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Integrated Writing Guide
Abstract
The rate of hydrolysis of sucrose by
beta-fructofuranosidase from
Saccharomyces cerevisiae was measured by
polarimetry. Experiments were performed
at 300 K, 310 K, and 320 K. The enzyme
catalyzed activation energy was 29.2 ± 0.2
kJ/mol. The rate constant at 300 K was
found to be 0.065 ± 0.001 min-1
. The
activation energy was comparable to the
activation energy for beta-
fructofuranosidases isolated from plant
sources.
The abstract should be a concise (short) and
specific summary of the report that allows
readers to decide whether they want to read
the report. It should include purpose,
methods, scope, results, and conclusions. A
technical document is not a mystery novel.
Give a very brief version of your conclusions
right away and support them later. For more
information, see the ACS Style Guide1, pp.
21-22.
• purpose
• method
• numerical results with error limits and
correct units
• conclusion
• clear
• concise
• no major conceptual errors
• no grammar errors
1 The ACS Style Guide: Effective communication of
scientific information, 3rd
ed.; Coghill, A.M, Garson,
L.R., Eds.; Oxford University Press: New York,
2006.
2
Introduction
The introduction must accomplish two
objectives: it must give the purpose of the
report and acquaint the reader with the
experiment. This should set the background
and the context of your experiment.
Primarily, you will be trying to explain what
you were trying to do and why it is
significant. Describe what others have done
in this area and cite the relevant references.
Ask your instructor if you need help
searching for literature articles. The
introduction should also provide whatever
background theory or formulas the reader
needs to know to understand your paper.
You may have to define the terms used in
stating the subject and provide background
such as theory or history of the subject.
Much of this information will be in the lab
manual, but the instructor will usually
expect you to show your own
comprehension of the problem by describing
it in your own words. For more
information, see the ACS Style Guide, pp.
22-23.
Plants and yeasts use -D-
fructofuranosidases (EC 3.2.1.26) to catalyze
the hydrolysis of the disaccharide sucrose into
the two monosaccharides, fructose and
glucose. Because sucrose rotates plane-
polarized light to the right, while an equimolar
solution of glucose and fructose rotates plane-
polarized light to the left, -fructofuranosidase
is commonly called invertase. Similarly, the
mixture of glucose and fructose is called invert
sugar. Invertase is used in the confectionary
industry, because invert sugar is less prone
than sucrose to form grainy crystals.1
Invertases can be isolated from plants2 and
from yeasts.3 The kinetics of these enzymes
under various conditions are of interest because
they can be so used.4 Invertase activity in
fruits and vegetables contributes to spoilage in
stored food.4
The rate of reaction for the invertase-
catalyzed hydrolysis of sucrose can be
measured by following changes in optical
rotation of an aqueous solution of sucrose and
invertase. When sucrose is hydrolyzed to a
mixture of glucose and fructose, the optical
rotation changes from clockwise (+) to counter
clockwise (-).
• background
• at least 4 literature references to prior
work
• equations
• significance of topic
• purpose
• clear
• no major conceptual errors
• no grammar errors
3
The optical rotation is monitored with an optical polarimeter and then used to
calculate the amount of sucrose left unhydrolyzed. The angle of rotation is determined at
the beginning of the experiment (a0) and at equilibrium (aeq). The algebraic difference
(a0 - aeq ) is a measure of the original sucrose concentration. The concentration of water
during the reaction remains essentially constant, since it is present in large excess.
All equations should be given a reference
number, so that you may refer to them later
in the text. Center equations, and format
them neatly. Introduce all variables in the
text the first time you use them in an
equation, so that the reader can interpret the
equation correctly. If you need help editing
equations, ask your lab instructor for help.
For more information, see the ACS Style
Guide, pp. 218-222.
