Fifty-six Abstracts

50 Abstracts:

Introduction:

This is a collection of all of the abstracts written for one assignment by students in my CHEM1415 course. Following this brief introduction, everything else is there work, not mine. In a few cases I have made minor reformatting changes (double to single spacing, etc.). I have not made other changes or tried to correct English or spelling. They are in no particular order.

The abstracts were produced by first year students all working from very similar data obtained while performing two experiments.

The purpose of presenting the collection of student abstracts is to give students a glimpse of what educators see from their side of the desk. It should be clear to anyone reading these, that there is a range of quality. Taking some time to skim these abstracts, should give an idea what makes a good abstract. The time spent analyzing them will not be wasted. My favorite was number 41. This was a uniquely well-done abstract, very high density of information in that one.

Finally, there may be one or two repeats. Several students used the same file name and this made the tracking of the individual papers more difficult. My apologies if I have gotten this wrong.


The abstracts:
1. In this experiment, two tests were carried out. In the first test, one coin was weighed ten times and standard deviation and mean of the masses were found. These results were compared to those of another student and T and F tests were performed. In the second test, twenty coins were weighed and the results of masses and year obtained along with the results obtained form the class were pooled. These results were tested by the use of a chi square test to determine if the masses showed a Gaussian distribution or not. In these two tests, multiple readings were taken to reduce error.

2. The mass of the Barbados pennies were weighed to see their distributions over a period of time. One penny was measured ten times to review its average mass. The other twenty pennies were each measured once to review the difference of their masses over a period of years. It was sought that their masses got smaller as the years past, though they were few exceptions. This is because the weight of some of these pennies vary due to corrosion, oxidation and even fingerprints.
The weight calibrations of a set of volumetric glassware were measured. They were done carefully accounting for thermal expansion of solutions and glassware.

3. The first set of experiments dealt with the mass distribution of Barbadian pennies and yielded two distinct distributions with 1987 being the intermediary date. The distribution after 1987 had a mass of 2.5± 0.02g and gave a curve which was not a true Gaussian distribution, according to the statistical tests performed. One penny weighed multiple tomes gave an average mass of 2.4284± 0.0001 g, and when compared with that of another student there was significant difference between the mean mass and the variance.

The next set of experiments gave two calibration curves. The curve for a 10.0mL Serological pipette was y=0.95x + 0.1861, “y” being the measured value and “x” being the nominal value. A 10.0mL graduated cylinder was found to have a calibration curve where y= 0.9682x – 0.1604. a 5mL Volumetric pipette showed an average 5.000± 0.005 mL delivered whilst using a serological pipette to transfer the same volume gave a 4.78±0.1 mL transferred. An f-Test performed showed that the variance in the two methods was significantly different.

4. In undergoing practical one and practical two, namely distributions and weight calibration of a set of volumetric glassware, statistical calculations were done by using the masses taken from an analytical balance.
For practical one twenty- one pennies were collected and weighed. Twenty pennies weighed once and one penny weighed ten times. The mean and standard deviation were computed for the penny weighed ten times plus significance at 95% level. This included using a t-test and an F-test. Moreover, the class data of twenty measurements were divided into two sections. These sections are 1973- 1986 and 1987- 2004. The mass of each section was arranged from lowest mass to highest mass. Each data was computed in the order of 0.01g intervals by using the data analysis feature on Excel. In doing this, a frequency and a 0.01g interval (Bin) table for each section was created, forming a histogram (bar chart). Mean (2.66& 3.06) and standard deviation (0.05& 0.11) of each section were computed in order to count the number of pennies lying +3s (2.66& 3.40) and -3s (2.36& 2.73) away from the mean. A chi- square test for each section was then done at 95% confidence level in order to established if data collected followed a Gaussian distribution or not. Certain steps were taken including using the feature on Microsoft Excel to compute the Gaussian curve, calculating the chi- square of all data collected(twenty pennies) and using chi- square inverse function on excel to create the critical value of chi- square. For each section, a linear regression statistical procedure was done in order to determine the relationship between the mass and the year of coins.
Under practical two, various glass wares were used to measure volumes of water in consecutive milliliters. Such volumes include 1ml, 5ml, 6ml and 10ml. The five glassware of particular interest were the volumetric pipette, a serological pipette, a graduated cylinder and a volumetric flask. Beakers were used to weighed volumes of water delivered by the two pipettes and the cylinder, but not the flask. The flask glassware is used to contain rather than to deliver. Therefore water volume was measured inside of it. Before the water was weighed, one had to tare the beakers in order to get the zero experiment for linear regression. The data collected from the volumetric pipette and the volumetric flask (five measured masses each) were used to compute the buoyancy corrected volume using the equation M=m’ ((1-da/dw)/ (1-da/d)), where ‘da’ is the density of the air, ‘dw’ the density of the calibration weights,‘d’ the density of water, and ‘m’ the mass that was measured. The mean and standard deviation of the buoyancy corrected volume calculated for them were computed and tabulated. The measured masses of the other two glassware were used to compute the buoyancy corrected volume. Each glassware measured volumes of 1ml, 6ml and 10ml. The mean and standard deviation of each of the three volumes were computed and tabulated. A linear regression graph for each, were created to find the slope, intercept and their errors, using the regression function in Excel. A chi- square test was used to test the hypothesis of the variance that the volumetric pipette has a different measurement from the serological pipette although they measured a similar volume. The hypothesis proved to be false.

