Determination of the Trends in Mass of a Penny - Lab Report Example

DETERMINATION OF THE TRENDS IN MASS OF A PENNY The change in composition of pennies after the year 1982 prompts for the study of the trends in mass of a penny. Initially, before 1982, copper was the major composition in pennies. However, the realizations of the usability of zinc, as a penny composition lead to change in composition pennies. Majority of Zinc could be found in composition as compared to copper. A histogram plot for masses of pennies for pre-1982 and post-1982 shows a clear transition between the two periods. Arriving at the major cause of the change required us to use density of the pennies. The use of density was critical since it does not depend on the size of a system or the amount of composition in a given system. Through graphing the mass vs volume of the given samples leading us to densities for the two groups, there was realization that the change in the composition, for the pre-1982 pennies, involving use of more zinc core as compared to copper was the main cause. The use of hydrochloric acid also helped in deducing the change in composition, as the main cause for the change in mass. The new penny reacted with HCL, when put in a solution of HCL, while the old one could not react. Introduction The composition of minted pennies before 1982 was a mixture of copper (95%) and zinc (5%). Advancement of time to post 1982, saw the change of preference from use of majority of copper to zinc, because of the expensive costs associated with using the former. Instead of 95% copper composition and 5% zinc composition, the minted pennies had around 97.5% zinc composition and 2.5 copper. The resulting change in the compositions leads to change in characteristics of the pennies. Mass, was one of the major characteristics, which changed because of the composition change. In this lab, penny masses were analyzed to determine the trends in masses for the years (pre and post 1982). Weight of each penny was found using analytical balance, followed by finding the weight of the 5 pennies together. The lab also included determining the major cause of the trend through calculating the densities of the older and newer pennies from the mass vs volume graph. The results obtained helped in explaining why the pre-1982 pennies followed a different trend as compared to the post 1982 pennies. The results legitimize the reasoning that change in composition of the pennies, from majority copper to majority zinc, was the main cause for the change in mass. Result and observations The histogram for pre-1982 shows masses above 3 grams while that for post-1982 shows masses below 3 grams. Further, most of the masses for pre-1982 lied around 3.09, as evident by the registered highest frequency of 19; while that for post-1982 lied around 2.49 as shown by highest frequency of 25. The percent variation for the pre-1982 data was 0.83% while that for post-1982 data was 0.79%. The standard deviation, averages and coefficient of variance obtained for the two, in excel, are as follows Mass of Pre-1982 Pennies (g) Mass of Post-1982 Pennies (g)   standard deviation 0.0308 0.0227   average 3.097 2.499   coefficient of variance 0.995% 0.910% Calculations for before 1982 Mean = 15.4723/5 = 3.094 X1 – mean) = 3.0767 – 3.09446 = -0.01776 = 3.0862 – 3.09446 = -0.00826 = 3.0682 – 3.09446 = -0.02626 = 3.1106 - 3.09446 = 0.01614 = 3.1306 - 3.09446 = 0.03614 X1 – mean)2 : -0.01776)2 = 3.154 x 10-4 : -0.00826)2 = 6.823 x 10-5 0.02626)2 = 6.896 x 10-4 0.01614)2 = 2.605 x 10-4 0.03614)2 = 1.306 x 10-3 Summing up the following results gives 0.002639 Average = 0.002639/4 = 6.599 x 10-4 Ð = √(6.599 x 10-4) = 0.02569 V = 0.02569/3.09446) x 100 = 0.83% After 1982 Mean = 12.4843/5 = 2.49686 (X1 – mean) = 2.5050 – 2.49686 = 8.1400 x 10-3 = 2.4789 - 2.49686 = -0.01796 2.5275 – 2.496686 = 0.03064 2.4840 - 2.49686 = 0.01286 2.4889 – 2.49686 = -7.9600 x 10-3 (X1 – mean)2 = 8.1400 x 10-3)2 = 6.6260 x 10-5 = (-0.01796) 2 = 3.2266 x 10-4 = (0.03064)2 = 9.3881 x 10-4 = 0.01286)2 = 1.6548 x 10-4 = (-7.9600 x 10-3)2 = 6.3362 x 10-5 Summing up the following results gives 0.0015565 Average = 0.0015565/4 = 3.891 x 10-4 = √(3.891 x 10-4) = 0.01973 0.01973/2.49686) x 100 = 0.79% The following is a frequency histogram showing the result for the pre-1982 Pennies results. Figure 1 showing a frequency histogram showing the result for the pre-1982 Pennies results. The following is a frequency histogram showing the result for the post-1982 Pennies results. Figure 2 showing a frequency histogram showing the result for the post-1982 Pennies results The following is the calculation of density of pennies when using the density values of copper and zinc. The density was determined based on the percentages of the elements in pennies. Pennies made before 1982 = 95% copper and 5% Zn *Density of pure Cu (DCu) = 8.92 g/mL *Density of pure Zn (DZn) = 7.14 g/mL DCu = (0.95 Cu)(8.92 g/mL) = 8.474 g/mL of Cu per “old” penny DZn = (0.05 Zn)(7.14 g/mL) = 0.357 g/mL of Zn per “old” penny Density of “old” pennies = DCu per “old” penny + DZn per “old” penny Density of “old” pennies = 8.474 g/mL + 0.357 g/mL Density of “old” pennies = 8.831 g/mL For the new pennies *correct density value of new penny = 7.1845 g/mL *experimental value of new penny = 6.56 g/mL % error = {correct value – experimental value)/correct value} x 100 % error = {(7.1845 – 6.56)/7.1845} x 100 % error = 8.6% Discussion The plotted histograms show a clear trend in the decrease of mass of the pennies from pre-1982 to post-1982. After carrying out the study of mass vs year, for both post and pre-1982, the report hypothesized that the witnessed drop in the mass for the post 1982 could have resulted from a possible change in the composition of pennies (Moore 192). The change in composition subjects the pennies to change in their mass over a period. Further, the experiment also included a change in the amount of material used to have caused the change in mass. The percent error found in measuring the mass of old and new pennies resulted when taking measurements. This may have happened because of possible mistakes encountered when taking readings from the analytical balance. Rounding up and truncating the readings acts as the main source for the slight percent error witnessed. The external interference, such as temperature and moisture in the atmosphere, on the readings may have also acted as a source of error. Moisture could have easily settled on the specimen thereby leading to increased weight. The readings obtained from the analytical balance showed that the pre-1982 pennies were heavier than the post-1982 pennies. These results legitimize the reasoning that change in composition of the pennies, from majority copper to majority zinc, was the main cause for the change in mass. An efficient way of reducing the percentage error exhibited in the experiment is through carrying out more trials. More trials are effective in improving the accuracy of the calculated averages. Further, A possible future experiment that could result from this lab is determining the reason why zinc is lighter than copper. Work cited Moore, John W, Conrad L. Stanitski, and Peter C. Jurs. Chemistry: The Molecular Science. Belmont, CA: Thomson Brooks/Cole, 2008. Print. 192 Hsu, Tom, and Tom Hsu. Foundations of Physical Science: Investigations. Peabody, Mass: Cambridge Physics Outlet, 2002. Print. Read More