge and settling of
suspensions (basic phenomenon: electrostatic repulsion)
-electrophoretic mobility vs. pH
curve
-mass titration curve
-key graph
and its message?
In-lieu-of-class
activity for August 23 (due in Angel dropbox by midnight 8/24): The
attached Excel
spreadsheet contains information about the use of the classical BET equation to determine the specific
surface area of an adsorbent on the basis of its adsorption isotherm. (Can you
retrieve the original 1938 article, by Stephen Brunauer and coworkers, from the
PSU library’s electronic database?) Based on this information do the following:
(i) Construct the graph of the amount adsorbed (in cm3/g) vs. gas
pressure (in atm) at the two temperatures shown. (ii) Determine the surface
area of the silica gel adsorbent.
Does your graph at 77 K look like this? Why is
77 K a convenient temperature for this adsorption experiment? Is 90.1 K a more
or less convenient temperature? Why is it informative (with respect to 77 K)?
Hint: Remember Le Chatelier’s principle?
Note: This analysis illustrates the importance of having reliable
experimental results over a reasonable range of values
of the independent variable (x-axis)… something to keep in mind when we
start doing the lab exercises! (If the results at 90 K do not “make sense”, and
if your reading of the 1938 article does NOT help, we’ll ‘resolve’ these issues
in class discussions and HW #1.)
In-lieu-of-class
activity for August 25 (due in Angel dropbox by midnight 8/26): The attached Excel
spreadsheet contains information about the use of the classical Langmuir
and Freundlich equations to rationalize the process of liquid purification, by
transfer (adsorption) of, say, a pollutant from solution onto the surface of a
solid ‘substrate’ (or adsorbent). The original article is cited there as well;
can you retrieve it from the library’s online database?
Based on this information do the following.
(i)
Construct the adsorption isotherm: uptake (in g/g) vs. equilibrium
concentration (in mg/L).
(ii)
Construct the linearized Langmuir plot and determine its two
characteristic parameters.
(iii)
Construct the linearized
Freundlich plot and determine its two characteristic parameters.
(iv) Compare your
numbers with those listed in the original article, and comment on their degree
of (dis)agreement.
Does your Langmuir plot look like this? If you
can’t find the original article, does google (say, wikipedia) help in finding
the relevant information (e.g., Langmuir eqn, Freundlich eqn)? And the
textbook?
Constituents
of matter: atoms (ca. 10-10 m), molecules (ca. 10-10-10-8
m), colloids (10-9-10-7 m), particles (ca. 10-9-10-3
m), bulk ‘materials’.
Note: ‘colloid’ means glue-like (in Greek), because Thomas Graham (Trans Roy Soc London 151, 183, 1861)
noted that amorphous solutes such as starch and caramel diffused very slowly.
INTERATOMIC/INTERMOLECULAR
FORCES:
There are
four fundamental forces in nature: (a) strong and weak (short-range)
interactions between sub-atomic particles (in the ‘microscopic’ world); (b)
electromagnetic and gravitational (longer range) forces between atoms and
molecules (and also between sub-atomic particles). The electromagnetic
(together with gravitational) forces determine the properties of gases, liquids
and solids and therefore the behavior of atoms and molecules in the
‘macroscopic’ world; a convenient, though somewhat arbitrary classification of
these forces is the following:
-‘physical’
(e.g., condensation)
-‘chemical’
(e.g., ionic or covalent bonding)
-‘electrical’
(e.g., coulombic
interactions, Debye-Hückel theory of electrolyte solutions): Here is a
summary (review?) of key physics/math concepts.
…
States
of aggregation of matter: gases, liquids, solids.
See
Table 1.4 (p10) in
textbook.
SURFACE (G/S,
L/S) AND INTERFACIAL (e.g., G/L, G/L, S/S) PHENOMENA IN ENVIRONMENTAL
ENGINEERING:
-partition
coefficient (e.g., Henry’s law constant)
-asymptotic
behavior: surface coverage, monolayer
-surface tension,
surfactants, critical micelle concentration
-affinity
vs. capacity: quantification using adsorption isotherm parameters (e.g., BET,
Langmuir, Freundlich, …)
Homework
1
(average grade=60%).