5. In experiments 1 and 2 masses were obtained, that is in experiment 1 the masses of pennies and in experiment 2 the masses of glassware were obtained. These masses were used to answer specific questions such as what makes a penny a penny? Is a penny a penny because of its weight or appearance? I am actually using the stated volume of liquid that the glassware states I am? Is my glassware properly calibrated? Since such questions can be raised methods of calibration using an analytical balance to obtain masses and specific test (T- test and F- test) were used in these experiments to draw conclusions. These conclusions which were made are 1/ a penny is a penny regardless of weight or appearance and 2/ the glassware had been correctly calibrated so as to deliver or contain the stated volume.

6. Distributions Lab
Everyone in the class was required to obtain twenty-one pennies. One penny was weighed ten times and this was done so that the results could be tested to determine whether individual results were the “same” or “significantly different” from each other. It was shown that Fcalculated was Ftable, this therefore meant that the difference was insignificant and that the readings were not “significantly different”. Also it can be said that they were the same due to the fact that the means observed were approximately the same. The remaining pennies were then measured once. This was done to observe how the masses vary over the years. It was observed that as the years increased, the mass of the coins decreased.

Weight Calibration of a Set of Volumetric Glassware
Different types of glassware used in the laboratory were calibrated, so as to determine the accuracy and precision of each type of glassware. The temperature was measured as this factor was crucial in determining the density of water. The water measured by the volumetric pipette was placed in a pre-weighed beaker and this mass was again measured. This was repeated five times to obtain replicates. This was then repeated for the serological pipette and graduated cylinder. However, three different volumes were used (10cm3, 5cm3, 1cm3 ) for both cases. A reading in which no water was added to the beaker was done and this acted as a control. A volumetric flask was also calibrated. This was done by first obtaining the dry weight. The flask was then filled to the mark and weighed, then emptied. This was repeated five times. It was observed that the most accurate glassware was the volumetric pipette, while the most precise was the serological pipette. The volumetric flask was the least accurate while the graduated cylinder was the least precise. Another observation was that the glassware used “to deliver” seemed to be more accurate than the glassware used “to contain”.

7. In experiment 1, knowledge of a set of mass measurements and statistical distributions was explored. Various statistical concepts were utilized on the class data set including computing the mean, standard deviation, T-test, F-test, χ2 test and linear regression. Those results were as follows: Mean: 2.52, Standard deviation: 0.044721, T-calculated: 2.39E-53, T-critical: 2.093025, F-critical: 3.137274, F-calculated: 2.09E+08, Chi value: 11335.72, Chi critical: 24.9958 and by doing Linear Regression, the following constants were computed: slope: -0.00472, y-intercept: 11.93116 and r2 value: 0.242764. This experiment was done mainly to test the precision of the balance using the masses of Barbados pennies.
In experiment 2, a set of weight calibrations were performed on different sets of glassware. The glassware used included a 5ml volumetric pipette, a 10ml measuring pipette, a 100ml volumetric flask and a 10ml graduated cylinder. The 5ml volumetric pipette seemed to be the best piece of apparatus with which to measure, being off from its target volume by less than 0.1ml in all trials. The other glassware were off from their target volumes by +/-0.2ml in most cases. The volumetric flask was the worst measuring apparatus as it was consistently off of its target volume of 100ml by ~2ml. Linear regression was attempted on the plots of measured volume and ‘nominal’ volume of the serological pipette and graduated cylinder. The hypothesis that the variance of a volumetric pipette differs from a measuring pipette used to measure a similar volume proved false under the F-test.

8. Analytical Chemistry is a subdivision of chemistry that deals with separation and the identification of components in a system. Analytical Chemistry can be divided into Quantitative and Qualitative analysis and involves some statistics.
In this lab the areas of Analytical Chemistry that are being tested are Distribution (primarily Gaussian distribution) and Weight Calibration. Gaussian distribution is another name for normal distribution, which is a frequency distribution that produces a bell shaped graph. And Weight Calibration of the volumetric glassware is checking the output of the glassware to see if their predicted measurements are correct. This can be used to increase the accuracy of results. These two parameters of Analytical Chemistry are very important in the interpretation and accuracy of results and although this is a simple experiment these factors should be taken very seriously.
Statistics are very important in chemistry it helps improve the interpretation of results and makes data easier to handle and easier to analyze. In this experiment, statistical tests such as the mean, standard deviation, t-test and f-test were used to construe the data obtained.

9. Two separate experiments were carried out on different occasions- ‘Distributions’ and ‘Weight Calibration of a set of Volumetric Glassware’. In the ‘Distributions’ lab each student weighed one penny 10 times, and 20- once each. Each weight obtained by each student, was recorded and used to perform various statistical operations on, such as mean, standard deviation and others. These various operations were carried out by using your data and another’s, and then using the entire class data excluding yours. By using these results one was able to determine whether the data would result being significant at 95% confidence level for t-test and f-test and in a Gaussian distribution. My results proved that it was significant for the t-test, however insignificant for the f-test. Also, they proved not to result in a Gaussian distribution. Now, in the other lab, a set of volumetric glassware was calibrated, results were obtained, and various calculations were carried out on them, such as mean, standard deviation, buoyancy correction and linear regression. I carried out an f-test proving that a volumetric pipette doesn’t differ from a serological pipette used to measure a similar volume. These 2 labs even though seeming unlike, they both however, test your ability to carry out various statistical functions on a series of data.

