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| The purpose
of this handbook is to provide the student with
a uniform set of policies and procedures for the
upper division Physical (CH 265), Analytical (CH
232, CH 234) , and Inorganic (CH 215) Chemistry
Laboratory courses at the University of Connecticut.
It deals with the issues of laboratory safety, chemical
disposal, laboratory reports, notebooks, data reporting,
and error analysis. It does not include instructions
for the experiments to be carried out or grading
policies for particular laboratory courses. Please
refer to your course syllabus for that information.
The following instructors contributed to this handbook:
Robert Bohn, Harry Frank, Jane Knox, Vijay Kumar,
Brenda Shaw, John Tanaka, James Stuart, and Steve
Suib. |
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It is essential that all students
work in a safe and responsible manner in the laboratory.
Your instructors will announce general safety
and emergency procedures at the beginning of the
semester, and more specific safety precautions
as appropriate. You are expected to be on time
to lab to hear this information as it is announced.
It is your responsibility to follow recommended
safety precautions, and to ask questions when
you are uncertain about appropriate safety procedures.
Eye
protection must be worn at all times in the laboratory.
Only officially approved safety
glasses and/or goggles will be allowed. Wearing
of contact lenses in the laboratory is discouraged
in most cases.
Please inform the instructor
of any health conditions, including asthma, wearing
of contact lenses, or other special needs that
you have that might require special attention
in case of an accident.
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Protect yourself by minimizing
your exposure to laboratory chemicals and potentially
hazardous samples (including biological hazards).
Exposure to chemicals and pathogens can occur
by inhalation, swallowing, or touching. Use volatile
materials in a hood.
Eating,
drinking or smoking in the laboratory is strictly
forbidden.
Be sure to wash hands carefully
before eating, drinking, or smoking outside the
lab, and at the end of each lab period. Do not
touch laboratory chemicals, or allow them to splash
onto you. If you are exposed to chemicals, inform
the instructor or teaching assistant at once.
General emergency procedures will be discussed
in class.
If you spill something on
you, inform the instructor immediately. Do not
feel embarrassed and leave the lab without telling
someone.
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You have a responsibility
to practice safe laboratory procedures to avoid
hazards for others in the laboratory. Carry laboratory
materials with extreme care. Support objects firmly.
Make two trips rather than risk dropping something.
Be especially careful when carrying awkward items,
such as burettes and desicators. Do not turn or
stop suddenly, or cut corners next to the wall
when walking in the hallway.
If you observe someone
who has an accident, be sure to inform the instructor.
Even minor accidents sometimes cause the person
directly involved to panic, or faint, which can
make the accident much worse. Help someone if
action must be taken immediately, and if you know
how to help. Summon the instructor as soon as
possible.
Please report any
mishaps involving the safety of yourself or others
to the instructor, no matter how minor they may
seem.
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In addition to personal safety,
scientists must also be responsible for the safety
of those who may be exposed to waste materials
generated in the laboratory, and to the well-being
of the earths environment.
The amount of waste you
generate should be minimized. Take only as much
of a chemical reagent as you know you will use.
You can get more, if needed.
General guidelines will be
given for disposal of chemical wastes. Specific
disposal procedures will be given along with introductory
material presented in pre-lab lectures.
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Science progresses because
scientists have access to information obtained
by other scientists. Knowledge builds on a foundation
of knowledge. Data are collected by one person
or group, and shared with other scientists through
lectures and publications. In order to be useful,
indeed not misleading, the data must be collected
carefully so it is true (i. e. accurate and precise).
It must also be reported in a manner that is accessible
to others and easily understood.
The process of communicating
scientific findings begins with record keeping.
Scientists keep detailed records of ideas, hypotheses,
plans for experiments, procedures (including diagrams
of apparatus), data, data analysis, conclusions,
and interpretation of results. There are several
reasons for keeping this information in a series
of permanently-bound notebooks:
1. Work is facilitated
because notes are organized and progress may be
observed easily. Time is saved, and loss of data
is more easily prevented than if data are recorded
haphazardly.
2. The original data are
accessible to others. Raw data are more likely
to be free of bias than published results. The
researcher who collected the data may have missed
some of the useful conclusions that may have been
drawn from the data, or theory may be developed
to help interpret the data long after it was collected.
Someone may wish to see the original data to test
a new hypothesis.
3. The notebook should
make it easy to find calculation errors because
data, calculations, and results are all found
in one place.
4. The notebook provides
an easy way to remember details of a procedure
or observation that might otherwise be forgotten.
Many new researchers are quite certain they will
remember experimental parameters and conditions
forever, only to find that as months pass, these
important facts are forgotten. In time one learns
to record more and more of the information that
might otherwise be lost.
