Density of material lab

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Purdue University *

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23500

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Chemistry

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Jan 9, 2024

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MSE 235: Density of Materials Lab 1 Instructions: This lab activity will meet in ARMS 2130 and you will need to wear proper lab attire (long pants, closed-toed shoes, safety glasses). Students in each lab session will divide into small groups. Each small group will make the same measurements working in parallel and should record their measurements on a datasheet (available on BrightSpace). At the end of the lab, you will work with your TAs to compile the results into a common comprehensive datasheet containing all lab groups’ data. This comprehensive datasheet will be posted on BrightSpace for use in preparing your lab report. You will not be allowed to leave lab without compiling your data into the comprehensive datasheet. Lab report instructions and questions are described at the end of this document. Background Reading • Statistics I & II Lectures and Related Assignments Materials: old and new pennies, 4 calipers with extra batteries, 4 immersion set-ups (which includes balances, wooden blocks, aluminum stands, copper wire baskets, beakers with water), tweezers, hardcopies of data sheet to fill out during the lab sessions, calculators (students will provide) Activity Introduction This course focuses on the properties of materials and their relation to the materials’ structures. Properties are physical quantities that characterize the responses of materials to particular environments (pressure, gravity, electric fields, heating, etc.). Properties are generally tabulated in books or computer databases, making it easy to forget that they are measured quantities and are thus uncertain, depending on the test method. The main goals of the density lab activity are to make a simple property measurement and understand the measurement uncertainty. One of the most basic properties of any material is density , mass per unit volume. For crystalline materials, the connection to the atomic-scale structure model is simple. The density is the atomic mass of the unit cell (atomic mass of the atoms times the number of atoms in the unit cell) divided by the unit cell volume, obtained by x-ray diffraction. This structural model has led to the notion of a "theoretical" density. If you think about it, however, this is really a measured property since the atomic masses and the unit cell volume are measured. Structural imperfections such as chemical impurities and pores would obviously affect the density. Density is more commonly determined by directly measuring the mass and volume of a macroscopic test specimen. If the specimen is pore-free, then the measurement yields the "true" density. The true density of elemental solids ranges from 0.53 g/cm 3 for lithium (Li) to 22.5 g/cm 3 for iridium (Ir). These values are given in g/cm 3 units, which are commonly reported in tables. The SI unit of density is kg/m 3 and the conversion is simply a factor of 1000, giving 530 kg/m 3 and 22,500 kg/m 3 for Li and Ir, respectively. Pennies are apparently made of copper (Cu), as you can tell from their metallic luster (when new) and characteristic reddish color. The true density of copper is 8.96 g/cm 3 . In this lab activity, you will measure the density of pennies using two different techniques, analyze the results and uncertainty of the measurements, and write an individual lab report based on your findings. One technique, the immersion method, relies on Archimedes’ Principle, which is that the buoyancy force of an object immersed in a fluid is equal to the weight of the fluid displaced by that object. This means that if an object weighed in

MSE 235: Density of Materials Lab 2 air is found to have a mass of m grams and the object is then submerged in a fluid ( e.g. , water) and found to have an apparent mass of m’ grams, then the amount of fluid (in grams) that the object has ultimately displaced is given by the following equation: m_displaced = m – m’ Eqn. 1 The amount of displaced fluid is directly related to the volume of the object. So as long as the density of the fluid is known ( e.g. , water is 1 g/cm 3 ), then the volume of the object can be calculated from the mass of the displaced fluid, using the following equation: V_object = m_displaced / density_fluid Eqn. 2 Experimental Method In this lab activity, each small group will be given a collection of 10 pennies: 5 “new” pennies mi nted after 1982 and 5 “old” pennies minted during or before 1982. Your objective is to determine the density (mass / volume) of the pennies using a digital electronic balance to measure the mass of each penny and two different techniques to measure the volume of each penny: (1) Measuring the volume directly with digital calipers (referred to as the “caliper method”) (2) Measuring the volume indirectly by immersion in water (Archimedes’ method; referred t o as the “immersion method”) In lab, for the caliper measurement of volume, each group member should take turns measuring and recording the dimensions of each penny in the sample, while the other members can record the data. In order to avoid bias, do not look at previous measurements of a penny or ask your data recorder, for example, "is that close to what you got?" Measure the diameter across two approximately orthogonal directions and average the values if there are measurable differences. Measure the thickness across the middle (don't worry about the effects of the coining). Compile all the data, and calculate and record the volume va lues. You will measure the penny mass when you measure the “dry mass” as part of the immersion density method. In lab, for the immersion measurement of volume, first measure and record the dry mass of each penny. Then hang the sample basket in the water and tare ( i.e. , zero) the balance. Carefully remove the basket, place a penny in it and hang it back in the water. Note that the beaker of water is not being weighed, only the immersed penny. Repeat the measurement of this “immersed mass” and average the values if there are measurable differences. The difference between the mass reading on the balance when a dry penny is weighed versus the mass reading when the penny is immersed in water is the mass of displaced water (see Eqn. 1 and 2). Calculate the mass of the penny and, then ultimately, its density. ** Considering the decimal places that are reported by your digital calipers and electronic scale, how many significant figures should you report on your datasheet? Why?