10. Practical 1 was the distributions lab. Twenty-one pennies were used from various years to see if the distributions followed a normal Gaussian distribution. The distribution was used also to answer the following questions: 1) Do pennies from different years have the same mass? 2) Do pennies from the same mint have the same mass?
Practical 2 is weight calibration of a variety of different glassware (measuring pipette, volumetric pipette, measuring cylinder and volumetric flask). These varieties of glassware have different tolerances depending on the volume measured and the temperature at which the calibration was carried out which results in a buoyancy correction. The previous statements are some limitations in this experiment. In addition to the tolerances of the varieties of glassware the analytical balance has a sensitivity of 0.01-0.1mg and tolerances dependent on the masses being measured. (This limitation may hold for Practical 1 and 2.)
Practical 1 and 2 were both carried out using the analytical balance. Precautions that were present in the labs were; parallax error (when reading the meniscus), significant figures (when doing calculations for weights),

11. This practical involves the use of statistics to compute data obtained from weighing pf Barbadian pennies. The pennies collected are weighed and the data obtained are used to accept conclusions with the high probability of being correct and to reject conclusions that are not statistically. This will be done also with the use of Microsoft excel, which will help to make calculations faster.

12. Pennies are weighed in order to a. Compare two different sample measurements for difference in mean and standard deviations using T test and F test. Repetitive measurements are done to get an idea of the uncertainty of the analytical balance used.
b. Create a distribution and test to see whether or not it follows a Gaussian distribution pattern.
Volumetric glassware is weight calibrated by weighing water measured, correcting for buoyancy and calculating measured volume to get idea of tolerances keeping in mind that there is always margin of error when using glassware and that transfer of liquid is not wholly quantitative. The apparatus are compared for accuracy and precision based on mean measured values and nominal values and standard deviation.
Statistical tests are used to ascertain with a percentage level of confidence and margin of error whether of not sets of data are significantly different from each other.

13. Two practicals were conducted which focused on fundamental aspects of experimental data analysis. A single penny weighed 10 times had a mean measured mass of 2.52 +/- 0.005g. The variance of the collect data was same when compared with different results of other trails. The distribution of pennies was examined. The pennies do not fit a normal distribution and the relationship between the masses of the pennies and the year of their make was determined. Volumetric glassware was calibrated. It was determined that the graduating cylinder gave the ‘worst’ results and the volumetric pipette gave the ‘best’. The variance of the volumetric pipette (s2 = 0.0004) differed from the measuring or serological pipette (s2 = 0.0016) when used to measure a volume of 5ml.

14. (No Abstract given)

15. The first experiment was about distributions and it was done by the use of penny statistics and the second one was done on the weight calibration of volumetric glassware. Twenty one pennies were weighed and their masses were taken. Also, a volumetric pipette, a serological pipette, a graduated cylinder and a volumetric flask were calibrated in the second experiment.
An introduction, the results of the experiment were shown and a discussion was done. The discussion and analysis of the data showed that volumetric glass ware gives the most precise results for weight calibration and that graduated cylinders are not good tools for volumetric analysis. Also, that linear regression is a good method to show the linear relationship between two variables and that the Q test should be avoided in the analysis of data points. Also, it was shown that precision is achieved when many replicate measurements are done.

16. Lab number one which was the Distributions lab, was experimentally carried out by selecting twenty-one (21) Barbadian pennies which varied by mint dates. These were then individually weighed on an analytical balance for accuracy.First one of the twenty-one pennies were chosen and it was weighed ten times. Then the remaining twenty were each weighed once, then results were recorded and a series of calculations were carried out. The different types of calculations were the T-test, the F-test, chi-square test and Gaussian distribution test which were the major calculations. Based on these series of calculations a conclusion was made that the pennies based on the data which was the entire class data obtained, varied significantly in mass. The drastic change could be seen from 1986 where the mass of the pennies decreased. Also based on the set of calculations primarily the chi-square test and the chi-inverse test, the set of data do not fit a Gaussian distribution.
Lab number 2 which was the weight calibration of a set of volumetric glassware this consisted of a volumetric pipette, serological pipette, volumetric flask and a graduated cylinder. The glassware was calibrated by weighing each one individually with a recorded amount of water which was either contained in or delivered by that specified glassware. Different volumes of water were used in order to have a variation. After the results of the experiment were recorded with the temperature recorded in order to have the correct density of water, the water’s mass was converted into the volume. Based on the results, it can be said that the best glassware was the volumetric pipette while the worst was the graduated clinder.

17. The objective of the Distribution experiment was to determine if there was a difference in the mass of Barbadian pennies and if the mass followed a Gaussian distribution. Using a sample size of twenty-one coins, one coin was weighed ten times and the remaining coins each weighed once. The class data was then compiled and analysed. Based on the results it was concluded that in the late nineteen eighties (after 1987) there was a dramatic decrease in the mass of the coins. Also the masses followed a gaussian distribution.
The objective of lab two was to weight calibrate a set of volumetric glassware. This was done by transferring specific volumes of water to a pre weighed beaker and obtaining the mass of the water. The volumetric and measuring pipettes, graduated cylinder were calibrated this way. As the volumetric flask is designed to contain rather than deliver the flask was filled the mass of water it contained determined. For each specific volume five mass readings were obtained. From the results it was concluded that the variance of a volumetric pipette differs from the variance of a measuring pipette used to measure a similar volume. Of all the glassware the volumetric pipette gave the best results: Volume five ml.

Buoyancy correction 1.001054823
Mean 4.982049641
Standard Deviation 0.033341964


18. In this experiment, several pennies were weighed and the class data was pooled and analysed.

19. In practical 1 a coin was weighed repeatedly ten times and the mean and the standard deviation were determined. A T-test and a F-test were performed at a 95 % confidence interval to test the Null hypothesis, which states the mean / standard deviation values from two sets of measurements are not different. A Gaussian distribution was plotted and a chi-square analysis was performed to further determine if the difference in observed and expected masses is significantly. In practical 2 various analytical tools such as volumetric and measuring pipette, graduated cylinder were calibrated, the true mass of water at 27 degrees Celsius was obtained and the accuracy of delivering water between the measuring pipette and the graduated cylinder and the volumetric pipette was obtained.