The reaction is known to be first order in
sucrose, so the concentration of sucrose as a
function of time follows the relationship
lnCt
C0= kt (1)
where C0 is the initial concentration of sucrose,
Ct is the sucrose concentration at time t after
the addition of invertase, and k is the first order
rate constant for the reaction. Since Ct is
proportional to (at - aeq) and C0 is proportional
to (a0 -aeq), wheret
a is defined as the rotation
angle at time t, equation 1 can be re-written as
follows:
• Numbered sequentially
• Properly formatted
• All variables introduced in text
• Grammar
Any figures used should be
labeled with a reference number
and a caption. The captions
should consist of complete
sentences, and give the reader
enough information to
understand the figure without
going back to the main body of
the text. Figures should be neatly
drawn and centered on the page.
If you need to draw chemical
structures your lab instructor will
help you find the necessary
software. For more information,
see the ACS Style Guide, p. 365
and pp. 375-383.
O
OHOH
OH
O
OH OH
OH OH
O
OH
OH
OH OH
O
OHOH
OHOH
OH
O
OH
invertase
+
Figure 1. Invertase catalyzes the hydrolysis of sucrose
into glucose and fructose. Sucrose has a positive specific
rotation ([ ]D = 66.5°), while the equimolar mixture of
glucose and fructose that results from hydrolysis has a
negative specific rotation ([ ]D = -22.0°) .
• Captions in complete
sentences
• Numbered sequentially
• Neat, centered
4
ktaa
aa
eq
eqt=
0
ln (2)
This implies that the rate constant k can be determined from a plot of ( )eqt
aaln versus
time. The rate constant k depends on the absolute temperature T according to the
Arrhenius Equation:
k = AeEaRT (3)
where Ea is the activation energy. Thus if the rate constant is determined at several
different temperatures, the activation energy can be determined via a modification of
equation (3) by plotting ln(k) versus 1/T.
lnk = lnAEaRT
(4)
Once the plot is constructed the slope can be used to calculate the activation energy as
follows.
Ea = -R•slope (5)
The data treatment consists of determining the rate constants for the invertase-catalyzed
hydrolysis of sucrose at three different temperatures followed by determining the
activation energy from an Arrhenius plot (ln(k) versus 1/T).
5
Methods and Materials
Start with a description of the chemicals you
used. Include the source, grade, and method
you used to purify them. If you used
chemicals as supplied without further
purification, say so. A diagram of
instrumentation used in the experiment can be
helpful. Be complete, accurate, and precise.
Do not give details that are common
knowledge in the field, but do provide
information of particular interest, such as the
brand name and model or a complicated
apparatus or unusual equipment (for example,
Oscilloscope – Tectronix Model 561B-CRO-
158, Serial #123456789).
For the experimental procedure, you
should use clear paragraph organization to
list all steps in the correct order. Be
complete. You should provide enough
information so that another researcher in
your field could use your description to
replicate the experiment. State what you
really did and what actually happened, not
what was supposed to happen or what the
textbook said. If you deviated from the
given procedure, describe the changes you
made and explain how the affected your
outcome. For more information, see the
ACS Style Guide, pp. 22-23.
Sucrose (Sigma-Aldrich, #47289) and
invertase (from baker’s yeast, Sigma-Aldrich,
#I9274) were used as received and all solutions
were made with distilled water. Optical rotation
was measured at a wavelength of 589 nm using a
digital polarimeter (Jasco, DIP-360) and a quartz
cell with a 10 cm path length. The concentration
of the sucrose solution used in each experiment
was 50 g/L. The invertase solution was prepared
in an acetate buffer with a pH of 5.0 at a
concentration of 0.04 g/L. Temperature was
controlled with a refrigerated circulating water
bath (VWR, 1140) connected to the polarimeter
cell. All solutions were placed in the
temperature bath prior to mixing for thermal
equilibration.
Experiments were conducted at 300K,
310K, and 320K using the same procedure.
First the polarimeter cell was filled with sucrose
solution (~10 mL) and the optical rotation was
measured producing a0. Next, 5 mL of sucrose
solution was removed and 5 mL of the invertase
solution was added. After the addition of
invertase the optical rotation was measured
every 5 minutes until the measured value
approached the equilibrium value (aeq). The
equilibrium optical rotation (aeq) was measured
at t = 60 minutes for each temperature.
