Density. Accuracy and Precision

Density: Accuracy and Precision Using your lab Notebook Print out the “Keeping a Lab Notebook” link from the CHM151 Lab website and keep it inside the back cover of your lab notebook for reference. You will record all lab data and calculations in your lab notebook for this course. To help you learn correct set-ups of data tables and calculations, the lab handouts will include example tables. Since the notebook pages use “carbonless” copies, you must use a pen. Do not use a pencil since mistakes cannot be erased from the copy. All data and calculations will be recorded only in your notebook. DO NOT fill in the data tables or calculations in this handout. You will complete the information in your lab notebook. Be sure to leave sufficient space between tables and calculations lines to show your work. It is better to overestimate and use plenty of room rather than underestimate and run out of space. Procedure 1. One of the purposes of this lab is to compare the water displacement method to the caliper measurement method for determining the volume of the cylinders. Write this question in the procedure section of your notebook now and answer it: Which method do you think will be more accurate? Explain your reasoning. 2. Use an analytical balance to weigh the 4 brass slugs. 3. Use calipers to measure the length and diameter of the four brass slugs. Be sure that the calipers are reading in millimeters (rather than inches). Convert the caliper readings from mm to cm. 4. Using a 100 mL graduated cylinder, place sufficient water in it to cover the sample but do not add any of the slugs yet. Place a rubber stopper on the bottom of the cylinder to serve as a cushion and prevent breakage. Measure and record the volume of the water and the stopper to the maximum precision possible as shown above. 5. Carefully insert one brass slug into the graduated cylinder by tipping the cylinder and sliding the sample down the side. Measure the volume of the water, stopper and slug to the proper number of significant figures. 6. Repeat Steps 4 and 5 for each slug. Volume of a cylindrical solid Volume of a rectangular solid π · radius2 · length 1st edge · 2nd edge · length 1st edge length diameter length 2nd edge page 1 of 5 Showing Calculations All calculations must be shown in your lab notebook during the semester. To receive full credit for your calculations, the following should always be followed Write down any formulas that you use in your calculations. Each step in the calculation should be shown clearly. Report the result of the calculation with units (unrounded) Report the final answer, with units, to the correct number of significant figures. Example: A=lxw A = 2.34 cm x 1.2 cm A = 2.808 cm2 A = 2.8 cm2 Calculations 1. From the linear measurements, use the formula for the volume of a cylinder to calculate the volume of each slug in cm3. The volume of a cylindrical object (depicted above) is calculated by: V = π radius (cm) 2 length(cm) where r is the radius of the cylinder (half the diameter); use the button on your calculator for better accuracy and more precision. 2. The volume of water displaced is represented in mL and can be calculated by: (volume of water + stopper + slug) minus (volume of water + stopper) 3. Density is defined as mass/volume, and is usually expressed as g/mL (or g/cm3 in the metric system). Calculate the density for each metal slug in two ways: #1 by using the caliper measurements(units of g/cm3), and #2 by using the water displacement (units of g/mL). density mass (in g) volume (in cm 3 or mL) Report all values to the correct number of significant figures. Also calculate the average density value for each type of slug. 4. The accepted value of density is 8.470 g/cm3 for brass. Determine the accuracy of your average measured values by calculating the % error for each of your average density values. Percent error values are always reported as positive numbers. Note that without taking the absolute value, this can result in a negative value for the error. % error = experiment al value - accepted value 100 accepted value page 2 of 5 Density: Accuracy and Precision: Lab Report In your lab notebook, create a table of mass and caliper measurements (both millimeter and centimeter) for the four brass slugs. These tables show the format you should use in your notebook. Data is not to be recorded here! DATA Density Using Calipers: Brass (4 cylindrical samples) Mass (g) Length (mm) Length (cm) Diameter (mm) Diameter (cm) Radius (cm) Volume (cm3) Density (g/cm3) Density Using Graduated Cylinder: Brass (4 cylindrical samples) Mass (g) Volume water + stopper (mL) Volume water + stopper + slug (mL) Data Summary Table: Average density from calculation (g/cm3) Experimental value Brass Volume (mL) Density (g/mL) Average density from displacement (g/mL) Experimental value Accuracy by percent error: Metal (Accepted Density) Percent Error: Calculation Density Percent Error: Displacement Density Brass (8.470 g/cm3) page 3 of 5 Name: _____________________________ Section: ___________________ Group members: _____________________________________________________ Post-Lab Questions: Write your answers on these pages and attach them to your report. 1. According to your experimental results which method (circle one) of determining volume gave the more accurate density? Discuss your results briefly. caliper graduated cylinder 2. List one advantage for the water displacement method. 3. List one advantage for the caliper method. 4. List one disadvantage for the water displacement method. 5. List one advantage for the caliper method. 6. 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 and explain your answer. page 4 of 5 7. Two objects have the same mass but different volumes. Which will be more dense, the one with the larger volume or smaller volume? ___________________ Explain your reasoning. 8. 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? Explain. 9. Liquid A has a density of 0.90 g/cm3, liquid B has a density of 1.15 g/cm3, and liquid C has a density of 0.65 g/cm3. A 10-mL sample of each liquid is poured into one graduated cylinder and allowed to sit overnight. Assuming the liquids do not mix into one another, which liquid will be on the bottom, in the middle, and on the top in the graduated cylinder? Draw a picture of the cylinder containing the liquids and identify each liquid in your illustration. page 5 of 5