Density. Part I: How Dense Is It?

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1 Density Density Part I: How Dense Is It? Everything on Earth is made of matter. Matter is anything that has mass and takes up space. Matter is as simple as a single element or as complex as the entire planet. In science, an amount of space is called volume. Matter can be any substance in the gas, liquid, or solid state. When we describe matter, we usually think of the physical properties of the object, for example: color, smell, taste, feel, volume, and mass. Another important physical property, density, is used to describe matter as a ratio, or a numeric comparison, of the matter s mass (m) to its occupied volume (v). The more matter squeezed into the space, the denser the substance will be. A small potato is denser than a handful of cotton balls because the potato has more mass contained within the occupied space (volume). A small potato would still be denser than a bag full of cotton balls because density describes how much mass is contained within a specific volume. Density is a physical property that relates the amount of matter to a certain amount of space. How do you think this physical property is measured? Density measures how much mass is in a certain space, so density is measured in mass and volume. The scientific definition of density is mass per unit volume. As you think and learn about density, consider the following questions: Does a part or slice of a substance have a different density than the whole piece? How can the density of irregularly shaped objects be calculated? Record your ideas about these questions in Part I of your Student Journal. 1

2 Part II: Density and Units for Solids with a Regular Shape To calculate density, divide the mass of the matter by the volume that it takes up. Here are the equations: Density mass volume or D = m V In order to calculate the density of matter, you must use units of both mass and volume. þ For solid materials you use grams (g) for mass, and cubic centimeters (cm 3 ) for volume. þ For liquid materials you use grams (g) for mass, and milliliter (ml) for volume. þ The letter D represents density. For solid matter: g D = cm 3 For liquid matter: D = The volume of a regularly shaped object is determined by measuring the l (length) x w (width) x h (height) of the substance, resulting in a measurement in cubic centimeters (cm 3 ). Procedure A: Calculate Density of a Solid with a Regular Shape 1. Use a piece of masking tape to label a Petri dish for each lab member. Use a triple-beam balance to find the mass of each labeled Petri dish. Record the mass in your Student Journal. 2. Carefully slice the end off a potato to create a flat side. Keep all unused portions of the potato for use later in the lab. Remove only enough potato for each lab member to cut out a regularly shaped potato cube with the following measurements: 1 cm x 1 cm x 4 cm. Place the potato cube in the appropriately labeled Petri dish. Warning: Be as precise with your measurements as possible because even small errors in measurement will affect your density calculation. g ml Continue to the next page of this Student Guide. 2

3 Part II: Density and Units for Solids with a Regular Shape, continued Procedure A (continued): 3. Each group member places their potato cube in their labeled and massed Petri dish. Determine the mass of the potato cube plus the Petri dish. Subtract the mass of the Petri dish to determine the mass of just the potato cube and record the measurement in your Student Journal. 4. Even though you tried to cut your potato cube to exactly 1 cm x 1 cm x 4 cm, there may be some variations. Carefully measure L, W, and H of the cube again and record the accurate measurements to the nearest whole centimeter in your Student Journal. Then use the volume formula (L x W x H = V) to calculate the volume in cm 3 for the potato cube. 5. Use the density formula to calculate the density of the potato cube. 6. Compare and record the measurement and density results of your cube with your lab partners and answer the Part II of your Student Journal questions. Part III: Density and Units for Solids using Displacement You have determined the density of a regularly shaped object by making a potato cube and using the volume formula of V = l x w x h and then measuring the mass of the cube in grams. You probably found that your original potato density calculation varied somewhat from that calculated by other students. It is difficult to precisely cut a potato into a perfect cube. It is very likely that your potato cubes are slightly irregular shapes, which makes it challenging to determine volume using a ruler. When calculating density, it is very important to be as accurate as possible. You will be able to obtain a more accurate volume by using a different technique, the displacement method. The volume of a solid can be obtained using the displacement method by slowly immersing the object into a graduated cylinder partially filled with water. The object will always displace an amount of water equal to its volume. Displacement a way to measure the volume of a solid by placing it in a known volume of liquid. Continue on to the next page of this Student Guide. 3

4 Part III: Density and Units for Solids using Displacement, continued Procedure B: Calculate Density of a Potato Cube using the Displacement Method 1. Pour 15 ml of water into a 25 ml graduated cylinder. Set the cylinder on the lab table and read the exact number of ml (remember to read the graduate scale at eye level at the base of the meniscus.) Record this reading in your Student Journal in the blank labeled Initial Volume of Water. 2. Slightly tip the graduated cylinder and slowly allow the potato cube to glide down the side so that it gently slides into the water. Place the cylinder on the lab table and read the new measurement on the graduate scale (again at eye level and at the base of the meniscus). Record this second measurement in your Student Journal in the blank labeled Final Volume of Water. 3. To obtain the volume in the graduated cylinder displaced by the potato cube, subtract the initial measurement from the final measurement. 4. Re-calculate the density of your potato cube using the displacement method to determine volume. Record your results in Part III of your Student Journal and then answer the questions. NOTE: 1 cm 3 = 1 ml 1 ml 1cm 3 = Complete Part III of the Student Journal. 4

5 Part IV: Comparing the Density of Substances You have used two procedures to calculate the density of your potato cube. First you measured the length, width and height of the cube with a ruler to determine the volume. This method is frequently used for regularly shaped objects. Then you used the displacement method to determine the volume. This method is frequently used for irregularly shaped objects that are not easily measured accurately with a ruler. Next determine the density of an irregularly shaped potato piece by using the displacement method. Procedure C: Calculate Density of an Irregular Solid using the Displacement Method 1. Use the potato scraps to carve an irregularly shaped potato sculpture. 2. Use the triple beam balance to measure the mass of your sculpture and record in your Student Journal. 3. Use the displacement method to measure the volume of your sculpture and record in your Student Journal. 4. Use the density formula to determine the density of your potato sculpture and record the density in your Student Journal. Complete your data and questions for Part IV of your Student Journal. 5

6 Part V: Calculating Density of Liquids Next you will determine the density of water. You will use the same process as you did for the irregular solids. Procedure: 1. Gather your materials: graduated cylinder, triple beam balance, 150 ml of water, and a plastic cup. 2. Find the mass of an empty and dry graduated cylinder. Record in The Density of Water data table in your Student Journal. 3. Pour 50 ml of water in the graduated cylinder and find the mass. Record the mass of the filled container in the data table. 4. Subtract the mass of the empty container from the mass of the filled container to get the mass of just the water. 5. Record the volume you massed in the volume column of the data table. 6. Calculate the density of the water in the graduated cylinder. 7. Repeat the process with 100 ml of water in the plastic cup. Record all data in your Student Journal. Complete Part V in your Student Journal, then answer Reflection and Conclusion questions. 6

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