MSE 235: Density of Materials Lab 3 Preliminary Data Analysis and Discussion After completing your measurements, calculate your density values and complete the data sheet. There are two things you might notice about the data. First, the density values determined from the caliper method are typically different than the density values determined from the immersion method. Why do you think this is? Second, the density you determined by the immersion method for the “new”, post-1982 pennies is different than that of pure copper (8.96 g/cm 3 ). This is because these new pennies are composed of two different metals (see Figure 1 below). What do you think the composition of the core is? How might you determine this? Consulting the table of densities in your Callister textbook might be a good place to start… Figure 1: A cross-sectional view of penny minted after 1982 (un-etched, optical light microscopy). Copper forms a thin layer on the penny’s surface; the penny’s core is composed of a different metal.

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MSE 235: Density of Materials Lab 4 Density Lab Report Instructions A short lab report from this activity will be due next week, prior to the start of your next lab session. In order to help you to prepare your lab report, the “ Density Lab Report Template” (.docx file) is available on BrightSpace. You should download and use/edit this document and then submit this document as a PDF using the appropriate BrightSpace assignment link. This lab report is worth 65 points . Section 1: Experimental Methods (10 pts) In less than 100 words, describe the experimental set-up that was used for the immersion method of determining the volume of a penny. To do this, please include at least 1 figure that you create yourself (and ensure it is properly labelled and includes a descriptive caption). Do not just duplicate the description of the immersion method on pg. 2, which you will notice does not actually describe the experimental set-up. Section 2: Reporting Results in a Data Table (15 pts) Complete the following table based on the comprehensive (i.e., all groups’) density data that is available on BrightSpace and include the completed table in your lab report. Make sure your data table is properly formatted and labelled with a table number and caption positioned above the table. Density (g/cm 3 ), by caliper method Density (g/cm 3 ), by immersion method Mean, pre-1982 (g/cm 3 ) Std. Dev., pre-1982 (g/cm 3 ) Mean, post- 1982 (g/cm 3 ) Std. Dev., post- 1982 (g/cm 3 ) Mean, pre-1982 (g/cm 3 ) Std. Dev., pre-1982 (g/cm 3 ) Mean, post- 1982 (g/cm 3 ) Std. Dev., post- 1982 (g/cm 3 ) Your small group’s data Data from all groups

MSE 235: Density of Materials Lab 5 Section 3: Reporting Results Using Histograms (15 points) The data on BrightSpace should include average densities for 4 groups of samples: (1) pre-1982 pennies measured by calipers, (2) pre-1982 immersion, (3) post-1982 calipers, and (4) post-1982 immersion. For each group of samples, plot a histogram using the data available from all lab groups showing the distribution of density measurements. You should use OriginPro to create your histograms. Make sure that your histogram bins are properly selected such that the trends in the data are obvious. Please ensure that your histograms are properly formatted as figures with a figure number and caption placed below the figure. Thus, your lab report should contain the following 4 figures: • A histogram showing the distribution of density values, measured using calipers , for pennies minted before 1982. • A histogram showing the distribution of density values, measured using immersion , for pennies minted before 1982. • A histogram showing the distribution of density values, measured using calipers , for pennies minted after 1982. • A histogram showing the distribution of density values, measured using immersion , for pennies minted after 1982. Section 4: Discussion (25 points, 5 points each) Question 1 : How does your group’s data compare with the data from all the lab groups? Please answer this question in less than 150 words, referring directly to your data table in section 2 and figures in section 3. Question 2 : The density of zinc is 7.13 g/cm 3 . Calculate the probability that a density measurement of the post-1982 pennies made using the caliper method is within 5% of the density of zinc. Use the caliper data that is available from all lab groups to perform your calculation, and assume that the data fits a normal distribution. Question 3 : The density of zinc is 7.13 g/cm 3 . Calculate the probability that a density measurement of the post-1982 pennies made using the immersion method is within 5% of the density of zinc. Use the immersion data that is available from all lab groups to perform your calculation, and assume that the data fits a normal distribution. Question 4 : When measuring density, the caliper values give consistently different results from the immersion values. Based on your answers to Question 2 and 3, which method do you think is more accurate and why? Question 5: In 150 words or less, please write a short paragraph that identifies the elemental composition of the modern (post-1982) pennies and explain how you know this information by directly referencing specific data in your figures and tables.