Density of Brass. Accuracy and Precision

Density of Brass: Accuracy and Precision Introduction Density is a measure of a substance’s mass-to-volume ratio. For liquids and solids, density is usually expressed in units of g/mL or g/cm3; these are equivalent since 1 mL is exactly equal to 1 cm3. Density is an intensive property meaning that a substance’s density will be the same regardless of the size of a sample. For example, steel has a density of 7.85 g/cm3 whether you have a tiny steel ball bearing or a large steel beam. The mass and volume of each piece will be different, but the mass-to-volume ratio is the same! In this lab, you will determine the density of brass as measured by two different techniques: 1) volume calculation using calipers to measure the radius of a cylinder and 2) volume calculation based on water displacement. You will then analyze the two methods regarding accuracy and precision of your technique. Accuracy is a measure of how close your measured value is to the correct value. For example, if a substance has a density of 1.23 g/mL and you measure its density to be 1.24 g/mL, then you are accurate. The difference between the experimentally measured value and the accepted value is very small. Precision is a measure of how close repeated measurements are to each other. For example, if you measure a substance with an actual density of 1.23 g/mL four times and calculate densities of 1.430 g/mL, 1.431 g/mL, 1.431 g/mL, and 1.429 g/mL, your measurements are very precise since the difference between the highest and lowest measurement (the range) is small. However, these measurements are not accurate since they differ greatly from the accepted value of 1.23 g/mL. Ideally, your measurements should be both accurate and precise. For more information: Chemistry: Atom’s First by OpenStax sections 1.4 - “Measurements”, 1.5 – “Measurement Uncertainty . . .”, and 1.6 – “Mathematical Treatment of Measurement Results”. Equations to use for the calculations: Volume of a rectangular prism: V = LxWxH where L = length, W = width, H = height Volume of a cylinder: V =  r2 L Volume of a sphere: V = 4/3  r3 Volume by displacement: V = VFinal - VInitial Density: density  mass (in g) volume (in cm 3 or mL) Average density = (d1 + d2 + d3 + d4)/4 experiment al value - accepted value  100 accepted value Recall that this is absolute value so there are no negative percent error values. Percent Error = page 1 of 7 Materials: 4 different sized brass cylinders 1 caliper set to millimeters 1 graduated cylinder 1 rubber stopper DI water bottle calculator Procedure 1. Weigh the mass of the four different brass cylinders. Refer to the “Using an analytical balance” technique on the course website for more information. Record the data in the appropriate data table. 2. Use calipers to measure the length and diameter of the four different brass cylinders and record the data. 3. Perform the following calculations making sure all work is neatly shown under the “Calculations” section of the lab report: (Refer to the “Significant figures and Showing calculations in your report” technique on the course website) Convert the caliper readings from mm to cm. Calculate the radius and volume of the brass cylinder. Calculate the density of the brass cylinder. Calculate the average density for brass. Calculate the percent error. The accepted value of density is 8.470 g/cm3 for brass. 4. Place a rubber stopper on the bottom of a 100 mL graduated cylinder to serve as a cushion and prevent breakage. Add about 50 mL of water to the graduated cylinder (this should be sufficient to cover the largest brass cylinder when it is placed in the glass graduated cylinder). Measure and record the volume of the water and the stopper. (Refer to the “Reading a meniscus in various pieces of glassware” technique on the course website) 5. Carefully insert one brass cylinder into the glass, graduated cylinder by tipping the cylinder and sliding the sample down the side. Measure the volume of the water, stopper and brass cylinder to the proper number of significant figures. 6. Repeat Steps 4 and 5 for each remaining brass cylinder. 7. Perform the following calculations making sure all work is neatly shown under the “Calculations” section of the lab report: Calculate the volume of each brass cylinder using the volume by displacement formula. Calculate the density of each brass cylinder. Calculate the average density. Calculate the percent error. The accepted value of density is 8.470 g/cm3 for brass. Please refer to the Laboratory Techniques Document on the CHM151LL Course Website for more detailed techniques and images of lab equipment. Clean-Up: Rinse everything well with tap water followed by a quick DI water rinse. Clean your benchtop. Put all equipment back exactly where you found it. page 2 of 7 Name: _____________________________ Partners: ________________________ Density of Brass Lab Report Turn in Pages 3-6 as your graded lab report Data Table 1: Density Using Calipers Data Table Brass (4 cylindrical samples) Cylinder # Mass (g) Length (mm) Diameter (mm) Data Table 2: Density Using Graduated Cylinder Data Table Brass (4 cylindrical samples) Cylinder # Mass (g) Volume water + stopper (mL) Volume water + stopper + cylinder (mL) Observations: Calculations for Data Table 1: (length in cm, diameter in cm, radius, volume, density) Cylinder 1: page 3 of 7 Cylinder 2: Cylinder 3: Cylinder 4: Average Density: Percent error: page 4 of 7 Calculations for Data Table 2: (volume of cylinder and density for each) Cylinder 1: Cylinder 2: Cylinder 3: Cylinder 4: Average Density: Percent error: page 5 of 7 Results: Results Table 1: Density Using Calipers Results Cylinder # Length (cm) Diameter (cm) Radius (cm) Volume (cm3) Density (g/cm3) Average Density (Measurement method) Percent Error Results Table 2: Density Using Graduated Cylinder Results Volume (mL) Density (g/mL) Average Density (Displacement method) Percent Error Conclusion: (5 pts) Summarize the results for determining the density of brass using the two methods, volume by measurement and volume by displacement. Use your data to support. page 6 of 7 Post-Lab Questions – These questions will not be graded as part of your lab report grade. You will be responsible for the information in these questions and able to answer these or similar questions on the post-lab quiz at the start of next week’s lab period. Questions will also be similar to your lab report data, observations, calculations, and results. 1. According to your experimental results which method (caliper or graduated cylinder) of determining volume gave the more accurate density? Briefly discuss the accuracy and precision of your results using data values to support. 2. Using complete sentences, list one advantage for the water displacement method. 3. Using complete sentences, list one advantage for the caliper method. 4. An object is known to have a density of 4.9435 g/cm3. A freshman lab class measures objects made of the same material to have the following densities: 4.57, 4.58, 4.55, 4.57, 4.55, 4.56, 4.58, 4.57, and 4.56 g/cm3. Describe the students’ data in terms of accuracy and precision. Explain your answer. 5. A solid cylinder of plastic has a density of 1.6 g/cm3. It is then cut exactly in half. What is the density of each of the pieces now? d = ______________ Explain. 6. Discuss two sources of error and how they can be corrected in the future. 1. 2. 7. Now that you have completed the experiment please write a “Purpose” statement that more accurately reflects the function of this lab. page 7 of 7