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Understanding Density: Concepts, Calculations, and Practical Applications

This chapter delves into the concept of density, defined as the mass of an object divided by its volume (D = mass/volume). Key examples include calculating the density of osmium and other metals, exploring volume displacement methods, and practical problems involving everyday materials like wood and ice. The text emphasizes the significance of density in identifying materials and understanding buoyancy. Learning checks and solutions reinforce comprehension, making it a valuable resource for students seeking to grasp fundamental scientific principles.

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Understanding Density: Concepts, Calculations, and Practical Applications

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  1. Chapter 1Measurements Density lecturePLUS Timberlake

  2. Density Density compares the mass of an object to its volume D = mass = g or g volume mL cm3 Note: 1 mL = 1 cm3 lecturePLUS Timberlake

  3. Learning Check D1 Osmium is a very dense metal. What is its density in g/cm3 if 50.00 g of the metal occupies a volume of 2.22cm3? a) 2.25 g/cm3 b) 22.5 g/cm3 c) 111 g/cm3 lecturePLUS Timberlake

  4. Solution 2) Placing the mass and volume of the osmium metal into the density setup, we obtain D = mass = 50.00 g = volume 2.22 cm3 = 22.522522 g/cm3 = 22.5 g/cm3 lecturePLUS Timberlake

  5. Volume Displacement A solid displaces a matching volume of water when the solid is placed in water. 33 mL 25 mL lecturePLUS Timberlake

  6. Learning Check What is the density (g/cm3) of 48 g of a metal if the metal raises the level of water in a graduated cylinder from 25 mL to 33 mL? 1) 0.2 g/ cm3 2) 6 g/m3 3) 252 g/cm3 33 mL 25 mL lecturePLUS Timberlake

  7. Solution 2) 6 g/cm3 Volume (mL) of water displaced = 33 mL - 25 mL = 8 mL Volume of metal (cm3) = 8 mL x 1 cm3 = 8 cm3 1 mL Density of metal = mass = 48 g = 6 g/cm3 volume 8 cm3 lecturePLUS Timberlake

  8. Learning Check3 Which diagram represents the liquid layers in the cylinder? (K) Karo syrup (1.4 g/mL), (V) vegetable oil (0.91 g/mL,) (W) water (1.0 g/mL) 1) 2) 3) K W V V K W W V K lecturePLUS Timberlake

  9. Solution (K) Karo syrup (1.4 g/mL), (V) vegetable oil (0.91 g/mL,) (W) water (1.0 g/mL) 1) V W K lecturePLUS Timberlake

  10. Practice Problems • What is the density of a piece of wood that has a mass of 25.0 grams and a volume of 29.4 cm3? D =25.0g= 29.4cm3 0.850340136 g/cm3 = 0.850 g/cm3 lecturePLUS Timberlake

  11. A piece of wood that measures 3.0 cm by 6.0 cm by 4.0 cm has a mass of 80.0 grams. What is the density of the wood? Would the piece of wood float in water? lecturePLUS Timberlake

  12. I threw a plastic ball in the pool for my dog to fetch. The mass of the ball was 125 grams. What must the volume be to have a density of 0.500 g/mL? lecturePLUS Timberlake

  13. An ice cube measuring 5.80cm by 5.80cm by 5.80cm has a density of 0.917 g/mL. What is the mass of the ice cube? lecturePLUS Timberlake

  14. A cup of gold colored metal beads was measured to have a mass 425 grams. By water displacement, the volume of the beads was calculated to be 48.0mL. Given the densities, identify the metal. Gold: 19.3 g/mL Copper: 8.86 g/mL Bronze: 9.87 g/mL lecturePLUS Timberlake

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