• source and grade of chemicals
• chemical purification/sample prep
• make and model of instrument(s)
• diagram of apparatus if needed
• complete
• clear
• no grammar errors
• past tense narrative format (not a list)
6
Results
State your actual, not expected, results.
Although results are usually presented
quantitatively, you should always introduce
each block of information with simple, clear
language. Do not rely upon figures, graphs and
tables exclusively to convey essential
information. Merely supplying the equations
or diagrams and expecting the reader to
interpret them without guidance from you is
not sufficient. You should describe all
significant results in words, clearly and simply.
Refer to the raw data only to point out trends
and identify special features. For more
information, see the ACS Style Guide, pp. 23.
Figures 2 through 4 show the change in
ln(at - aeq) as a function of time for 300K,
310K, and 320K respectively. As described
above by Equation 2, the slope of the graph of
ln(at -aeq) versus time will be equal to the
negative of the rate constant. The rate
constants for each temperature are indicated in
each figure and will be used to determine the
activation energy for the catalyzed reaction via
an Arrhenius Plot. Errors in the rate constants
were determined by a linear regression using
Excel. The linearity of each graph is quite
good, R2 values greater than 0.99 in each case,
which confirms the reaction is first order with
respect to the sucrose concentration. Further,
as expected the rate constants increase with
increasing temperature.
• All results presented
• Results explained
On all graphs, label both axes
and include the units of any
physical quantity. If you
have fit a curve to the data,
state the equation and the
values for the parameters in
the caption. Also, scale the
axes so the data occupies the
entire graph; don’t crowd the
data into one corner or side of
the graph. For more
information, see the ACS
Style Guide, pp. 344-360.
• axis labeled and units
• regression equation(s)
• Scaling
Figure 2: The optical rotation of sucrose is graphed versus time for hydrolysis at 300K.
The data were fit to Eq. 2, resulting in k = 0.065 ± 0.001 min-1
.
7
Figure 3: The optical rotation of sucrose is graphed versus time for hydrolysis at
310K.The data were fit to Eq. 2, resulting in k = 0.095 ± 0.002 min-1
.
Figure 4: The optical rotation of sucrose is graphed versus time for hydrolysis at 320K.
The data were fit to Eq. 2, resulting in k = 0.135 ± 0.006 min-1
.
The data obtained from Figures 2 through 4 is shown in Table 1 along with the
calculated values lnk and 1/T. Errors in the calculated values were determined by using
the propagation equations shown in Appendix A. The data in Table 1 was used to
8
construct an Arrhenius Plot (lnk versus 1/T) and to determine the activation energy for
the reaction.
Tables should be labeled and
given a reference number.
All Tables should be labeled
with titles, such as “Table 1.
Mass of Chloride Samples”.
Tables should be neatly
formatted and centered on the
page. Rule of thumb: If there
are more than ten rows or
columns, consider moving the
table to an appendix. For
more information, see the
ACS Style Guide, pp. 369-
374.
Table 1: Rate Constant Data For Different Temperatures
T ± error
(K)
k ± error
(min-1) lnk± error 1/T •10
-3± error
(K-1
)
300 ± 1 0.065 ± 0.001 -2.73 ± 0.02 3.33 ± 0.01
310 ± 1 0.095 ± 0.002 -2.35 ± 0.02 3.22 ± 0.01
320 ± 1 0.135 ± 0.006 -2.00 ± 0.04 3.13 ± 0.01
• Titled
• Proper units
• Error values
• Numbered
sequentially
• Neat, centered
9
Figure 5 shows the Arrhenius Plot obtained from the data in Table 1. As described in the
introduction the activation energy can be determined from the slope of a plot of lnk
versus 1/T via Equations 4 and 5.
Figure 5: Arrhenius plot for the hydrolysis of sucrose resulted in an activation energy of
29.3±0.2 kJ/mol.