5. Many routine analyses
are reported to doctors, government agencies,
the police, and so on. If questions arise as to
the validity of the results, it is useful to be
able to see the original record. The performance
of an instrument, or the purity of a reagent used
on a particular day may have affected the results
of the analysis. In some cases where difficulties
were not noted directly, the original record will
give a clue about possible problems.
Most instruments are accompanied
by a logbook, which is a research notebook for
recording parameters that indicate instrument
usage and performance. This information is helpful
in prescribing maintenance or determining the
effects of maintenance procedures on instrument
performance. This is especially important in case
data become suspect.
6. Finally, the research
notebook is a legal document when dated, signed,
and witnessed by someone who understands its contents
and the implications of results it contains. This
aspect of the notebook is most important in industrial
research, and perhaps academic research, when
the researcher wishes to apply for a patent based
on data obtained in the laboratory.
In many cases it is useful
to have an exact duplicate of the research notebook.
Most employers and professors insist that the
original notebook remain in their possession after
an employee or student leaves. The person who
prepared the notebook may find it useful in the
future, so may wish to have a duplicate. In the
case of field work, or work in a laboratory damaged
by explosion, flood, fire, etc. a notebook may
be lost or destroyed. The existence of a duplicate
notebook would save tremendous amounts of time,
money, and frustration.
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Clearly, it would be inefficient
to publish photocopies of research notebooks as
a means to share information among scientists.
A more formal report is written with a reader
in mind. The theory behind the experiment is explained
in more detail than in the notebook, since after
the results are obtained, more is known about
the system being studied. The introductory portion
of a report presents the theory that guides the
reader through the rest of the report: procedure,
data, calculations required to obtain final results,
and significance of the work.
It should be clear from
the report how data were obtained and analyzed,
and how reliable the results are. The experiment
should also be evaluated to inform the reader
of pitfalls and suggestions for improvements.
It also should be clear
from the report what are indisputable raw data,
what are results calculated from raw data, and
what are interpretations, which may be open to
disagreement.
Reports should begin with
general considerations and move toward specific
aspects of the work.
Enough information should
be given so another scientist who is unfamiliar
with the experiment could repeat the work exactly
from the information contained in the report.
In most cases, it is possible to refer the reader
to earlier work by oneself or others for some
portion of the experimental details.
Reports should give at
least a sample of raw data in some form. This
could be in tables or graphs. If a graph is given,
the table of data used to generate the graph would
be redundant.
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| The
oral presentation of scientific information is very
important for the careers of many scientists. Of
course the oral presentation must be different from
the written report in both content and format. There
is not enough time to present all the details that
make a written report rigorous and believable. The
speaker must therefore use other means of gaining
the confidence of his or her audience. This is usually
done by providing a careful and thorough introduction
to the topic, then presenting samples of relevant
data. Summaries can be given to show general trends.
The samples are important because they show the
audience the degree of care, the quality of data,
and the standards of the speaker. The speaker should
be prepared to provide additional written materials,
references, and so on, to members of the audience
who have a special interest in the topic. |
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| Calculators
and computers can greatly reduce the effort required
for computations. However, you must demonstrate
an understanding of the mathematics and statistics
you use, as well as an ability to use available
computing devices. Your lab notebook should show
the general equations you use, and a sample calculation
in most cases. Mean, standard deviation, confidence
intervals, linear regression, and so on may all
be obtained via calculator or computer, as long
as you demonstrate an understanding of the calculation
involved in your lab notebook. |
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The notebook itself should
be a permanently-bound book with numbered, graph-paper-ruled
pages. The book should also have removable pages
for use in keeping carbon copies of each original
page. No original pages should be removed from
the notebook. Because the notebook will serve
to collect data as well as to report results,
discussion, etc. for grading, a 100-page book
is recommended.
All entries should be
made in ink, except graphs. Graphs may be drawn
in pencil. Data should be recorded directly into
the lab notebook. Other entries (e.g. theory,
calculations, discussion) should be thought out
carefully and perhaps written first on scrap paper
before being recorded neatly in the notebook.
Erasure, obliteration
or writing over data are not acceptable. Incorrect
entries should be crossed out with one or two
lines in such a way that they may still be read.
Corrections should be entered nearby with an explanation
for the change.
The cover of the book
should bear your name, the date (semester and
year) and the institution at which the data were
collected (University of Connecticut). If additional
notebooks are used, these should be numbered.
A table of contents should appear at the front
of the book. Leave two or three pages blank at
the front of the book for filling in the Table
of Contents as you do experiments.
Each page should have
your name or initials or some other distinctive
symbol near the page number. This is important
since any filled, duplicate pages will be torn
out and collected at the end of each lab period.
Any partially filled pages to be continued
in the next period should be initialed by the
T.A. as duplicate pages are handed in. The
date should be clearly noted for all entries into
the notebook. Partners names should be recorded
when applicable.