20. In write-up two practicals are being discussed. In the first experiment the distributions Barbadian pennies was being analysed and in the second a number of volumetric glassware were being calibrated.
In the penny statistics lab one penny was weighed ten times and its mean and standard deviation was calculated and used for comparison with another penny which was also weighed ten times. These two values were compared to prove whether the data sets were similar or if they were different and also to show if their errors in measurement differed. The class data set was analysed to see if it meet the Gaussian curve so as to determine whether the errors in the data were random. A relationship between the year of issue of the pennies and their masses was also calculated.
In the calibration experiment the masses were used to determine the buoyancy corrected volumes of the glassware. The relationship between the measured values and the nominal measurements were calculated. Analysis was also carried out to determine whether the variance of two instruments the measuring pipette and the volumetric pipette was significant or just due to chance.
The data collected was analysed and several conclusions could have been made from the data.

21. In this experiment glassware would be calibrated in effort to provide sufficient practice in using various volumetric glassware and obtaining the best possible data (most accurate) from the materials or equipment provided.

22. Practical 1 focused on investigating mass distribution of pennies in Barbados. Twenty-one pennies were weighted on an analytical balance by each member of the class, to obtain their masses and the results were statistically analyzed at the 95% confidence interval. It was found that the masses of pennies decreased around 1987 from approximately 3.1g to 2.5g. The experimental results showed that the average penny in Barbados weights 2.5312g. However, analysis also showed that the investigated distribution was not a Gaussian distribution. The weight calibration of a set of volumetric glassware was the aim of the practical 2. The weights of varying glassware were obtained by a method of differences with water, using an analytical balance. It was established that the numerical value was almost never obtained when the instruments were used; the degree of accuracy differed according to the glassware.

23. In practical #1 statistical tests were performed such as the t- test to determine if there was any difference in mass among the pennies in the class data set. This experiment was also performed to determine the amount of variation from a normal distribution. From the results obtained in this experiment it was observed that the results followed the normal distribution and it was also observed that according to the t- test performed the masses of the two coins were significantly different.
However, in practical #2 pieces of glassware which were designed to contain or to deliver liquid were calibrated using buoyancy corrected volumes to see how much water each piece of glassware actually held at particular stated volumes and how far from the nominal volumes were the measured volumes.

24. Pennies are made of a metal and are bronze in color when freshly minted. Therefore recent pennies have a splendor shine while pennies over the years tend to be dull and corroded. The means of the class data set shows varying masses of pennies with year and the one penny weighed 10 times shows that the weights obtained are not exactly the same.

25. Practicals 1 and 2 introduced certain statistical concepts which were new to most students in this course. In Practical 1, you were required to obtain the mass of one coin ten times and perform tests to determine whether the means and the variances of your data and the person following you, were significantly different at the 95% level. If the calculated value for either the F or T-tests was greater than the critical value the parameter was said to be different. For example the F test calc. value was 1.817844 which was less than the crit. Value which was 3.178893. The standard deviations were therefore not statistically different.
Part 2 of lab 1 required that we use the data of the class set (except your own) to determine if the distribution of pennies from the class follow the Gaussian distributions.
In Practical 2, you were required to calibrate volumetric glassware by weight calibration. First the temperature was measured. Then the weight of the water in a pre-weighed beaker transferred from the glassware was used to calibrate the glassware. The volume was calculated using the formula from page 29 of “Quantitative Chemical Analysis by Daniel Harris.”

26. In Practical (1), the distribution of the mass of various pennies was observed. In part (A) of the practical, one penny was measured and the mean and standard deviation were calculated and compared to another student using and F-test and a T-test. Based on the standard deviations the penny measurements were found to be precise. In the latter part of the practical the twenty pennies were weighed by each student and the data was pooled together. The distribution of the class data was explored.
In the second practical weight calibration of a set of volumetric glassware was carried out. It was observed that that measured volume and the corrected volume differed for each piece of equipment. The corrected volumes were calculated using the buoyancy equation. It was also discovered that some glassware was more accurate and precise than others.

27. One would assume that the mass of a penny does not determine its value, or our entire financial market would be askew. This experiment is done to determine that if by doing statistical functions on the mass of measured pennies, if the previous statement is true, that the mass of the penny does not determine its value. However, the weight of pennies may be altered by such uncontrollable variables such as corrosion, oxidation, wear-and-tare and fingerprints. Therefore there is some discrepancy by using the mass as it may be altered, however testing the composition of the penny may also be used to determine the same hypothesis. Despite this, in this experiment the mass is used and the results will be discussed, bearing in mind the variables.

28. Experimental measurements always provide a large amount of variability. The procedure used known as “penny statistics” helps to conclude a more accurate conclusion for the distribution of experimental data. In this procedure twenty one pennies are randomly collected in order to give an accurate sampling range. From the collected pennies, one penny is weighed ten times in order to estimate the experimental variance recorded from weighing the same penny on the same balance but obtaining a different weight each time. This provides the experimental error needed. The remaining pennies were then weighed one time each recording the year it was made. This new information shows how penny weights have changed over the years. The collection of this data uses the application of many statistical methods such as Gaussian distribution, t-test, f-test and chi-square. Each of these different tests provides some means of statistical data necessary for the analysis process. The results obtained a good correlation with the initial hypothesis. Data collected during this procedure also provides good statistical information necessary for the analysis of the conclusion.

29. Statistical functions such as the t-test, f-test and Chi-square are introduced in this lab. Each person brought 21 Barbados pennies and weighed one ten times and the other 20 pennies once. The data were pooled as class data and statistical analyses were carried out. The Barbadian pennies have decreased in weight over the years.

