DENSITY, MASS, AND VOLUME

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1 DENSITY, MASS, AND VOLUME Name(s) Part 1 Describe what happens when two fluids (or a fluid and a solid) are brought into contact and one of the fluids is more dense than the other. Your response to the question above provides an operational definition for density. It does not give a full definition of density, but it does give a way a way to distinguish between a less dense and a more dense material. When the particle model of matter is applied to the question of density, it becomes evident that there are only two possible causes for the varying densities of substances. Both possibilities are considered below. PARTICLE SPACING A)Consider water in the liquid state and water in the solid state (ice). Which of these is more dense, and how do you know? B)Does your answer to A)depend upon the amount of liquid water or ice present, or is your answer independent of the amounts present? C)Suppose one container is filled with liquid water, and a second, identical container is filled to exactly the same level with ice. Which of the two containers would weigh more? D)Since liquid water and ice are made out of exactly the same kind of molecule, how can you account for the fact that a container of ice would weigh less than an equal sized container of liquid water? (In addition to explaining with words, also make a rough sketch on the next page showing the relative spacings of the molecules in liquid and solid water.) UNIT 2 PARTICULATE NATURE OF MATTER II-19 CALVIN COLLEGE

2 E)Given your responses above, explain why gases are always so much less dense than liquids and solids. F)Given what you know about the changing density of a gas that is heated up, what do you think would happen to the distance between the molecules of the air in this room if the air were heated up? PARTICLE WEIGHT A)Consider a piece of lead and a piece of aluminum. It is known that lead is much more dense than aluminum, but the distance between the atoms in lead is about the same as the distance between the atoms in aluminum. What does this suggest about the relative weights of lead and aluminum atoms? B)What might cause one type of atom to be heavier than another type? (Consider the makeup of an atom in order to answer this.) C)What are some possible reasons why one type of molecule might be heavier than another type? UNIT 2 PARTICULATE NATURE OF MATTER II-20 CALVIN COLLEGE

3 Part 2 DENSITY, MASS, AND VOLUME Activity #1 The Changing Density of Water In this activity you will see whether the mass and/or volume of a water balloon changes when it freezes. Begin by filling a small balloon with water, but keep it small enough that the balloon will still fit easily inside a small beaker. Make sure ALL of the air bubbles are out of the balloon before you tie it closed. Cut off any excess balloon material beyond the point at which you tied your knot. A)Use a balance to determine the mass of the balloon containing water. (Make sure the balloon is dried off before you measure its mass.) It is very important to perform this measurement with the most accurate equipment available. Be sure the scale is properly zeroed. (If you are not familiar with the use of the scale, ask your instructor for help.) Mass = gm B)Determine the volume of the balloon in the following way: (This is known as the water displacement method.) i. Place a beaker into a small plastic dish as shown here. ii. Fill the beaker with water until it begins to overflow and a little of the water pours into the plastic dish. iii. Carefully lift the beaker and discard the water that has spilled into the plastic dish. iv. Replace the beaker in the plastic dish. v. Slowly lower your balloon into the beaker. The balloon will cause some more water to flow into the plastic dish. vi. Pour the water now found in the plastic dish into a graduated cylinder to determine the volume of the balloon. Volume = ml Repeat your mass and volume measurements as a check on your work. Do you get the same results? 1)Is your balloon (plus the water inside)less dense or more dense than water? How do you know? 2)Is your balloon (not counting the water inside)less dense or more dense than water? Explain how you know. UNIT 2 PARTICULATE NATURE OF MATTER II-21 CALVIN COLLEGE

4 Place your balloon in a freezer, and leave it there until the water inside the balloon is completely frozen. (This will take several hours.) Before removing the balloon from the freezer, make sure you answer the following questions: 3)Predict whether you think the mass of the balloon and its contents will increase, decrease, or remain the same when the water freezes. Give a reason for your response. 4)Predict whether you think the volume of the balloon and its contents will increase, decrease, or remain the same when the water freezes. Give a reason for your response. 5)Predict whether you think the density of the balloon and its contents will increase, decrease, or remain the same when the water freezes. Give a reason for your response. Remove your balloon from the freezer when the water inside is completely frozen. Quickly find the mass and the volume of the balloon by using the same procedures as you used earlier. (This time you will have to hold the balloon down with your finger or a pencil so that it is completely submerged in the water. Mass = gm. Volume = ml. UNIT 2 PARTICULATE NATURE OF MATTER II-22 CALVIN COLLEGE

5 6)Did the mass of the balloon change? Explain why or why not. 7)Did the volume of the balloon change? If so, explain how it happened. 8)Did the density of the balloon change? Explain why or why not. 9)Explain, using a particle model of water, what can happen to water to make its density change. Activity #2 Volume Change in a Liquid to Solid Phase Change In the previous activity it was found that water increases in volume as it freezes. This increase in volume causes the density of the water to decrease. In Unit 1 it was pointed out that water is unusual in the way it behaves as it freezes. Almost all other known substances decrease in volume as they freeze. The activity presented here explores this volume change in a substance other than water. Obtain a substance which is easily melted in a bath of boiling water, but which is a solid at room temperature. Suggested substances include paraffin or salol (also known as phenol salicylate or salicylic acid phenol ester). UNIT 2 PARTICULATE NATURE OF MATTER II-23 CALVIN COLLEGE