All entries should be
identical on original and duplicate pages. When
an experiment is due, all remaining pages for
that experiment must be handed in at the beginning
of the lab period in which it is due. The student
is responsible for assembling and stapling the
full set of duplicate pages in numerical order,
and submitting the report to the instructor or
teaching assistant. Reports handed in on the due
date but after the start of lab will be considered
one day late along with those handed in the next
day. All late reports must be handed to the instructor
of record in person, rather than
to the T. A.
In case of severe
circumstances, special arrangements may
be approved by the instructor. These must be entered
into the lab notebook and signed by the instructor
in order to be honored by the T. A. It is the
responsibility of the student to obtain this permission
as soon as possible after the problem arises.
In general, the notebook
should be readily intelligible to another chemist
who is not familiar with the experiment. Someone
should be able to reproduce the experiment based
on entries in the notebook.
The table of contents,
and overall quality of the notebook will be checked
and graded.
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| 1. Before Lab |
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The success of any experiment
depends on advance preparation. In this course,
preparation will be demonstrated by entries in
the lab notebook before each experiment. When
the T.A. is free, ask him or her to examine and
initial the work appearing in the notebook early
in each lab period that you begin a new experiment.
The following entries should be made before coming
to lab:
Title of the experiment
(both in Table of Contents and start of new experiment
write-up in notebook).
Purpose: This should
consist of two parts, of one or two sentences
each.
A. Scientific objectives
B. Objectives for training
the student
Introduction: The
theory behind the experiment should be summarized
in one or two paragraphs; this is to ensure that
each student reads enough about the experiment
to understand the procedure.
Procedure: The
procedure should be recorded as a list of simple,
numbered steps. This is to make the experimental
work easier to carry out, both because breaking
the procedure into simple steps makes the student
familiar with it, and because it is much easier
to follow than the paragraph form found in the
lab manual.
Results: Tables
should be prepared with titles and units, just
waiting to be filled in.
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| 2. During Lab |
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Record all data, changes in
procedure, and observations directly into the
laboratory notebook. At least one sample calculation
should appear for each type of calculation you
do. Use the notebook for making a rough graph,
or to calculate whether precision is satisfactory.
As mentioned before, this should be done before
cleaning up, so that experiments may be repeated
if necessary.
When instruments are used,
a block diagram should appear in the procedure
section.
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Once an experiment has been
completed, carry out all final calculations and
answer all questions. This may be done first on
scrap paper. Use the Results section to record
sample calculations, tables, and so on. When fine
graphs are required, which is quite often, these
should be drawn carefully on good, high-precision
graph paper. A straight-edge and French or flexible
curve should be used where appropriate. Such graphs,
or recorder output from instrumental experiments,
should be presented neatly on 8 1/2" by 11"
paper. This may require cutting and pasting or
fan-folding, etc. These pages should then be stapled
to your report, and referred to by number in the
text of the report.
Summary: Once all
results are available, a Summary should give the
final outcome of the experiment. It also should
include all values obtained in multiple trials,
even those excluded statistically from the final
determination of the "best value."
Every major result should
be accompanied by an estimate of precision, and
its accuracy when the value is known. An explanation
should be given for how the precision and accuracy
were determined, even if statistical methods cannot
be used. Propagation of error should be used to
estimate precision when statistical methods do
not apply.
Note that the major portion
of the grade is often based on the values obtained,
and this portion of the grade is based on the
Summary section of the laboratory notebook.
Discussion: The
experiment should be evaluated in some way. Give
your reactions to the experiment. Is the precision
good or poor? Is the method reliable? Comment
on improvements that could be made based on your
experience with the experiment.
Answers to Questions
should be included in the Discussion section in
numerical order. These should be answered using
good English. The responses may be included in
the notebook or written on separate sheets to
be stapled at the end of the report.
The Summary
and Discussion sections together should take up
only half a page or so.
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Human accomplishments are
best rewarded by self-satisfaction, money, and
credit. It is not acceptable to take credit for
the creative work of another.
Each
student is required to work independently on all
out-of-class assignments. Discussion among
students is encouraged, but all written work should
be the result of an individual effort. Reports
on the same subject by a class of students are
remarkably unique. Each student organizes information
differently in his or her mind, and on paper.
The process of preparing a report is part of the
education gained in the course, and should not
be reduced to copying the ideas or efforts of
others.
For experiments in which
data are collected by pairs of students, raw data
(e.g. recorder traces) should be made available
to both students before they part company at the
end of the experiment. (There is a photocopying
machine in the building.) Each student should
carry out all measurements and calculations independently.
When writing reports,
information considered to be "general knowledge"
(e.g. acid-base theory) need not be referenced.
