# Density Lab

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Density- COVID-19 edition Purpose: To measure the density of an object using measurement, displacement, and calculation. How often do you hear the term “massive”? Have you stopped to think about what it means? Is it big? Is it heavy? Not necessarily either, as will be shown in the discussion below. Because size and mass frequently are proportional to each other, this term is misused in conversation. Mass relates to the number of particles present. An object that is massive, then, has many particles. Because the force of gravity attracts these particles to the earth, these objects are said to have weight, defined as: Fw=mg where m=mass and g = gravity. The more particles, the more mass, and the heavier the object appears to be. Thus the units that we use to express mass are the same as for weight. Many scientists label the units as “gf” or “gm” meaning “gram force” or “gram mass” to make their observations clear. Since weight depends on gravity, its value will change depending on the distance of the object from the center of the earth. Mass does not change, making it a unit of value in scientific relationships. Hence, an object may be “weightless” in space, but will never be “massless.” In this course, we will always measure the mass. The equipment used to measure mass is a balance. As the name suggests, a balance relates one mass to a known mass. When the object to be massed balances the known mass, its mass is known. Since the known and unknown masses are both subject to the same gravitational attraction, gravitational effects are negated. Weight is measured using a scale. In a scale, the mass is pulled by gravity and presses down on a spring which compresses. Different weights will compress the spring by different distances and this spring height change is measured. Since gravity causes the compression, changes in gravity would lead to differing weight readings. Volume is a measurement of space occupied by matter. Liquid volumes can be measured directly using such objects as a graduated cylinder or a cup measure as in cooking. Volume can also be calculated for regular shaped objects (cylinders, spheres, etc...) using dimensions measured in distance. For irregular shapes, however, direct measurement or measurement by displacement is used. If volume is calculated, it is helpful to remember that one cubic centimeter (cc) is the same as one milliliter (mL). In displacement, a cylinder is partially filled with water or a non-reacting fluid. The volume of the fluid is measured. The object to be measured is dropped into the fluid. Because it occupies volume, the volume inside the cylinder has increased. The new volume is measured. The volume of the object is then s=V 3cube r3 4=V 3sphere π LxWxH=V rsolidrectangula hr=V 2 cylinder π calculated as total volume minus the initial volume. Many cooks measure shortening for baking in this way. The volume of a sample varies with temperature, so the measuring equipment is usually marked to indicate the temperature at which it was calibrated. Now that we know what mass and volume mean, we are left with a small conflict- Does a massive object really take up a large volume? Not necessarily- Hollywood spends a great deal of time painting Styrofoam to look like walls and boulders for films. It is obvious that we do not lack real boulders, but that the Styrofoam boulders are lightweight and easy to move. Thus a real boulder and a Styrofoam boulder occupy the same volume but vary widely in their mass. Density relates the mass and volume of a substance, a property that could be used to differentiate the Styrofoam from rock. V m=d Since volume varies with temperature, density will too. Since it is a ratio, however, density is an intensive property- that is to say that no matter what the sample size of matter, the density will be the same for the same substance provided the temperature is the same. You can pour out different volumes of solution, and each volume will have a different mass under the conditions, but the density will be the same. Thus, density can be used to identify a substance. In this way, a geologist can easily distinguish the expensive jade from common serpentine. Pre-lab: Record the purpose of the lab in your own words. Prepare your notebook by copying the following tables A1 and A2 into your notebook. Leave enough room to record your data. Table A1. Data Organizer for 10 pennies in a cylindrical shape. Appearance of Cylinder_____________________________________________ Mass (g) length (cm) diameter (cm) Volume Before (mL) Volume After (mL) A B C D E Volume from Dimensions (mL) Volume from Displacement (mL) Density from dimensions Density from displacement Average density F G H I J Table A2. Data Organizer A (mass) Measurement: 24.98 B (length) n = ____, m = ____, M = _____, u = _____, U = _____, Measurement_______ C (diameter) n = ____, m = ____, M = _____, u = _____, U = _____, Measurement_______ D (volume) n = ____, m = ____, M = _____, u = _____, U = _____, Measurement_______ E (volume) n = ____, m = ____, M = _____, u = _____, U = _____, Measurement_______ F v = π(C/2)2B G E-D H A / F I A / G J (H + I) / 2 Procedure A. Determining the Density of a 10 pennies: Obtain 10 pennies preferably newer than 1982. Since you do not have a balance, please use my mass measurement. Measure the diameter and length of the pennies and record it. Half fill a 100 mL graduated cylinder with water and record the volume. Carefully add the pennies down the wall of the graduate to avoid splashing. Record the new volume. Calculations: 1. Calculate the volume of the pennies in mL from dimensions 2. Calculate the volume of the cylinder from displacement data. Vdisplaced =Vf-Vi 3. Calculate the density of dimensions by using the mass and the volume from dimensions. 4. Calculate the density of displacement by using the mass and the volume from displacement. 5. Calculate the average of the densities. 6. Determine the % Error. The correct value can be determined from the table below. The correct value is 7.185 g/mL. %* luecorrect va lue)Correct va-density (average* luecorrect va lue)Correct va-x( 100100=%E = lengthdiameterlr=V cylinder 2 2 2 = ππ Density Lab- Instant Lab Report Name _________________________ Instructor ______________________ Date Lab Performed____________________ Purpose: The purpose of this lab is to determine the density of ten pennies using different methods to determine volume. The calculated density was compared to a known value. Procedure: The procedure was followed as described in the FSCJ lab manual. Data: Appearance of the pennies_____________________________________________ Mass (g) length (cm) diameter (cm) Volume Before (mL) Volume After (mL) A B C D E Volume from Dimensions (mL) Volume from Displacement (mL) Density from dimensions Density from displacement Average density F G H I J Sample Calculations to the correct number of significant figures and with units: 1) Volume from dimensions 2) Volume from displacement 3) Density from dimensions 4) Density from displacement 5) Average density 6) % Error Discussion: My metal results were (good/bad) because Error Analysis: Two sources of error and their effect on the calculated density were: A. B. Modification: To avoid some of these errors in the future, the following modification should be made: A. Conclusions: The average density of the pennies was __________. The average density was in error by _______%. Post Lab Questions: 1. Examine the number of significant figures in the densities of your cylinder of pennies. Which method (displacement method or calculation from dimensions methods), provided the most precise answer? Explain. 2. Which method (displacement or dimensional) provided the most accurate answer? Explain. For the next four questions, use Dimensional Analysis (also known as the Factor-Label method), show work and report answers to the correct number of significant figures. Given: 453.6 g = 1 pound (lb) The density of mercury is 13.5 g/mL The density of alcohol is 0.780 g/mL 3. What is the volume, in mL, of 1.47 lbs of alcohol? 4. How many pounds of mercury are in 8.54 x 102 mL? 5. What is the volume in liters of 57 g of alcohol? 6. What is the volume, in mL, of 32.0 kilograms of mercury?

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