6 Place some of the material into a large test tube, and place the test tube into a narrow beaker of water on a hot plate. Use enough material so that there are a couple inches of the material in the test tube. You need not start with a single chunk of the material; shavings or small pieces will work just as well. As soon as the substance is melted in the test tube, remove the tube from the bath (a folded paper towel works well to protect one s fingers from heat), dry the test tube, and while holding the tube vertically, mark the level of the liquid or place a small piece of transparent tape so that the bottom of the tape is at the level of the liquid. Then rest the test tube vertically in a holder. As you wait for the substance to turn back into a solid, answer the following questions: 1)What will happen to the volume of the substance in the beaker as it turns back into a solid? 2)Will the density of the substance increase, decrease, or remain the same as it turns back into a solid? 3)Predict where in the container the solid will first begin to form: on the top, on the bottom, or in the middle. Explain the reason for your answer. 4)As the substance solidifies, check to see if your predictions are correct. If any are not, explain below how you would modify them. UNIT 2 PARTICULATE NATURE OF MATTER II-24 CALVIN COLLEGE

7 Part 3 DENSITY, MASS, AND VOLUME Obtain the following items: five small cups One 25 ml graduated cylinder One tall, clear 100 ml graduated cylinder squirt bottle waste bucket Label the five cups A through E, and put about 20 ml of each test liquid into the appropriately labeled cups. You need not measure the volumes of the liquids precisely at this time point. You will do so later. i)find, as accurately as possible, both the mass and the volume of 15 ml of water. (Liquid A) Place these values in the data table on the next page. The density of a substance can be defined to be the mass per unit volume of the substance. ii)calculate the density of the water in grams/ml. Report your results to your instructor, and place this value in the data table on the next page. Pour your sample of liquid A into the tall, clear graduated cylinder. Save this cylinder with liquid A in it, because you will later add liquids B, C, D, and E, in sequence, to it. iii)determine the mass of 15 ml of liquid B. (Good lab procedure would necessitate that you clean your small graduated cylinder before adding the new liquid.) Calculate its density, and then carefully add the liquid to the clear graduated cylinder by tilting the tall cylinder slightly and pouring liquid B carefully down the side of the tall cylinder. The cylinder will thus contain both liquids A and B. Remember to add the mass, volume, and density measurements of liquid B to the data table. iv)determine the mass of 15 ml of liquid C, and carefully calculate its density. Predict what will happen if liquid C is added to the cylinder containing liquids A and B. Test your prediction by carefully and slowly pouring liquid C down the tilted side of the graduated cylinder. UNIT 2 PARTICULATE NATURE OF MATTER II-25 CALVIN COLLEGE

8 v) Repeat step iv) with about 15 ml of liquid D. Prediction: Test your prediction by carefully and slowly pouring liquid D down the side of the graduated cylinder. vi) Determine the density of liquid E. Where do you predict that liquid E will layer if you pour liquid E into the cylinder containing liquids A through D? Test your prediction by carefully and slowly pouring liquid E down the side of the graduated cylinder. vii) Identify the relative positions of the liquid layers by numbering the layers 1 (top) to 5 (bottom). Add the rankings to the data table in the column labeled Layering Order. DENSITY DATA TABLE Liquid Volume Mass Density Layering Order A water with green food color B vegetable oil C liquid soap D isopropyl alcohol with red food color E corn syrup with purple food color UNIT 2 PARTICULATE NATURE OF MATTER II-26 CALVIN COLLEGE

9 What is the relationship between a liquid's density and its order of layering? In this activity you used nearly equal volumes of each liquid. What do you think would happen if you used different volumes - say 30 ml of liquid B and only 10 ml of liquid A? Would the layers of liquid form in the same order as before? Dispose of the mixed fluids by pouring them into an appropriately labeled waste container. If you wish to keep your layered creation, top the column off with a little baby oil. This will keep the alcohol from evaporating and from creating an annoying odor in the room. UNIT 2 PARTICULATE NATURE OF MATTER II-27 CALVIN COLLEGE