In this case, a list of sources at the end of
the report is sufficient. However, new information
obtained from research must bear a reference to
give credit to the scientist(s) who did the work.
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Warning about Academic Misconduct!
Please pay particular attention
to the fact that all laboratory reports and laboratory
papers that you submit to be graded fall under
the general category of "studentss
original work". If it is observed that there
has been deliberate copying from another students
report and both reports are handed in, both will
be considered as acts of plagiarism which would
be with dealt under the rule of "Academic
Misconduct" as specified in the Student
Handbook.
Similarities and Differences
between Lab Reports and Lab Papers.
Both Lab Reports and Lab Papers
should report the results of experimental work
in a timely and correct manner. Thus, these written
lab reports or lab papers are due exactly
one week, or by the announced date,
after the experiment is completed
unless otherwise specified or agreed upon by the
Laboratory Instructor. If either the lab report
or lab paper is late, there will be a cumulative
10 per cent deduction per
lab period that
the lab report is over due.
If the results are poor, or
have not been correctly worked up, you will be
asked to redo them correctly. Ultimately, you
must find the correct answer, but your grade will
reflect the necessity of redoing the laboratory
work, or calculations or the actual lab report
itself.
The second component is evidence
of a broader understanding of the analysis method.
In most cases, you are expected to describe the
basis of the methods in one or more paragraphs,
even though the topic might not yet have been
covered in the lecture part of this course.
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The lab report
(as opposed to a paper) should consist of the
following:
1. Summary (1-3 sentences)
2. Introduction (1-3 paragraphs)
Changes in the described experimental
procedure
3. Results and Discussion
including pertinent calculations
and statistical analyses
4. Conclusions to the experiment.
(Include your candid evaluation of the experiment
and its instructional worth and how it
may be made better).
5. Appendix 1 Carbon-copy
of the experimental laboratory data
6. Appendix 2 Example
of relevant calculations
7. Appendix 3 Computer print-outs,
Recorder output, if not included in the Results
and Discussion section.
8. Answers to any questions
in the laboratory write-up.
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The lab paper should consist
of the following sections:
1. Summary (1-2 paragraphs)
2. Introduction (1-3 pages)
3. Experimental (only the
changes from the written procedure, properly referenced
or a complete description in the case of a special
lab project)
4. Results and Discussion
5. Conclusions (with comments,
suggestions)
6. Appendix 1 (carbon-copies
of the lab book pages)
7. Appendix 2 (recorder and/or
computer output, again if not included in the
results section).
What follows is elaboration
of certain sections to the reports and papers.
Some of what follows was taken from the description
of what makes a good scientific paper presented
in "The ACS Style Guide" published in 1986
by the American Chemical Society. This booklet
is a good source of information on writing chemical
papers. However, because the function of a paper
in the teaching lab is not the same as the function
of a published scientific paper, there are some
differences between them.
The summary
of a paper serves several purposes. One is to
give the reader a brief introduction of
why the work was done. Also it should give a very
brief overview (executive summary) of the
major findings of the work. In the case of the
teaching lab, the summary should also help the
marker to determine the writer's understanding
of the main thrust of the lab experiment while
again summarizing the results that were obtained.
2.
Introduction
The
intention of this section is to introduce the
experiment and place it in the context of the
appropriate theoretical material. An "Introduction"
is neither an account of the experiment itself
nor an abstract discussion of theory. The "Introduction"
should be a synthesis of the two. Common errors
are to write the Introduction as a procedure or
to include only theory without mention of the
specific experiment. This section should show
that you have digested all important theoretical
aspects of the subject as found in the textbook.
In an
"Introduction" a brief description of the chemistry
involved, along with relevant chemical equations,
needs to be included. Any important mathematical
relationships, which allow the measured quantity
to be converted to the value of interest, should
be included here, or may be more appropriate in
the calculations section of the Results and Discussion
section.
3.
Experimental
The
experimental section should contain the important
steps of the procedure so as to enable a reader
to reproduce the experiment. Note you do
not have to copy word-for-word or even summarize
the procedure given in the laboratory handouts!.
But any deviations from the instructions should
be carefully noted with what explanations that
you feel are relevant. A block diagram of the
instrumentation may be included in this section.
This is a diagrammatic (as opposed to representational)
drawing showing the basic components of the instrument
and their relationship to each other.
4.
Results and Discussion
In this
section the results of the experiment should be
presented. When appropriate, it is most effective
to use either table(s) or figure(s). The tables
and figures should be placed in close proximity
where they are referred to in the text. When warranted,
discussion should be divided into topics with
each topic having a sub-heading started on the
far left side. The discussion should elucidate
the material in the tables and figures, and should
also relate back to the purpose and background
presented in the Introduction section.