30. The distribution and weight calibration labs were carried out with the use of simple materials in an effective manner. They provided enough variability in the data to perform Chi-square, calculate the mean and standard deviation, as well as plot graphs. The majority of the results were quit consistent with each other- as seen with the mean in lab 1 and the variance in lab 2 – although the computation of the linear regression may be questionable.

31. For practical number one distributions, twenty-one Barbados pennies were used. One penny was weighed ten times and then each of the twenty remaining pennies was weighed once using an analytical balance. For two sets of results, the mean, standard deviation, T-test and F-test were calculated. The pooled class data were sorted and arranged from highest to lowest mass and the mean and standard deviation also calculated in addition to this the chi-square testing done, as well as linear regression. The results of this showed that the distributions followed a normal Gaussian distribution. In lab number two, weight calibration of a set of volumetric glassware, a volumetric pipette, serological pipette, graduated cylinder and volumetric flask were calibrated. This was done by repeatedly using the glassware to measure volumes of water. Buoyancy calculations were done to find the corrected volumes of water delivered by each set of glassware. The results were then used to plot regression and to find the mean and standard deviation of the data. The conclusions of the experiments showed that the data in practical one follow a normal distribution. The actual volumes delivered and contained by volumetric glassware are not the volumes stated on the glassware. Also, the volumes delivered by a serological pipette and a volumetric pipette are the same (at 5.00cm3).

32. Data was collected using various analytical devices such as analytical balance volumetric glassware. First coins were weighed on the analytical balance and their masses were used to determine amount of error that can be produced from using the apparatus. This was done by calculating the mean and standard deviation and representing that data on graphs. A linear regression was also calculated to show the differences in masses over the years.e.g. (1979, 3.1066g compared to 2004, 2.5071g).The second experiment was conducted to calibrate the glassware because they are being used at a higher temperature therefore would give different readings than what would have been reading at the original calibration. The calibration was done by measuring volumes for each glassware and performing statistical tests such as standard deviation, linear regression etc. The Buoyancy Correction equation (m = m (1- da/dw)/ (1- da/d)) was also used. All data values were recorded and tabulated.

33. In practical one and two, different means of statistical analysis are carried out.
Practical 1: Penny Statistics. Two variances are noted. 1 coin measured (weighed) 20 times takes into account the total overall variance whereas 1 coin measured (weighed) 10 times takes into account the analytical variance.
Practical 2: Weight calibration of a set of volumetric glassware. Four volumetric glasswares are used for this experiment. The mass of water delivered by each vessel was recorded and the corrected density of water at 26 O C was used to calculate the volume.

34. Each experiment conducted involved numerous repetitions if measurements of the coins as in experiment 1 and of the apparatus used in labs as in experiment 2.
In experiment 1, a coin was weighed a total of ten times and compared to a coin weighed by one other person in the lab. The mean, standard deviation, a t-test to test the difference between the means and an f-test to test the difference between the precisions of the values were calculated. Twenty other coins were weighed only once and those were then compared to coins weighed by all other persons in the class. A Gaussian distribution graph was done to give a better view of how the masses varied amongst the class. The mean of the class data was a value of 2.51g.
In experiment 2, different glassware used for measurements and storage in the labs were calibrated using volumes of water. Such glassware were the 5ml volumetric pipette, the measuring or serological pipette, and the graduated cylinder, which are all used for delivering volumes of solutions, and the 100ml volumetric flask which is used to contain volumes of solutions. Corrections made to the values were done using the buoyancy correction, a t-test was conducted on the means and a variance was tested and compared between the volumetric pipette (which had a variance of 9.7931 x E-5) and an equal volume of the measuring pipette (with a variance of 2.3574 x E –4).
35. In this experiment twenty-one pennies were weighed in total, one penny was weighed ten (10) times and then the remaining twenty (20) pennies were weighed individually and the masses and year produced tabulated.
This was done in order to provide us with a data sheet so as to help compare the masses of the varying coins as the years went by, and to determine how much the masses differed due to different reasons. Some might have been of a higher mass due to it oxidizing and a layer forming over it or it might have been lower because of chipping or because less of the metal was used to produce the coin.

36. To obtain great accuracy, the volumetric glassware was calibrated to measure the actual volume in or conveyed by a particular piece of equipment. Measuring the mass of water in or emptied by the vessel did this and then the density of the water was used to convert the mass into volume. Noting the temperature at the time and using this value to obtain the density to work out the calibration accounted for thermal expansion.
Various volumes of water were discarded into a beaker, which the mass was noted, from a serological pipette, volumetric flask, measuring cylinder and measuring pipette, each separately. The mean and standard deviations were calculated and various tests carried out to calibrate the recorded masses and find out which piece of equipment is most accurate.

37. For the distributions practical, each student collected 21 Barbadian pennies (one cents), of which one was chosen and weighed 10 times, while the remaining 20 were each measured once. The data collected was pooled and distributed to the entire class. Statistical analysis was then carried out on this data in order to discuss the relevant aspects and make conclusions.
In Practical 2, calibration of the volumetric pipette, measuring pipette, graduated cylinder and volumetric flask was done. In this case, only personal data was obtained and used in the statistical analysis and deduction of conclusions.
Conclusions made in these practical include:
1) The average mass of my penny dated 1993 is significantly different at 95 % confidence from that of Tricia’s penny dated 1995.
2) The variance of my data is significantly different from Tricia’s at 95 5 confidence.
3) The class data for the masses of pennies does not allow a Gaussian distribution.
4) The masses of pennies generally decrease from year to year.
5) The measured volume is directly proportional to the nominal volume for the measuring pipette and graduated cylinder.
6) The variance of a volumetric pipette does not differ significantly from measuring pipette used to measure a similar volume.
7) The results for the transfer pipette reflect the greatest precision and those of the 100 ml volumetric flask reflect the lowest precision.