(1) (a) A simple but powerful method that takes
into account the fact that intermolecular forces may be important (even for
gases) in real (vs. idealized) situations is the venerable van der Waals
equation of state. Use the attached spreadsheet
to show how the compressibility factor (Pv/(RT)) depends on pressure.
-Does your
graph look like this?
(Do you agree that a reasonable range of v values is 0.05-25 L/mol?)
(b) A dilute
solution of an electrolyte is not ideal, i.e., its activity coefficients
deviate significantly from 1.0. Show this to be the case by using the
Debye-Hückel theory to complete the attached table
for an aqueous solution of NaCl whose molality (at, say, 298 K and 1 atm)
varies between 0.01 and 0.1.
(2) Complete
Problem 1.7 (see above). In particular, verify (and explain!) the meaning of
the (n=0,d=0.401) data point, by consulting the original source of information.
Do the answers change if you remove this point from the data set?
-Do
you get (again?) that the number-, surface- and volume-mean are 293, 297 and
302 nm, respectively?
(3) Make a graph
of the Debye length vs. solution concentration for NaCl, CaCl2 and
MgSO4. (Extra credit: Does it matter whether the relevant geometry
is spherical (e.g., potential vs. radial distance surrounding a spherical particle)
or ‘linear’ (e.g., potential vs. thickness of the electric double layer)?]
-Does
your graph for NaCl look like this? And the
final one like this?
(Do you agree that m=Im/3 for CaCl2 and m=Im/4
for MgSO4? And for Na3PO4, Im=0.5(3m+9m)
– see handout “Ionic strength: exercises” – so m would be Im/6…
Right?)
(4) Compare the uptakes
of benzene and methylene blue on a GAC and evaluate the effect that this
difference has on the breakthrough time under otherwise comparable (but
representative!) conditions.
-Does
your MB graph look like this? If you
have difficulty finding Langmuir or Freundlich parameters for benzene on GAC
(similar to the one used to adsorb MB?), let me know!
Here is
the JChemEduc article that we shall analyze carefully in class, as an important
exercise (also carried out in the labs!) in learning methodology:
(i)
use a calibration curve
to construct a graph that contains “raw data”,
(ii)
use such a graph to establish a trend in the relevant dependent variable over a reasonable range of
values of the independent variable, and
(iii)
identify (and understand!) the behavior of a key concept that governs the observed phenomenon.
And
here
is its “supporting information”, which contains key elements of a typical (and
excellent!) lab report. Let’s develop a spreadsheet to
‘digest’/reproduce this exercise!
Using
this same methodology, can you find this (very recent)
article? Do its figures 2c and 2d resemble the results you obtained in your
soil washing experiment? (Should they? If not, why not?)
http://www.ems.psu.edu/~radovic/CMC_2a.nb
Homework #2 (average
preliminary grade=63%):
Note: If (you are of the opinion that) more points can be
squeezed out of your answers, let’s discuss them in more detail! (In
particular, let’s analyze whether and how you used the class handouts and/or
the various ‘templates’ to simplify your tasks.)
1. Complete the
handout “CMC: a closer look” by constructing a series of graphs like the one shown,
using n as the parameter (say, n = 25, 50, 75 and 100).
-Here is
a template based on the handout “Surfactants”. Note that it requires solving an
implicit equation, which can be done using, say, Solver in Excel or Mathematica (attached).
-Note: If values of n that are very different from 20
(using the same equilibrium constant) give you (only mathematical?) problems
(or physical as well?), try using values of n that are NOT very different from
20; for example, n=22 with
cT between 0.6e-4 and 2.2e-4… This shows you that, upon changing n (while
keeping K constant), the range of cT values has to be adjusted ‘accordingly’!
2. Solve at
least one problem in the handout “Contact angle/surface tension”.
3. Solve at
least two problems in the handout “Surface tension & capillarity
exercises”.
4. Complete the
exercise summarized in the handout “Methodology of learning (1)”.
-Does your key graph look like this? And the
supporting “calibration curve” (actually a straight line) like this?
5. Complete the
exercsie summarized in the handout “Adsorption 2”. For gas-phase adsorption,
select two adsorbates whose isotherm data are readily available. Be sure to
select and document carefully your source(s) of information! Can you ‘extract’
a reasonable value for the methylene blue uptake from the slope of the
breakthrough curve obtained in the lab experiment?