A common
problem is to have too many numbers embedded in
text rather than in tables. The reader should
be able to find the numerical results summarized
in tables and figures without having to wade through
verbiage to find the numbers of interest. Tables
and figures should be labelled and have a title
as described.
5.
Statistical (Error) Analysis
In the
laboratory paper, one of the sub-sections of the
Results and Discussion section should be
an error analysis in which the results are evaluated.
Each situation is somewhat different, but the
following should be considered:
a.
Accuracy.
If the true value is known (e.g. from a primary
standard), a numerical error should be calculated.
Discussion of factors leading to the deviation
from the true value is appropriate. Was the result
obtained from an absolute measurement or a calibration
curve? How does the calibration affect the accuracy?
b.
Precision. If several
trials were done report an average deviation (AD)
or a standard deviation (SD) as well as a relative
average deviation (RAD) or a relative standard
deviation (RSD), which certain textbooks call
coefficient of variation. Answer such questions
as what contributes to the uncertainty in the
reported value? Is there an obvious limiting measurement
or is the uncertainty the result of many equally
contributing factors? Was a least squares analysis
done? Can a precision be reported from a calibration
plot? Is it meaningful to do a propagation of
error study? If only one trial was done, then
the only way to obtain a precision is by propagation
of errors method.
c.
What not to say in a Statistical Analysis.
Do not
say, "This experiment went moderately well", or
"The results were not very good". Say instead
... "Results were obtained with relative accuracy
of 1.5 per cent and a relative precision of 1.0%...
Changes which might be made in the procedure to
improve the outcome are ...." or ..."The accuracy
of 3.0 per cent is well within the range of what
one could expect for the determination of the
element (Praseodymium, atomic number 59) by the
instrumentation and the method used ...".
In other
words, use an explanation supported by numerical
values whenever possible and be specific.
6.
Conclusion
A conclusion
should briefly summarize the key findings reported
in the Discussion section. Basically the Conclusion is a statement of the information obtained;
what was found out. A common error is to put
too much information in the conclusion which really
belongs in the discussion. If your conclusion
is more than a paragraph, it should really be
in the discussion.
Example of
an acceptable Conclusion: "The determination of
the percentage of Uconium in the sample by our
method was 5.00 ± 25% (ARSD), whereas the
standard method gave 5.05 ±10% (ARSD). The use
of an acid catalyzed reaction in the preparation
of the topane derivative decreased the analysis
time by ten hours, but also decreased the precision
in terms of ARSD by 15%. Hence a quicker, more
precise analysis could be done by Circular Monotopic
Voltammetry, but this involves expensive equipment
which is not commonly available. The developed
analysis method provides for a viable alternative
to the tedious standard procedure.
7.
Appendices
1.
Appendix 1 should contain all carbon copies of
the data pages from the Lab Notebook.
2.
Appendix 2 should contain all of the relevant
calculations which were not included for one reason
or another in the Results section. Note that graphs
are not calculations and do not belong
in Appendix 2.
3.
Appendix 3 should contain the original or good-quality,
photocopies of the recorder or computer outputs.
These should be taped or pasted onto 8 x 11.5
inch paper. Never include a long partial roll
of recorder or integrator output with the
report!
8.
Format for both the Lab Reports and Lab Papers.
Please follow the format given here.
1.
The Lab Reports and Lab Papers should be divided
into the sections that have been described previously.
2.
The headings for the major sections should be
in the center of the page and should be
underlined.
3.
Sub-headings should be placed at the left margin
and be underlined.
4.
Figures and tables should be set off from the
text and be given a number (Arabic numerals, -e.g.,
1,2..10) and a title. They should appear
as close to the pertinent text as possible.
A.
Writing
A
portion of the grade for each lab report or lab
paper grade will be based on the writing itself.
Grammar, spelling, clarity, and style will all
be considered. Remember
to use a Spell and Grammar Check associated with
the Word Processing Software that you are using.
(You have the tools, use them!)
When describing things done in the lab, the past
tense should be used.
For
example- " the lab experiment was done according
to the description of the laboratory handout"
... and not "I did the following experiment according
to the description of the laboratory handout".
When describing established, factual material,
the present tense can be used. Most of the time
the passive voice is more appropriate, although
this rule is not considered to be as hard and
fast as it once was. Avoid using personal pronouns
(I,we,you) in scientific writing.
B. Graphs
Graphs
are a very effective at summarizing and presenting
experimental data. Graphs may be done by computer
or by hand. Computer generated graphs usually
will not give a very precise answer unless the
equation for the function is known, as when using
linear regression. Thus sometimes, a computer
generated graph will not give answers containing
the number of significant figures commensurate
with the precision of the measurements.
Some
guidelines for creating graphs follow:
a.
Graphs should be labelled FIGURE 1, FIGURE 2,
etc.
b.
