Chemistry 4595
Midterm #2 – Take Home
Fall 1998
Due before class on Thursday, December 3—no exceptions!
Rules: Work entirely alone! Do not talk to anyone except me. I will clarify questions,
help with computer problems, etc., but I will not directly provide answers. You can use
your notes, books and lecture notes in the library (do NOT hog these! The library has
been instructed NOT to let you remove them).
1. Why do we have (at least) two different systems for electromagnetic units? That is,
why do we sometimes refer to charge in Coulombs and other times in esu?
2. We said that light scattering functioned like an osmometer without a membrane?
What kind of nonsense is that? Explain in your own words.
3. Compare the average distance between gas atoms (assume normal, ambient
conditions) to the wavelength of a green ion laser operating 5145 Å. Describe the
consequences of this observation.
4. The following data were determined for a homologous polymer series by light
scattering and classical intrinsic viscosity measurements. Find the two MarkHouwink parameters (K and a) and speculate on the shape of the polymer.
M
91400
181600
175900
190300
176800
65900
65800
64300
63900
35900
35800
35500
36300
90000
[] in dL/g
1.623
2.692
2.642
2.813
2.624
1.296
1.295
1.294
1.280
0.821
0.812
0.805
0.815
1.615
M
112300
114500
111500
114200
45000
51800
45100
46100
115200
106400
107300
113100
129800
128700
132200
131400
48000
46200
47600
48600
90900
[] in dL/g
1.890
1.856
1.857
1.905
1.036
1.027
1.040
1.029
1.900
1.835
1.771
1.860
2.127
2.131
2.152
2.137
1.029
0.980
1.012
1.022
1.620
5. Convert your Mark-Houwink "a" value from the previous problem into the exponent,
, as in Rg ~ M
6. Those of you who did the problem correctly found that a star-functional polymer with
f arms on it had a narrower molecular weight distribution: Mw/Mn = 1 + 1/f. In your
own words, why do you suppose that the distribution narrows down compared to the
linear polymer (f=1; Mw/Mn = 2).
7. Someday, a class like this won't be necessary (if all one wishes is to determine molar
mass of polymers, that is). That's because our friendly analytical chemists will
eventually learn to measure real polymers in a mass spectrometer. Meanwhile, let's
consider a pretty good effort on very small polymer. Below is mass spectrum of a
small polybutadiene. The height of each peak above the baseline is proportional to
the number of atoms detected at a particular mass. Compute Mn, Mw, Mz by any
means at your disposal (I recommend a ruler and Excel).
8. If it should eventually happen that the mass spectrometrist can reliably measure real
polymers, what other useful things might a class like this teach us? Summarize in
100 words or less what else we have learned or tried to learn!
9. Use the internet to find a good Teddy Roosevelt quote (something other than the talk
softly/big stick one). In times like these, it's fun to remember politicians who were
not simpering, self-serving idiots.
ANSWERS TO MIDTERM 2
Fall 1998
1. The difference is really one between historical convenience and physical insight. A
"Coulomb" is the amount of charge that flows through a conductor in one second at a
current of one ampere. Presumably, this is enough to deflect a magnet of certain size
by a certain amount. In other words, it was a convenient way to measure charge. No
one knew that electrons would be so small that it would take 6.25 x 1018 of them to
make one Coulomb. Indeed, the thought that there would even be a fundamental unit
of charge may have not been widely accepted at the time. But that didn't prevent
experiments, and it was learned that the force between two spherical, charged objects
separated by a distance R was proportional to Q1Q2 and inversely proportional to R2
and also reduced by an amount in the presence of a dielectric medium. If that's the
case, why not simply define charge directly in terms of this force? And while we're at
it, let's use dynes (e.g., g-cm/s2) for force and cm for R. Thus,
F(in dynes) = (esu1)(esu2)/R2
Since esu charge is defined in terms of a fundamental law, this system sometimes
confers more physical significance than the coulomb units, which are the result of
convenience alone. For example, the in the esu system, polarizability naturally comes out
as a volume. The SI units of polarizability do not convey any physical significance.
When it comes to electric field, both kinds of units are helpful. For SI, E is given in
Volt/cm, which is convenient if you have a voltage source. For esu system, E is given in
esu/cm2 which suggests that, if you have a current source, you could create an electric
field by spreading out some charges on a plate capacitor of a given area.
2. In an osmometer, you use a semipermeable membrane to force the existence of a
large concentration gradient. You then assess the chemical potential associated with
that concentration gradient through the osmotic pressure. Light scattering also
responds to concentration gradients, and it also returns information about the
associated chemical potential gradients. The difference is that LS relies on the small
and spontaneous thermal fluctuations instead of large and forced ones. In fact, you
could imagine a light scattering experiment set up inside of an osmometer cell.
x
Laser
Detector
Now you could plot the concentration as a function of position, x.
Light scattering works from these tiny,
spontaneous concentration fluctuations
c
Osmometry relies on this huge
concentration fluctuation imposed by
the semipermeable membrane.
x
3. Start with the ideal gas equation: PV = nRT where. Let n = 1/6.02 x 1023 mol --i.e.,
one atom. Then choose typical pressures and temperatures (1 atm and 300 K). Solve
for V. This is the volume given to a single gas particle. The characteristic length, l,
between particles is therefore V1/3.
 RT
l  
 PN a