-Do you agree that the
equilibrium uptake ‘extracted’ from the slope (129 min/cm?) is obtained when
the slope is multiplied by the pollutant concentration and flow rate and
divided by the cross-sectional area and density of the packed adsorbent column?
(Note: Doesn’t the relevant table in your
Lab ‘manual’ indicate that the slope is actually 129 h/m? Does that help you to
obtain a reasonable value for the equilibrium uptake of MB?)
6. Following up
on our discussion of the handout “Adsorption 2”, use the data that we were able
to locate with the help of the Web of Knowledge to analyze the relative
effectiveness of an adsorbent in removing a pollutant (e.g., benzene) from the
gaseous vs. the liquid phase. Construct a
meaningful graph and comment on the degree of (dis)agreement of these results
and the ability to compare ‘apples’ and ‘apples’.
-Does your graph look like this? (If it
does, be sure to document clearly HOW you obtained it! And then show that it is
actually ‘easier’ to remove this pollutant from the gas phase than from the
liquid phase!? Why?)
In-lieu-of-class
activity #3 (week of 10/10): In preparation for the midterm exam (to be
scheduled during the week of 10/24), review as many of the class handouts as
necessary/possible. If not completed/clear, e-mail me specific questions
about them, and/or about HW1 or HW2.
-For example, does your BET plot for
benzene and toluene vapors look like this? And do you
agree that the analogous results shown in Chapter 9 of the textbook imply that
the heat of adsorption (of nitrogen) is 2.9 kJ/mol higher than the heat of
condensation (of nitrogen)?
Midterm exam (average
grade=57%).
Experimental design: from ‘scratch’ or extension of a familiar experiment… tbd in
consultation with Prof. Klima.
In-lieu-of-class
activity #4 (due in Angel dropbox before class on 11/3): Show schematically
and discuss briefly the key graphs and the key equations in the soil washing
and reverse osmosis lab experiments. Be prepared to discuss them in class on
11/3.
In-lieu-of-class
activity #5 (only two of us showed up for class of 11/3; due in Angel dropbox
before class on 11/8): Complete the attached class
handout and be prepared to discuss it in class on 11/8!
-Here is one
version of the completed class handout.
Homework
#3:
Experimental design exercises (and not
just “electrokinetic phenomena”), due 11/20 in Angel dropbox, accepted (without
penalty) at the same time as the experimental design project (during the finals
week, at the latest).
1.
Complete the in-lieu-of-class #5 handout and discuss its relevance to the SW
experiment.
-To obtain a variety of CMC values (including those of Triton
X-100 and Dispersit SPC 1000?), can you find in the Knovel database (PSU
library) Chapter II-19 of the “Handbook
of Applied Surface and Colloid Chemistry”?
2.
Complete the 11/10 class handout and discuss its relevance to the PF
experiment.
-Here it is. And here is one
completed version.
3.
Complete the 11/15
class handout #1 and discuss its relevance to the RO experiment.
-In order for 0.255 gpd/ft^2/psi to
indeed be a “typical value” of the water permeability coefficient, the membrane
area should be ?? ft^2, and this is (or is not?) a realistic number… Etc.
-Can you find ‘typical’ values of
the water permeability coefficient in units of m/s? How is this related to the
liquid-phase mass transfer coefficient? Should it be similar to the kL value
that we ‘back-calculated’ from the results of the GAC experiment (3e-5 m/s)?
4.
Complete the 11/15 class handout #2 and discuss its relevance to the GAC
experiment.
-Do you agree that a column whose
diameter is 1 m (and is 1.5 m long) will remove 95% of the pollutant with a
breakthrough time of ca. 189 h?
5.
Complete the 11/17 class handout and discuss its relevance to the SC
experiment.
-See, for example, the double-layer compression graphs in
ZetaMater’s brochure coag.pdf; see Experiment #5 above.
Class
of 11/29: general discussion of experimental design assignments.
‘Classes’
of 12/1, 12/6 and 12/8: individual discussions of design project reports,
especially their theoretical background sections. (Send me an e-mail to set up a 30-60 min meeting!)
The final grades have been posted. Class average=76% (B-). (If your
records disagree with mine, please contact me asap…) Have a wonderful Holiday
Season!
lrr3@psu.edu (updated 12/19/2011, 12:15)