Graphs should have a good title. "Calibration
Plot" is not a good title. "Calibration Curve
for the Spectrophotometric Analysis of Fe..."
is better.
c.
Axes should be completely and appropriately labeled.
d.
If drawing your own graphs, use millimeter graph
paper.
e.
Don't make straight lines out of data unless the
data is linear! Circle or somehow identify the
data points.
f.
Graphs should indicate the trend with smooth curves
and not by just "connecting the dots". (Computer
are good at connecting points and such plots should
be avoided).
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This
section gives some explicit instructions for various
policies in the laboratory. Use these in conjunction
with the preceding material.
A.
Experimental Work
1. Balance Policies
Analytical
balances, especially the four or five place, digital
or substitution balances, are capable of measuring
the weight of an object to 0.0001 or even 0.00001
grams-, -i.e. (0.1 mg or 0.01 mg). These balances
if properly calibrated and maintained are possibly
the most accurate and precise measuring instrument
found in any laboratory. Whether
those balances might be in analytical, physical,
advanced inorganic and organic and whether they
might be in academic or in such industrial laboratories
as: biotechnical, forensic, pharmaceutical or
polymer laboratory.
Hence,
it is imperative that our
shared analytical balances be kept in excellent
operating condition. I
should be noted that each balance in the Advanced
Chemistry Courses of the Dept. of Chemistry of
UCONN is checked daily by a member of the
teaching staff for its proper operation and general
cleanliness. Also each year, an outside balance
servicing company is hired to come in to properly
service and if necessarily perform major repair
on each balance.
It
is absolutely imperative that each student needs
to first hear "Introductory Balance Talk"
and do the introductory about five minute weighing
experiment conducted by a qualified laboratory
instructor or teaching assistant. Then each student
needs to adhere to the rules that are given below.
Repeated failure to do
so, after having received a clear warning from
their proper teaching staff member, will cause
that student to be assigned to do weightings on
the older substitution balance, (which takes about
2 min.) to accomplish the same weighing measurement
that otherwise could be done on the newer digital
balances (within about 30 seconds).
(Note these
substitution balances are just as accurate but
perhaps not as reproducible as the newer digital
balances). And as is evident take at least four
time longer to achieve the same weighing.
General
Rules for the Use of Analytical Balances
1.
No one may use a balance without first hearing
an "introductory balance talk" given
by a laboratory instructor or teaching assistant.
2.
Use only the balance
to which you are assigned. This must be done even
if the assigned balance is in use by another assignee
at this particular time. (Remember it usually
takes within 30 seconds. to accomplish one weighing
or only a matter of a few minutes to complete
a series of weighings). Posted near the balance
will be a list of those students that have been
assigned to use that particular balance for the
current semester.
3.
If there seems to be a problem with the balance,
report it immediately, to the instructor
or teaching assistant. Do not use another balance,
unless instructed to do so.
4.
It is imperative that you
keep the balance and the immediate area around
the balance clean!
Clean-up all chemical spills and excess chemical
after each use of the balance. Do not leave
old Kimwipes® or crumpled papers on the balance
table.
5.
When the balances are not in use, the balance
should be always turned-off and in the case of
the substitution balances the beam arrested,
all weights on zero and the doors closed.
2. Classical Experiments
You
should obtain at least three experimental values
for each analysis. Report all experimental values
and your final value, which is your best
judgment
for the true value of the percentage, concentration,
etc. being determined. Also report the accepted
statistical methods used to arrive at the final
value from all available data. If the first three
experimental values obtained do not give acceptable
precision, be sure to continue experimental work
until you are satisfied with your results. In
some cases, time may limit the number of trials
that may be performed.
3. Experiments Involving
Instrumentation
Follow procedures
for the number of trials to be performed in instrumental
experiments. Three trials are not always necessary,
or possible in the time available.
You will
be scheduled by the lab instructor for a time
block and a partner for performing each instrumental
laboratory experiment. Obtaining a schedule that
accommodates all students in time to meet report
deadlines, sharing of instruments with other classes,
occasional instrumental breakdowns, illness of
students, and rotation of partners is more of
a challenge than it may appear.
It is
important that students be in lab on time when
scheduled for an instrumental experiment. In order
to make the best use of instruments, someone may
be given your time slot if you are late to lab.
If you must miss a lab period because of some
emergency, please call the instructor as far in
advance as possible. A telephone is located in
each of the advanced laboratories and its number
will be made available at the beginning of the
semester.
If you
miss a scheduled time for an instrumental lab,
you may lose your chance to collect data, causing
you to receive a very low grade for the lab notebook
for that experiment. If arrangements can be made
easily to reschedule the lab after the rest of
the class has been accommodated, you may have
a chance to make up the work.
