1
Chem 111 (Chemical Kinetics), Kahn 2010
Final Exam
Your Name:
Q1 (30)
Q2 (30)
Q3 (24)
Q4 (15)
Q5 (35)
Q6 (20)
Q7 (20)
TH (26)
Total (200)
1.
a) You are given a familiarlooking printout of
Mathematica
file that illustrates analysis of
multiwavelength kinetics of an enzymatic reaction.
Unlike typical examples or answer
keys, this printout is sparse in comments (similar to some homeworks by our students).
However, it shows all the relevant
Mathematica
commands and results.
Write a onepage
explanation about this analysis.
Summarize the key findings about the reaction under study.
Highlight any clever approaches that were taken to learn as much as possible from this data.
(20 pts)
The analysis starts with plotting 3D graph of noisy absorbance data vs.
and time.
This reveals the
disappearance of reactant (
max
≈ 300 nm) and appearance of product (
max
≈ 500 nm).
The action
spectra show no isosbestic point suggesting the presence of at least one intermediate (with
max
≈ 400
nm)
Singular value analysis leads to three significant singular values, three nonrandom basis spectra, and
three nonrandom basis profiles, confirming that three species contribute to absorbance.
Considering the
timedependence of absorbance, it is reasonable to suggest that we have a consecutive A
B
C
process.
Individual doubleexponential fits to basis profiles are challenging due to a large number of unknowns.
However, C0 can be determined for each fit based on the value at completion of the reaction.
One of the
basis profiles yields reasonably well determined rate coefficients (0.97 and 0.53), which are further con
firmed via global fit.
Note that we do not know which step each of these rate coefficients corresponds to.
Armed with the knowledge that we have only three species, we reconstruct the absorbance matrix and
display it as a 3D graph.
This time the formation and disappearance of intermediate is clearly visible,
lending support to the A
B
C model.
Because we were not given the pure spectra of species, we have to extract that information out from the
absorbance data.
The key idea here is that at time zero, we only have A, and at the end, we only have C.
The mixing was quick enough and the data was collected long enough, so we can get spectra of pure A
and C from data.
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We note that the intermediate reaches maximal concentration around 1.8 seconds. Because we think that
we know the rate constants from SVD analysis, we can calculate how much A is left after 1.8 seconds,
and how much C has formed by 1.8 seconds.
Subtracting the contributions of A and C from observed
(SVDreconstructed) data, we obtain the spectrum of B.
This was a clever approach!
Armed with spectra of A, B, and C we can calculate the real concentration profiles for A, B, and C via
matrix algebra.
Global fit to analytical rate expressions describing the consecutive A
B
C process
yields rate constants with small errors.
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 Fall '08
 KAHN
 Reaction, Kinetics, Mathematica

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