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).

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.

    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:

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,