4. "Unknowns"
When an unknown
is needed for an experiment, check the list in
the lab to determine which series unknown you
need (e.g. Series D). Ask for the appropriate
unknown from the laboratory instructor or teaching
assistant. Stockroom personnel purposely know
as little as possible about unknowns. Be sure
to ask for the right one.
After receiving
the first unknown, future unknowns may be obtained
by presenting the clean (and rinsed with distilled
water) vial, without label from the previous unknown
and asking for the next one by series.
Immediately
record the unknown number directly into your lab
notebook. You are responsible for reporting which
sample you are analyzing in order to receive credit
for your data. No one else will have this information.
If the unknown
is to be dried, transfer to a clean, dry, LABELED
weighing bottle and place in the oven as described
in class. Do not put vials in the oven.
Chemists
generally have a small, finite amount of a sample
to work with. Samples provided will also be available
in limited amounts. Be sure to plan your work
so that reliable data are obtained before you
run out of "unknown".
B.
Grading
Please
refer to your course syllabus for the specific
manner in which grades will be assigned. Generally,
high standards of safety, cleanliness, honesty,
and cooperation are part of laboratory work and
are assumed in all courses. If these are not met,
penalties commensurate with the infraction will
be applied to the experiment grade or course.
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A.
Introduction
1. Accuracy
When a quantitative
value is determined experimentally, our main concern
is that we obtain the "right" answer. The comparison
between our experimentally determined value and
the true value is a measure of accuracy.
Definition:
Accuracy
is the degree of agreement between the experimental
value and the true value.
The accuracy
has a sign associated with it and that sign indicates
whether the experimental value is high (+) or
low (-) with respect to the true value.
Example:
A solution
known to have a pH of 8.00 pH units is measured
with a pH meter and the average of several trials
is found to be 7.90 pH units.
The accuracy
is 7.90 pH units - 8.00 pH units = -0.10 pH units.
This
gives an absolute error because the units
of the error are the same as the units of the
measurement. A relative error can also
be calculated with respect to the true value:
Note that
the relative error is unitless.
The accuracy
can only be measured if the true value is known
which is not always the case; someone has to have
found it in the first place by some method. Different
methods might inherently give slightly different
answers. Which method will ultimately be used
to provide the "true" answer? Even standards change
occasionally as the ability to make certain types
of measurements change. Up until 1948 the coulomb
was defined as the quantity of electricity which
must pass through a circuit to deposit 0.0011180
grams of silver from a solution of silver nitrate.
Now it is defined as the quantity of electricity
on the positive plate of a condenser of one farad
capacity when the electromotive force is one volt.
We will
not deal here with the problem of what is the
true value. You should be aware, however, that
it is not as straightforward as you might have
thought. For that reason, perhaps accepted
value is a better term.
2. Determinate Errors
and Accuracy
What is it
that keeps every measurement or analysis from
being completely accurate? That is, what causes
the discrepancy between the accepted value and
the measured value? The discrepancy is caused
by many small deviations which can be divided
into two groups: determinate and indeterminate
errors.
Definition:
Determinate
errors are errors which have a definite value
that can, in principle, be measured and accounted
for.
Determinate
errors, also called systematic errors, can be
divided into arbitrary categories. The most common
divisions are instrumental, operator, and method
errors. Determinate errors are often unidirectional,
that is they are all positive or all negative
with respect to the accepted value. Be aware that
determinate errors can be corrected for but only
after the cause is determined. This might take
some detective work. For example, an incorrectly
calibrated instrument might give results which
are too high; this determinate error would be
the fault of the operator. On the other hand,
an instrument signal drifting downward might give
a low value and illustrates instrumental error.
3.
Indeterminate Error
and Precision
Even when
all determinate errors are corrected and compensated
for, the same measurement taken several times
will not necessarily give the same answer. This
is because of indeterminate errors also called
random or statistical errors.
Definition:
Indeterminate
errors are errors which fluctuate randomly
and do not have a definite value; They cannot
be positively identified.
To further
understand indeterminate errors, consider the
weight of an object obtained by doing five different
weighings on a four place analytical balance.
trial
1: 0.7952 g
trial
2: 0.7950 g
trial
3: 0.7951 g
trial
4: 0.7953 g
trial
5: 0.7951 g
The first
three figures are the same in all cases. The last
figure has an uncertainty associated with it.
This uncertainty is a function of the type of
sample, the conditions under which it is being
weighed, the balance, and the person doing the
weighing. Even when all factors are optimized,
there will still be some variation in the weight.
This variation or uncertainty is the result of
pushing the balance to its limit.
We could
cut the last figure off; then all the weights
would be the same, but the weight would be known
only to the nearest milligram. We obtain more
information if we keep that last figure but remain
aware of its uncertainty. That uncertainty arises
because of indeterminate error; and is indicative
of the precision of the measurement.