10
Discussion
This section is the single most important part
of your report. Here, you have the opportunity
to of show that you understand the experiment
beyond the simple level of completing it. You
must explain, analyze, and interpret your
results. Be especially careful to account for
any errors or problems. You must not only
report the proper information, but also provide
evidence that you understand the material that
you are presenting.
The underlying question for this section is
“What is the significance of the results?” More
particularly focus your attention on questions
like these:
• What results were expected? What
results were obtained? If there are
any discrepancies, how can you
account for them?
• Do any of your results have particular
technical or theoretical interest?
• How do your results relate to your
experimental objective(s)?
• How do your results compare to those
obtained in similar investigations?
• What are the strengths and limitations
of your experimental design?
• If you encountered difficulties in the
experiment, what were their sources?
How might they be avoided in future
experiments?
For more information, see the ACS Style
Guide, p. 23.
As shown in Figure 5 the activation
energy for the invertase-catalyzed hydrolysis
of sucrose is 29.2 +/- 0.2 kJ/mol. This value is
a measure of the energy barrier that the
reactants (sucrose, water, and invertase) must
overcome before products can be formed. The
uncertainty in the activation energy was
determined by a linear regression using Excel.
It is important to note that the R2 value for the
Arrhenius Plot is 1, which indicates excellent
agreement with the Arrhenius equation. In
addition, since a linear regression of the data
was used to determine the uncertainty in the
activation energy the value obtained is quite
small and may underestimate the error in the
experiment. A significant source of error was
temperature drift in the water bath, which was
approximately 1 °C.
The rate constants for the hydrolysis of
sucrose are summarized in Table 2.
Table 2: Rate Constants
The activation energy as determined from
the slope of the plot in Figure 5 is: Ea = 29.2
+/- 0.2 kJ/mol. Reference (1) gives a value of
31.4 kJ/mole for the value of Ea and thus the
actual error in our measured Ea value is [(31.4
– 29.2)/31.4]x100% = 7 %. However, the
actual value of 31.4 kJ/mol does not fall within
the uncertainty of our reported value, 29.2 +/-
0.2 kJ/mol. The fortuitous good fit exhibited in
the Arrhenius Plot led to underestimation of
the error in the experiment.
Temperature
(K)
Rate Constant
(min-1
)
300 0.065 ± 0.001
310 0.095 ± 0.002
320 0.135 ± 0.006
• sources of error
• clear
• concise
• no major conceptual errors
• no grammar errors
• comparison of literature value
• future work suggested
Note on combining sections:
The results and discussion sections can be combined in various ways.
Use whatever combination is most appropriate for your situation.
11
Conclusion
Draw conclusions from the results and
discussion that answer the question, ”So
what?” Then go on to explain your
conclusions. In this section, you may also
criticize the lab experiment and make
recommendations for improvement. For
more information, see the ACS Style Guide,
p. 23.
Repetition of the experiment over a wider
temperature range may lead to a better estimate
of the activation energy.
• significance of your result
• improvements suggested
• clear
• concise
• no major conceptual errors
• no grammar errors
12
References
In your references section, include only
those papers that you have read and cited in
your report. Be sure that the citation
numbers match those in your report, and use
a consistent format. It is useful to have a
journal article at hand so that you may
duplicate the format. Journals differ in their
format styles, so if you are unsure of which
one to use, ask your lab instructor. For more
information, see the ACS Style Guide, pp. 7-
8 and 287-339.
1. “New and modified invertases and their
applications.” In: Topics in Enzyme and
Fermentation Biotechnology, A. Wiseman,
Editor, Chapter 6, Wiley & Sons, New York
(1979), pp. 267–284.
2. Huang, Y. H.; Picha, D. H.; Johnson, C. E.;
J. Agric. Food Chem.; 1998; 46(8); 3158-3161.
3. Rubio, M.; Runco, R.; and Navarro, A.
Phytochemistry, Volume 61, Issue 6,
November 2002, pp 605-609 27.2536 kJ/mol
• Numbered as in report
• Correctly formatted
4. Picha, D. H.; Kilili, A. W.; Johnson, C. E.; J. Agric. Food Chem.; 1999; 47(12); pp.
4927-4931.