38. For these two Practicals “Distributions” and “Weight calibration of a set of volumetric glassware”, the following was done.
For Practical 1, each person from the class obtained 21 pennies from various places, such as personal saving banks, purses and wallets, and some were even obtained from their backyard or maybe the streets.
Each student used 21 pennies for the experiment. One penny was weighed 10 times, while the remaining 20 were weighed once each. It was ensured that in addition to the mass of the coin, that the year and appearance of each coin was noted.
These results from each student were accumulated and were used to make up a class data set, which was then analyzed. The results were analysed by first comparing my data to that of the student below me in the class data set, for the results of measuring the mass of one penny ten times. Then my data was discarded from the data for measuring 20 pennies once, and tests were performed.
For Practical 2, the glassware was calibrated so that the actual volume contained in or delivered by the glassware was measured. This was done by measuring the water contained in or delivered by the glassware. Then the density of water was used to convert mass to volume.

39. Practical.1.Distributions involves repeated weighing of pennies on an analytical balance to obtain a large data set which can be analysed statistically. Many measurements were made to give a better data ‘spread’. F-tests and T-tests were done as well as graphs showing the distributions of penny mass.
Practical.2. Weight Calibration of a set of Volumetric Glassware includes taking the masses of water measured in volumetric glassware, calculating the volume of water measured by dividing the masses by the density of water to obtain volumes. A buoyancy correction was made which accounts for masses incorrectly recorded due to the displacement of mass in air.

40. In order to perform any chemical experiment the use of laboratory apparatus must be used. The procedure done is known as calibration of volumetric glassware which helps to manipulate chemical methods. In this procedure four different types of instrumental apparatus were calibrated to give the buoyancy correction of the apparatus used. The various glassware used, were filled with the required amount of water according to their different scales (example 5ml, or 10ml) five different times and the weight of the water recorded. By caring out this procedure the data collected provided the information needed to observe the experimental errors obtained from the different instruments. The empty apparatus were also measured. This part obtained the zero values necessary to estimate if the inside of the apparatus is ever equal to zero. This data therefore provides useful information about the experimental errors introduced by each instrument. Once the data is obtained the mean, standard deviation and buoyancy can assist in the assessment of the instruments in order to accept the initial hypothesis. The results obtained a good correlation with the initial hypothesis and the data collected provided the correct statistical information.

41. The accuracy of two electronic balances in the balance room was investigated and it was found that the standard deviation in taking ten measurements of the same penny was found to be 0.000358391 and 0.000155 grams respectively. An F test was done on the variances and they were found to be significantly different at 95% confidence. The difference in mass between two pennies of the same year was also investigated. Taking 10 measurements of each of the 2 coins and doing a T test on the average masses of the 2 pennies was done. The average masses were found to be 2.49882 and 2.5071 grams. The difference between the two average masses was significant at 95% confidence.
The masses of 960 pennies were measured. A graph was plotted of mass of penny versus the year the penny was minted to see how mass of coin changed over time. It was found that pennies minted after 1986 were less in mass by approximately half a gram less in mass than those minted in 1986 and before. The pennies minted in 1986 and before were removed and the remaining 916 mass measurements were tested to see if they followed a Gaussian distribution using a Chi squared test. It was found that the distribution of mass in pennies does not follow a Gaussian distribution.
Different types of volumetric glassware were calibrated. The nominal volume of water was weighed and a buoyancy correction was done to calculate the actual volume delivered or contained by or in the glassware. It was found that for the nominal volume of 5 ml delivered by the volumetric pipette, the actual volume was 4.96± 0.02. For the nominal volumes of 1, 5 and 10 ml the actual volumes were 0.98± 0.03 , 4.97 ± 0.02 and 9.92 ± 0.03 ml. For the nominal volumes, 1, 5 and 10 ml delivered by the measuring cylinder, the actual volumes were 0.94 ± 0.06, 4.88 ± 0.05 and 9.84 ± 0.04 ml. For the nominal volume of 100ml contained by the volumetric flask, the calculated volume was 99.35 ± 0.19. It was also found, using the F test, that the hypothesis, “the variance of the volumetric pipette differs from the serological pipette used to measure the same volume,” was false. Calibration curves of nominal volume versus measured volume for the serological pipette and graduated cylinder were plotted.

42. In practical 1, each class member collected 21 pennies and each person selected 1 penny of their choice, to weigh 10 times. The additional 20 pennies were each weighed once. All results obtained were grouped together and many tests were carried out. The conclusions reached included: in part a) Shamika’s single penny weighed was significantly different from mine, according to the average mass and the variance comparison using the t test and F test carried out respectively; and in part b) for the 20 singly weighed pennies: the distribution curve was not Gaussian, and the plot of year and mass gave a negative gradient which implied that the mass of the pennies decreased form year to year.
On the other hand, for practical 2, each person weight calibrated a volumetric pipette, serological pipette, graduated cylinder and a volumetric flask. Each person carried out his/her own calculations to determine how close his /her assumptions of the calibrations were. The conclusions reached were, the 10mL serological pipette delivering 5mL was the most precise, while the 100cm3 volumetric flask was the least precise. In addition, according to the F test carried out, the volumetric pipette differed significantly from the serological pipette. It was also observed that the plots of the measured volume and nominal volume were all direct proportional.

43. In the first experiment, the masses of the one-cent coins of the students were determined and were use to generate a distribution graph which was compared to that of a normal distribution. In the second experiment, the volumetric apparatus including volumetric and serological pipettes, graduated cylinder and the volumetric flask were weight calibrated to determine the precise volume of water they contain or deliver. The distribution of the masses was determined by each student measuring the mass of one penny ten time and then measuring the masses of twenty pennies once. This allowed the variance in the analytical balance and the variance of the sample of pennies to be determined. The weight calibration involved measuring a know volume of water using the volumetric analysis and using the mass of the volume of water to determine the corrected or nominal volume delivered or contained in the apparatus. From the distribution experiment it was found that the observed distribution of the masses of the coins was not consistent with that of normal “Gaussian” distribution. The major conclusion of the weight calibration was that the variance of volumetric pipette is not significantly different from that of a serological pipette used to measure the same volume.