Definition:
Precision is the degree
of agreement between replicate measurements of
the same quantity.
Note
that even if the precision of a measurement is
excellent, the value obtained can have poor accuracy
if there has been a determinate error. For example,
an incorrectly calibrated instrument cannot give
an accurate reading although the precision very
likely will not be affected. On the other hand,
poor precision rarely results in an accurate value
being obtained.
B.
Uncertainty
The element
of uncertainty in experimental data can be quantified
and is often reported along with the actual experimental
value itself. The value of the uncertainty gives
one an idea of the precision inherent in a measurement
of an experimental quantity. So important is the
concept of uncertainty it actually has a principle
named after it. With the uncertainty being reported
along with the experimental quantity one has an
idea of how "good" the reported experimental value
is. Consequently, comparisons of the numbers obtained
in a series of measurements with the same or different
techniques are made more meaningful by the inclusion
of uncertainties.
There
are many ways to quantify uncertainty, ranging
from very simple techniques to highly sophisticated
methods. The method used will depend upon how
many measurements of a single quantity are made
and on how crucial the reporting of the value
of uncertainty is with regard to the interpretation
of the experimental data. The following is a list
of many of the ways in which uncertainty is reported.
1.
Standard Deviation
a.
Deviation of the Expression for Standard Deviation
The
most widely used method for calculating uncertainty
is representing it by the standard deviation of
a series of measurements. This can be easily accomplished
if it is assumed that a gaussian distribution
function best describes the spread in the error
values for a series of measurements made on a
single observable. The distribution function is
then termed a "normal" error probability function
and written

where
represents the error in a measurement (negative
or positive) and
is a parameter known as the standard deviation.
One can see from this equation that
is related to the width of the distribution of
errors. If
has a small value, the probability function decreases
rapidly from its maximum value (where
=0) indicating that the probability of large errors
in the measurement is small. If
has a large value, the probability function is
broad indicating a high degree of probable error
in the measurement. Mathematically
is defined as the root-mean-square error associated
with this probability function.

where
2
is the mean of the squared errors. If each individual
error,
is known exactly (through knowledge of the true
value of the observable) an approximate formula
for
can be derived; it is given by

where
is the number of independent data or degrees of
freedom on which the calculation of is
based, and
is the difference between the observed value and
the true value of a quantity (i.e., = ).
In a
typical experiment one would not know the true
value of an observable (or why do the experiment?).
A good approximation to the true value of an observable
is the arithmetic mean, ,
of a series of n measurements (neglecting systematic
error),

where
the
are the values for the individual measurements.
Because it is known that the sum of an entire
set of deviations from the mean must necessarily
add up to zero, i.e.,

then a knowledge
of only n-1 values of
is necessary to define the nth or last value.
That is any value
can be determined from the remaining
values provided the mean
has been calculated. Thus, it is found that calculating
the mean value, ,
reduces the number of independent variables or
degrees of freedom with which one can determine
the precision inherent in a series of measurements.
The problem
of determining the uncertainty (which is a measure
of precision) in a series of measurements of a
single observable by the standard deviation method
is solved by using the formula

where
s2
is termed the variance, and the n-1 term
in the denominator follows from the above discussion.
This represents the best estimate of the standard
deviation for a finite set of data. Note that
is being approximated by ,
hence n-1 appears in this equation.
b.
Calculation of the Standard Deviation
The standard
deviation of a set of five weights can be calculated
as shown:

|
0.7962
|
0.0010
|
1.0
10-6
|
|
0.7950
|
-0.0002
|
4.0
10-8
|
|
0.7941
|
-0.0011
|
1.2
10-6
|
|
0.7953
|
0.0001
|
1.0
10-8
|
|
0.7955
|
0.0003
|
9.0
10-8
|



Note
that the standard deviation has the same units
as the measurement itself, i.e., g, and is thus
a measure of absolute precision. The number
of figures used to express x and s
is explained in Section IV, Significant Figures.
The
standard deviation can be expressed relative to
the mean giving a measure of relative precision.
Relative precision can be expressed as a fraction,
a percentage, parts per thousand, or any other
desired relative measure. When it is expressed
as a fraction, it is usually referred to as the
coefficient of variation.


Notice
that the relative error is a unitless number.
2.
Average Deviation
Sometimes
to get a quick estimate of the uncertainty or
precision, it is easier to use the average deviation.
The average absolute deviation is simply the mean
of the sum of the deviation of individual trials
from the mean without regard to sign (if the sign
were taken into account, the sum of deviations
would of course be zero).

In
the case of the weights which we have been looking
at, the average absolute deviation is:


The average
absolute deviation is a measure of absolute uncertainty
because it is in the same units as the measurement, | | |