13
Appendix A: Error Propagation
Introduction
Appendices may include raw data, calculations,
graphs, and other quantitative materials that were
part of the experiment but not detailed in any of
the above sections. Refer to each appendix at
the appropriate point in your report. For
example, at the end of your results section, you
might have the note, “See Appendix A: Raw
Data Tables.”
The uncertainty in reading a is estimated to
be about ± 0.02˚ and is based on the
fluctuations in the readout of the digital
polarimeter. The uncertainty in the
temperature at which reaction rates were
measured is about ±1˚C and is based on the
observed temperature drift during each
experiment. Uncertainties in time
measurements were 4 seconds and were
estimated as the amount of time required to
record the rotation and time simultaneously.
The errors in (at – aeq) and ln(at – aeq) were
calculated by propagating the error from the
optical rotation using the equations shown in
below.
• raw data
• calculation spreadsheets
• error equations that you used
(A1) ( ) 2•=aeqat
(A2) ( )( )
eqt
aa
aaaa
eqt
eqt=
ln
(A3) Errors in the rate constants were determined from a linear regression
performed in Excel using ln(at - aeq) versus time data.
(A4) lnk =kk
(A5) 1/ T =T
T2
(A6) The error in the slope obtained from the Arrhenius plot was determined
from a linear regression performed in Excel using lnk versus 1/T data.
(A7) Ea = R• slope
14
Appendix B: Raw Data
Tables 1 through 3 give the values of t (the measured optical rotation), ( t - ), and
ln( t - ) measured as a function of reaction time.
Table B1: Optical Rotation as a Function of Time for the Hydrolysis of Sucrose at 300K
Time (min) error at (deg) error at – aeq (deg) error ln(at – aeq) error
0 0.07 22.52 0.02 26.02 0.03 3.259 0.001
5 0.07 14.54 0.02 18.04 0.03 2.893 0.002
10 0.07 10.51 0.02 14.01 0.03 2.640 0.002
15 0.07 6.52 0.02 10.02 0.03 2.305 0.003
20 0.07 3.41 0.02 6.91 0.03 1.933 0.004
25 0.07 1.53 0.02 5.03 0.03 1.615 0.006
30 0.07 0.51 0.02 4.01 0.03 1.389 0.007
35 0.07 -0.99 0.02 2.51 0.03 0.92 0.01
40 0.07 -1.72 0.02 1.78 0.03 0.58 0.02
45 0.07 -2.03 0.02 1.47 0.03 0.39 0.02
-3.5 0.02 0.00
Table B2: Optical Rotation as a Function of Time for the Hydrolysis of Sucrose at 310K
Time (min) error at (deg) error at - aeq (deg) error ln(at – aeq) error
0 0.07 22.00 0.02 25.50 0.03 3.239 0.001
5 0.07 11.97 0.02 15.47 0.03 2.739 0.002
10 0.07 5.95 0.02 9.45 0.03 2.246 0.003
15 0.07 3.00 0.02 6.50 0.03 1.872 0.005
20 0.07 0.25 0.02 3.75 0.03 1.322 0.008
25 0.07 -1.04 0.02 2.46 0.03 0.90 0.01
30 0.07 -2.12 0.02 1.38 0.03 0.32 0.02
-3.50 0.02 0.00
Table B3: Optical Rotation as a Function of Time for the Hydrolysis of Sucrose at 320K
Time (min) error at (deg) error at – aeq (deg) error ln(at – aeq) error
0 0.07 22.20 0.02 25.70 0.03 3.247 0.001
5 0.07 8.90 0.02 12.40 0.03 2.518 0.002
10 0.07 3.48 0.02 6.98 0.03 1.943 0.004
15 0.07 0.32 0.02 3.82 0.03 1.340 0.008
20 0.07 -1.92 0.02 1.58 0.03 0.46 0.02
-3.50 0.02 0.00