44. Practical 1 and 2 were experiments carried out with specific objectives. In lab 1 this was to investigate the properties and interpretation of results when experiments are performed and data retrieved. In lab 2 this was to determine the most accurate piece of glassware using statistical methods. All of the equations used were relevant to investigating the properties of the results collected.

45. (lab 1) By comparing my self and (student’ results it was observed that the difference in the standard deviations was 0.0002g. In other words the mass of the Barbadian penny has rose by 0.0002g. Having this difference all calculations done will be varied. By calculating an F-test and a t-test, the variances showed the different results.
(lab 2) By analising the masses from the entire class it is seen that more recent pennies are the easier ones to locate compared to the one that are older.

46. Abstract: the two experiments covered in this report illustrate the fundamentals of measurement in analytical methods. The first set of trails utilized Barbadian pennies to examine their mass distribution. One penny weighed multiple times gave a mass of 2.5149 ± 0.0005g which was statistically compared to another analyst’s result of 2.466±0.02g for another penny on the same type of balance. Both the variance and mean mass were found to be significantly different at the 95% confidence level. Measurements were made on other pennies by a group of student analysts and two distributions were observed, the first being for pennies before1987 and the second being for pennies from 1987-2004. The latter showed a mass of 2.50± 0.02g.

At 26 oC a 5mL Volumetric Pipette was found to deliver 4.99±0.02 mL and a100mL Volumetric Flask contained 99.09±1.02mL. A 10.0mL serological pipette transferred 4.914±0.007mL for a nominal value of 5.0mL, which was found to have a significant variance form the volume delivered by the volumetric pipette. The calibration curve computed for the serological pipette had the equation Nominal Value=1.0033(Measured Value) +0.0339 and the graduated cylinder gave the equation Nominal Value = 1.0182(Measured Value).

47. The mass the pennies, which were made after 1985, fall along a general Gaussian distribution which has a mean of 2.5298 grams. Those which were made before this time fell within another distribution which was not under the study of this experiment. Also, the difference of means of the mass of one penny between myself (having a 1997 coin) and another one of my colleagues (having a coin 2004) was significant at the 95% confidence level, thus meaning that there is some important variance between the mass of coins from year to year even after 1985. The error incurred by the use of certain glassware was calculated using a calibration involving the weighing of water delivered from the piece of glassware in question. It was seen that the error incurred by the glassware is also dependent on the temperature as well as the use or absence of a buoyancy correction. It was also seen that the error for pieces for pieces of glassware which can measure varying amounts can have varying errors for these amounts.

48. In the Distributions practical a single penny was weighed 10 times. The measurements obtained were then compared to a classmate. It was found that there was a significant difference between these two pennies. A c2 test was carried out to determine whether the penny population fit a Gaussian curve, it was realised that it did not fit such a curve. It was found that the mass of the pennies declined after the year 1987.
A volumetric pipette, a measuring pipette, a graduated cylinder and a volumetric flask were calculated. Buoyancy correction volume was carried out on the volumetric and measuring pipettes. The volumetric pipette was found to give the best results while the volumetric flask was found to give the worst results.

49. In these experiments, precise measurements of the weights of each of 21 pennies (1 penny weighed ten times and the remaining pennies weighed once) and the quantity of water contained and delivered by each set of volumetric glassware were obtained using the analytical balance. All these results were then recorded and analysed using various statistical tests so as to determine the accuracy of both the mass of the Barbadian penny and the printed calibrations on the glassware. From these examinations, it was found that over the years, the mass of the Barbadian penny has never been the exact proposed value of 2.5g but in some cases has been relatively close and also there are no two pennies that were identical as determined from the t-test and the f-test results obtained when the average masses and variances were examined respectively. In terms of the weight calibration lab, it was found that the printed calibrations on the various volumetric glassware are neither very accurate for glassware to be contained nor to be delivered. However, amongst the to be delivered glassware calibrated for delivering 5ml, it was found that the volumetric pipette was the most precise whilst the serological pipette was the most accurate. It was also found that the variance of a volumetric pipette is significantly different from that of a serological pipette.

50. In practical 1, the masses of 21 pennies were measured using an analytical balance and recorded. Practical 2 involved weight calibration of a set of volumetric glassware. Recording the masses of water delivered by the particular instrument and using the density of water to convert mass to volume did this. Statistical analysis was carried out in both practicals to determine the standard error in the instruments used.

51. In practical No. 1,each student weighed coins of various years using an analytical balance to determine whether each coin produced every year was the proposed mass of 2.5g as suggested by the Mint and if the masses follow a Gaussian distribution. A batch of twenty- one coins of varying years were weighed by each student, where twenty coins of them were weighed once and their respective masses noted and one coin was weighed ten times. Various calculations were done to determine if the above aim. It was concluded that no set of ten measurements was the same for a penny, which was determined by the use of the T-test, and F-test conducted, only a few number of coins of various years actually weighed the proposed value of 2.5g and the masses did follow a Gaussian distribution.
In practical No.2, one tried to calibrate different types of the volumetric glassware to determine if they were calibrated correctly and learned how to use them properly. Various volumes were measured using the different volumetric glassware, where maximum, minimum and volumes in between where measured and weighed in order to determine how much volume was actually delivered by a particular glassware. All the results were noted and various calculations were conducted to determine the aim. It was concluded that the glassware was not accurately calibrated where the serological pipette was the most precise and the volumetric the least. And the volumetric flask was the most accurate.