10 Density and Mass Content Overview A formal definition of mass is the amount of matter making up a substance. This definition works well for memorization, but memorization does not necessarily imply understanding. A very common misunderstanding arises from confusing mass with volume, which is the amount of space taken up by a substance. The major weakness of the formal definition of mass is that it doesn t tell us what is meant by amount or how to determine the mass of a substance. To understand mass we really need to have some everyday experiences that help us to develop an intuitive understanding. We could, for example, compare a steel ball with a wooden ball of exactly the same size. Anyone working with the two balls will soon realize that they behave quite differently. The steel ball feels heavier. The steel ball is also harder to start rolling- -and harder to stop it once it is rolling. These differences exist because the balls have different mass. Physicists formally define the mass of an object in terms of its resistance to changes in its state of motion. An object that is difficult to start moving or to stop moving has a large mass, while an object that is easier to start or stop has a smaller mass. The physicist s definition is made using Newton s second law of motion, but we ll skip over that right now. Mass and weight are very closely related, and sometimes at the elementary school level no distinction is made between them. The weight of a substance is equal to the force of gravity on the substance. On the surface of the earth, weight is proportional to mass, and most scales measure the mass by actually measuring weight. This procedure works fine until one leaves the earth. A scale taken to the moon would need to be recalibrated to the moon s gravity because objects weigh less on the moon, even though their masses do not change. (The steel ball would be just as difficult to start or stop on the moon as on the earth--its weight changes, but not its mass.) Mass is a fundamental property of matter. In the particle model of matter, every atom possesses a certain amount of mass. The amount of mass varies from one type of atom to another, but the mass of an individual atom is permanently fixed and cannot be altered. Hydrogen atoms have the least mass, and helium the second least. An atom of lead has the most mass of any atom we encounter regularly. Uranium has the greatest mass of any naturally occurring atom, but is not something we work with very often. The mass of a molecule is simply the sum of the masses of the individual atoms that comprise the molecule. For example, the mass of a water molecule, H2O, equals the mass of two hydrogen atoms plus the mass of one oxygen atom. Similarly, the mass of any macroscopic object is just the sum of the masses of the multitude of atoms that comprise the object. Although the mass of an individual atom is small, on the order of to grams (10-21 = ), macroscopic objects typically contain many (1023 or more) atoms. UNIT 2 PARTICULATE NATURE OF MATTER II-28 CALVIN COLLEGE

11 In the particle model, atoms are the only things that have mass. All material objects are made of atoms, and thus have mass, but non-material things, such as light or ideas, have no mass. (Actually the question of whether light is made up of a stream of little particles containing mass has received considerable attention from scientists every since the time of Isaac Newton. In the particulate model of matter used in this course, however, light has no mass.) Another feature of the particle model is that atoms are indestructible. Atoms cannot be created or destroyed, and it is impossible to change one kind of atom into another kind. Atoms can be rearranged in a vast number of ways to form molecules, but individual atoms themselves are unchangeable. It follows that for a given collection of atoms, the mass will be the same no matter how the atoms are rearranged. For example, if a carbon atom [C] combines with two oxygen atoms to form carbon dioxide [CO2], the resulting mass equals the mass of the carbon atom plus the mass of two oxygen atoms. Period. If a particular container is closed tightly so that no atoms can get in or out, then the mass of the container cannot change, no matter what happens within it. There might be a rat eating food inside the container. There might be firecrackers exploding. There might be paper burning and consuming the oxygen inside the container. In all these cases, the mass of the sealed container cannot change. Similarly there is no change of mass when a substance changes phase. For example, when ice melts, the mass of the liquid water is the same as the mass of the ice before it melted. When water evaporates, water molecules go into the air as gas, but the mass of the water vapor is equal to the mass of the original liquid water. Therefore, in the particulate model of matter, mass is conserved, i.e., the amount of mass within a system cannot change unless atoms enter or leave the system. The density of an substance refers to the amount of mass per unit volume contained in a substance. A dense object contains a relatively large amount of mass in a small amount of space. Therefore, a dense substance either has its atoms very closely spaced together, or the atoms themselves are relatively massive. Gases tend not to be very dense, because the molecules making up a gas are generally far apart. Liquids and solids tend to be much more dense than gases, because their molecules are relatively close together. Since the particle model assumes that atoms can not change mass, the only way a particular substance can change in density is if the atoms or molecules making up the substance move farther apart or move closer together. This is generally what happens when a substance heats up or cools off, which is why the density of a substance often changes when its temperature changes. Throughout this discussion about mass and density, it has been emphasized that a particulate model for matter is being used. It is important to remember that this model is not completely correct. No model is. The particle model does not account for the substructure of individual atoms (atoms are made of electrons, protons, and neutrons), and it is not correct to say that atoms UNIT 2 PARTICULATE NATURE OF MATTER II-29 CALVIN COLLEGE

12 are indestructible. However, we will not concern ourselves with these shortcomings of the model until later. Test Yourself: The mass one hydrogen atom is 1.00 atomic mass unit, and of oxygen atomic mass units, where one atomic mass unit equals approximately 1.66 x kilograms. a) What is the mass of one water molecule, in kilograms? Answer: 2.99 x kg. b) How many water molecules are there in one liter of water? (Recall--and don t forget--that one liter of water has mass 1.00 kg) Answer: 3.35 x 1025 molecules. UNIT 2 PARTICULATE NATURE OF MATTER II-30 CALVIN COLLEGE

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