1/ 3
lit  atm


 0.082
3 
300
K
1000
cm
mol  K 



1atm
lit


N a mol 1




1/ 3
 3.4  10 7 cm
= 34 Å which is much less than the wavelength of visible light. The practical
consequence is that there is always a gas atom positioned so as to cancel the scattering of
any other gas atom, so air at sea level behaves as a fluid: low scattering. By contrast, the
air in the outer reaches of the atmosphere scatters strongly. That's why the sky looks far
away. It probably accounts for the ancient impression that the sky was a kind of blanket
over the world, and the stars seen at night were the result of holes in the blanket.
4. You have to make a log-log plot of [] vs. M and then perform a linear fit. Here's the
Origin result; you could do it in Excel or other program, or even by hand. Since a =
0.724, this is close to the "polymer in good solvent" limit of 0.8. The polymer is
probably a random coil in a pretty good solvent.
[]/ dL-g -1
K = 10-3.3782 = 4.19 x 10-4 dL/g
a = 0.724
Pretty close to a = 0.8 like random coil polymer
A -3.3782 0.03684
B 0.72379 0.0075
------------------------------------------------------------
1
R SD N P
-----------------------------------------------------------0.99818 0.01009 36 <0.0001
-----------------------------------------------------------10000
100000
Mw
5.   
Rg3
M
 M a so Rg3 ~ Ma+1 so Rg ~ M
That is…. =
a 1
3
a 1
= (1 + 0.724)/3 = 0.575
3
The expectation for a random flight chain in a good solvent would be  = 3/5 =
0.6. So this is again pretty close to the random flight expectation.
6. Well, getting physical insight out of equations is always difficult but sometimes
rewarding. I personally rationalize this result by thinking that the arms are as
polydisperse as ever. But if you force the whole star molecule to have several arms,
you have a good chance of joining some long ones and some short ones on the same
molecule, thereby cancelling out some of the polydispersity. You can often draw a
parallel to your daily world. Parts of Baton Rouge are rich and parts are poor.
However, taken together, Baton Rouge is about the same as any other Southern City,
such as Birmingham. One of the main reasons for studying science is to learn to
identify such parallels to and from the world around you.
7. What I did was simply mark the peak heights (above the baseline, which I estimated
graphically with a French curve) with a ruler (in millimeters, but the units don't really
matter). I put these into Excel along with the M data from the x-axis. Then I just
computed the sums. I did this in a particularly efficient way, though. Please
download the Excel file from the website to see how. Here are the answers:
Mn:
Mw:
Mz:
814
852
888
Mw/Mn:
Mz/Mn:
1.05
1.09
The remarkable thing is that this UGLY looking polymer, which is OBVIOUSLY
not at all monodisperse, actually winds up having pretty low Mw/Mn. This makes
nature's achievements (a single peak or Mw/Mn = 1,.for both small and large
molecules) all the more remarkable.
8. Defining various ways to determine M is an important part of this class, and it
requires a fair amount of thermo and other stuff to do so. However, I really hope that
someday everyone will get their M values from MALDI-TOF. The hoops we have to
jump through to get M prevent us from doing really fun stuff that this class also trains
for: like diffusion in complex solution, study of shape and size (different from M),
study of aggregation and materials that can be made from polymers. The MALDITOF people get better all the time, but it will be some time before they can measure
real synthetic polymers. They do a good job with monodisperse natural polymers
already, however, so there may be hope.
9. "If you drop a hammer on your foot, it's hardly useful to get mad at the hammer."