52. From previous reading (Quantitative Chemical Analysis-pg 37), it has been noted that manufacturers usually certify that the indicated quantity lies within a certain tolerance from the true quantity. The quantity to be looked at in this experiment is mass. It should also be noted from further reading that buoyancy is a factor that decreases measured mass. This results in the buoyancy correction equation, which is used to find the true mass.
The Buoyancy Correction Equation:
m= m' (1-da/dw)/(1-da/d)
Where---
da=0.0012g/ml
dw=8.0000g/ml
d=0.9970g/mlm=true massm’=
(1-da/dw) = 0.99985
(1-da/d ) = 0.9988
The experiment is therefore carried out based on these factors, in an effort to give adequate exposure in using the volumetric glassware and obtaining the most accurate results from them.
The calibration techniques include repeated readings at various volumes (see method) and zero experiments, which allow for better analysis of information.
“We calibrate volumetric glassware to measure the volume actually contained in or delivered by a particular piece of equipment. We do this by measuring the mass of water contained or delivered by the vessel and use density of water to convert mass to volume.” This is made evident in page 37 of the book, Quantitative Chemical Analysis.

53. The main objective of Practical One was to randomly collect a set of 21 pennies varying in the year in which they were produced and condition and measuring the masses of these twenty-one pennies. Statistical tests such as the t-test and F-test were performed and this assisted in making certain deductions.
The main objective of Practical Two was to calibrate glassware. These include the volumetric pipette, measuring pipette, graduated cylinder and volumetric flask. The calibration was done by taking various volumes of water in the glassware and delivering it in a beaker. The electronic analytical balance was provided to facilitate successive measurements. The same volume was delivered from the different glassware five times. In the case of the measuring pipette and the graduated cylinder three volumes were delivered five times making a total of fifteen different values for the measuring pipette and the graduated cylinder. This was done to determine the mean, standard deviation of the masses, the buoyancy correction and the corrected volume.
Different statistical tests such as the t-test were performed to examine the accuracy with which the experiments were carried out, and examine the glassware.

54. In the first experiment, the masses of the one-cent coins of the students were determined and were use to generate a distribution graph which was compared to that of a normal distribution. In the second experiment, the volumetric apparatus including volumetric and serological pipettes, graduated cylinder and the volumetric flask were weight calibrated to determine the precise volume of water they contain or deliver. The distribution of the masses was determined by each student measuring the mass of one penny ten time and then measuring the masses of twenty pennies once. This allowed the variance in the analytical balance and the variance of the sample of pennies to be determined. The weight calibration involved measuring a know volume of water using the volumetric analysis and using the mass of the volume of water to determine the corrected or nominal volume delivered or contained in the apparatus. From the distribution experiment it was found that the observed distribution of the masses of the coins was not consistent with that of normal “Gaussian” distribution. The major conclusion of the weight calibration was that the variance of volumetric pipette is not significantly different from that of a serological pipette used to measure the same volume.

55. The aim of these experiments was to introduce students to the statistical concepts used in analytical chemistry to better understand and improve results. This was done through the help of two practicals. The first practical entitled distributions introduced the concept of the f-test, t-tests for part 1, the comparison of two set of similar data (obtained by measuring one penny ten times) and chi- squared tests, Gaussian distribution and curves as well as linear regression for part 2, the class set of data obtained through the measurement of 20 pennies by every student to give approximately 1400 results. From statistical tests it was determined that part’s data was not significant at the 95% confidence level as P (=3.26735663697289E-20) greater than 0.05 for the t-test and P=(3.00318148351433E-06) greater than 0.05 for the f-test. However for the class data, which was spilt into the pennies before and after 1986 did in fact follow a Gaussian distribution since χ2 is greater than χ2 critical (calculated based on the number of bins). Using Excel χ2 was calculated to be 1694256 and Χ-critical to be 150.9 for the data before 1986 and 3.57209E+28 and 139.9 respectively for the data after 1986.
The second practical dealt with the weight calibration of a set of volumetric glassware by measuring and weighing five replicate volumes of water for each volume selected on the glassware. Using the various results it was determined that that the serological pipette was the most accurate (0.0565 grams less than the expected mass) followed by the volumetric pipette (0.0651 grams), volumetric flask (0.1005 grams) and graduated cylinder (0.1946 grams.) (Please see table 11.) It was also determined that the volumetric pipette did not vary from the serological pipette as the t- tests run on the data indicated that t critical (2.30600562645122) was less that t statistical (232.872759837471)

56. The two experiments covered in this report illustrate the fundamentals of measurement in analytical methods. The first set of trails utilized Barbadian pennies to examine their mass distribution. One penny weighed multiple times gave a mass of 2.5149 ± 0.0005g which was statistically compared to another analyst’s result of 2.466±0.02g for another penny on the same type of balance. Both the variance and mean mass were found to be significantly different at the 95% confidence level. Measurements were made on other pennies by a group of student analysts and two distributions were observed, the first being for pennies before1987 and the second being for pennies from 1987-2004. The latter showed a mass of 2.50± 0.02g.

At 26 oC a 5mL Volumetric Pipette was found to deliver 4.99±0.02 mL and a100mL Volumetric Flask contained 99.09±1.02mL. A 10.0mL serological pipette transferred 4.914±0.007mL for a nominal value of 5.0mL, which was found to have a significant variance form the volume delivered by the volumetric pipette. The calibration curve computed for the serological pipette had the equation Nominal Value=1.0033(Measured Value) +0.0339 and the graduated cylinder gave the equation Nominal Value = 1.0182(Measured Value).