Welcome to the Fundamentals of Analytical Science

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Welcome to the Fundamentals of Analytical Science
109 is a one semester survey course that covers
all the basics of the interesting aspects of
chemistry. This semester we going beyond last
semesters superficial treatment of equilibria,
and examine the field in depth.
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Fundamentals of Analytical Science

• This course covers complex equilibria including
  acid/base, chelation, oxidation-reduction, and
  precipitation equilibria.
• Tools of the trade include absorption
  spectroscopy, gas chromatography, liquid
  chromatography, and instrumental methods.
• There is an emphasis on speciation and the
  control of equilibria through competing
  equilibria.
• There is a close connection to the laboratory.

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Three examples of the importance of equilibria
aA bB cCdD

• Protein folding
• Environmental pollutants
• Wine making

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Designing protein dimerizers the importance of
ligand conformational equilibria Carlson JC et
al. (JACS 2003).

• To elucidate the role of ligand conformation
  in induced protein dimerization, we synthesized a
  flexible methotrexate (MTX) dimer, demonstrated
  its ability to selectively dimerize Escherichia
  coli dihydrofolate reductase (DHFR), and
  evaluated the factors regulating its ability to
  induce cooperative dimerization. Despite known
  entropic barriers, bis-MTX proved to possess
  substantial conformational stability in aqueous
  solution (-3.8 kcal/mol gt/ DG(fold) gt/ -4.9
  kcal/mol), exerting a dominant influence on the
  thermodynamics of dimerization.

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On the importance of black carbon to
sediment-water equilibria of PAHS, PCBS AND
PCDDS R. Lohmann et al. lohmannr_at_mit.edu

• Solid-water distributions coefficients (i.e.
  Kd) of "native" PAHs, PCBs and PCDDs in Boston
  and New Harbor sediments were determined using
  passive samplers incubated in sediment-water
  suspensions. The organic contaminants required
  several months to reach equilibrium. Observed Kds
  exceeded by 1-2 orders of magnitude predicted
  Kds. It is suggested that black carbon present in
  the sediment is responsible for the additional
  sorption. Black carbon-normalized adsorption
  coefficients, KBC, were deduced for numerous
  PAHs, PCBs and PCDDs.

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AcidBase and Precipitation Equilibria in Wine
Miguel Palma et al. Departamento de Química
Analítica, Universidad de Cádiz-Spain (JCE 2004)
Acidbase and precipitation equilibria in wine
are used to teach the importance of chemical
equilibria to the wine industry. The stability of
wines is dependent on chemical equilibria, mainly
the precipitation equilibrium of potassium
hydrogen tartrate. However, this precipitation
equilibrium is influenced by acidbase
equilibrium and vice versa. A simple but
effective experiment demonstrates the
interactions between simultaneous equilibria
involving hydrogen tartrate and highlights the
importance of multiple equilibria in real-world
systems.
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http//www.chem.wisc.edu/sibert/tci/329
Chemistry 329 Web Page
It contains the syllabus, problems sets, and
power points.
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Course Objectives
Chemistry 329 is the intermediate level
analytical chemistry course for majors that
require mastery of chemistry or for students
preferring a more challenging and in depth
presentation.
It emphasizes quantitative laboratory skills,
fundamental analytical chemistry, and problem
solving involving complex chemical equilibria.
The courses use example applications in
chemistry, biology, environmental science,
medical science, and engineering.
This course will cover acid/base, chelation,
oxidation-reduction, and precipitation equilibria
and absorption spectroscopy, gas chromatography,
liquid chromatography, and instrumental methods.
There is a particular emphasis on speciation and
the control of equilibria through competing
equilibria.
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Problem Sets
There will be 9 weekly homework assignments.  
The homework is the most important component of
the class.  Assignments will be posted on the web
on Wednesdays and are due on the following
Wednesday during class period. You may and should
discuss the homework with other students in the
class, but you must write up your answers
independently.  Problems sets are not accepted
after class on the Wednesday that they are due,
so that we can post the solutions in the library.
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Tests, Final Exam and Grades
The final exam is cumulative.  There are two
midterm tests. Your final course grade will be
based on the following weighting laboratory
(50), two evening exams  (20),  problems sets
and discussion (15), and final exam (15).  The
two evening exams are Thursday Feb. 24 and
Tuesday April 5 between 715-915.  The final
will be 12.25 P.M. TUESDAY MAY 10.  
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Honors in Chemistry 329

This course is recommended for students planning
an honors program. Honors candidates should
enroll for honors credit. Given the difficulty
of the course, no additional work is required.
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Assigned reading
The part of the text that is associated with each
power point will appear at the beginning of each
power point presentation as shown below. Today
is an exception, since it is the first lecture so
I couldnt assign reading. Moreover, the first
part of this text is a mix of new material and
review. The associated reading for this power
point.
Read Chapter 1 and 2. Much of this is review.
Look it over and just focus on those parts you
dont understand. The error analysis begins in
Chapter 3. If you dont know how to use Excel,
read 2-10 with care.
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Many students, engineers and chemists
underestimate the importance of error analysis.
There are two kinds of errors random and
systematic.
For the remainder of this period, I will talk
about propagation of errors.
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Propagation of Errors
Assume you are using Beers law to determine the
absorbance. Beers law is Aecl, where A is
absorbance, c is concentration, e is molar
absorptivity, and l is the length of the
cell. If the uncertainty in the concentration is
Dc what is the uncertainty in the absorbance?
A
To answer this question make a plot of A
versus c, using Aecl
c
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Error Analysis
Assume you are using Beers law to determine the
absorbance. If the uncertainty in the
concentration is Dc what is the uncertainty in
the absorbance?
A
DA/ Dc slopee l
2DA
Multiply both sides by Dc to obtain DAe Dc l
c
2Dc
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Error Analysis
Given Ae c l, we found DAe Dc l where e l is
the slope of the line in our plot.
The more general formula is
The funny symbol is the derivative of A wrt c
treating all other variables as if they were
constants. Remember the derivative is just the
slope.
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Error Analysis with 3 variables
Repeat the absorbance problem but now assume that
there are uncertainties in c, e, and l.
The previous formula is
is replaced with a formula with 3 contributions
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Error Analysis with 3 variables continued.
Use the below formula and the formula for the
absorbance to obtain an explicit expression for
DA.
The answer is
If we divide both sides of this equation by A, we
find
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Error Analysis with 3 variables continued.
The below formula is only correct for systematic
errors where we know the signs of the
uncertainties
If the errors in c, l, and e are uncorrelated
then a better formula is
This formula is completely general.
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Making a connection with the book.
Explicitly evaluating the below formula
gives
The formula in the book is Eq. (3-6).
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Practice problem 1
Given the formula fxyz and given the
uncertainties In x, y and z, derive a simple
expression for Df.
Instead of using this formula
Use this formula
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Practice problem answer 1
Given
We find
Thus
Or using the notation of the book we find Eq.
(3-5)
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Practice problem 2
Solve
This is just f x y z with x 9.23 Dx .03
Using the equation
We find