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# 2.8 Density[1]

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### 2.8 Density[1]

1. 1. <ul><li>2.8 </li></ul><ul><li>Density </li></ul>Chapter 2 Measurements Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings
2. 2. <ul><li>Density </li></ul><ul><li>Compares the mass of an object to its volume </li></ul><ul><li>Is the mass of a substance divided by its volume </li></ul><ul><li>Density expression </li></ul><ul><li>D = mass = g or g = g/cm 3 </li></ul><ul><li> volume mL cm 3 </li></ul><ul><li>Note: 1 mL = 1 cm 3 </li></ul>Density
3. 3. Densities of Common Substances
4. 4. <ul><li>Osmium is a very dense metal. What is its density in g/cm 3 if 50.0 g of osmium has a volume of 2.22 cm 3 ? </li></ul><ul><li>1) 2.25 g/cm 3 </li></ul><ul><li>2) 22.5 g/cm 3 </li></ul><ul><li>3) 111 g/cm 3 </li></ul>Learning Check
5. 5. <ul><li>Given: mass = 50.0 g volume = 22.2 cm 3 </li></ul><ul><li>Plan: Place the mass and volume of the osmium metal </li></ul><ul><li>in the density expression. </li></ul><ul><li>D = mass = 50.0 g </li></ul><ul><li> volume 2.22 cm 3 </li></ul><ul><li> Calculator = 22.522522 g/cm 3 </li></ul><ul><li> Final answer (2) = 22.5 g/cm 3 </li></ul>Solution
6. 6. Volume by Displacement <ul><li>A solid completely submerged in water displaces its own volume of water. </li></ul><ul><li>The volume of the solid is calculated from the volume difference. </li></ul><ul><li>45.0 mL - 35.5 mL </li></ul><ul><li>= 9.5 mL = 9.5 cm 3 </li></ul>Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings
7. 7. Density Using Volume Displacement <ul><li>The density of the zinc object is </li></ul><ul><li>then calculated from its mass </li></ul><ul><li>and volume. </li></ul><ul><li>mass = 68.60 g = 7.2 g/cm 3 volume 9.5 cm 3 </li></ul>Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings
8. 8. <ul><li>What is the density (g/cm 3 ) of 48.0 g of a metal if the level of water in a graduated cylinder rises from 25.0 mL to 33.0 mL after the metal is added? </li></ul><ul><li>1) 0.17 g/cm 3 2) 6.0 g/cm 3 3) 380 g/cm 3 </li></ul><ul><li>25.0 mL 33.0 mL </li></ul><ul><li> object </li></ul>Learning Check
9. 9. <ul><li>Given: 48.0 g Volume of water = 25.0 mL </li></ul><ul><li> Volume of water + metal = 33.0 mL </li></ul><ul><li>Need: Density (g/mL) </li></ul><ul><li>Plan: Calculate the volume difference. Change to cm 3 , </li></ul><ul><li>and place in density expression. </li></ul><ul><li> 33.0 mL - 25.0 mL = 8.0 mL </li></ul><ul><li> 8.0 mL x 1 cm 3 = 8.0 cm 3 </li></ul><ul><li> 1 mL </li></ul><ul><li>Set Up Problem: </li></ul><ul><li> Density = 48.0 g = 6.0 g = 6.0 g/cm 3 </li></ul><ul><li> 8.0 cm 3 1 cm 3 </li></ul>Solution
10. 10. Sink or Float <ul><li>Ice floats in water because the density of ice is less than the density of water. </li></ul><ul><li>Aluminum sinks because its density is greater than the density of water. </li></ul>Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings
11. 11. <ul><li>Which diagram correctly represents the liquid layers in the cylinder? Karo (K) syrup (1.4 g/mL), vegetable (V) oil (0.91 g/mL,) water (W) (1.0 g/mL) </li></ul><ul><li> 1 2 3 </li></ul>Learning Check K K W W W V V V K
12. 12. <ul><li>1) </li></ul><ul><li>Vegetable oil 0.91 g/mL </li></ul><ul><li>Water 1.0 g/mL </li></ul><ul><li> Karo syrup 1.4 g/mL </li></ul>Solution K W V
13. 13. <ul><li>Density can be written as an equality. </li></ul><ul><li>For a substance with a density of 3.8 g/mL, the equality is: </li></ul><ul><li>3.8 g = 1 mL </li></ul><ul><li>From this equality, two conversion factors can be written for density. </li></ul><ul><li>Conversion 3.8 g and 1 mL </li></ul><ul><li>factors 1 mL 3.8 g </li></ul><ul><li> </li></ul>Density as a Conversion Factor
14. 14. <ul><li>The density of octane, a component of gasoline, is 0.702 g/mL. What is the mass, in kg, of 875 mL of octane? </li></ul><ul><li>1) 0.614 kg </li></ul><ul><li>2) 614 kg </li></ul><ul><li>3) 1.25 kg </li></ul>Learning Check
15. 15. <ul><li>1) 0.614 kg </li></ul><ul><li>Given: D = 0.702 g/mL V= 875 mL </li></ul><ul><li>Unit plan: mL  g  kg </li></ul><ul><li>Equalities: density 0.702 g = 1 mL </li></ul><ul><li> and 1 kg = 1000 g </li></ul><ul><li>Set Up: 875 mL x 0.702 g x 1 kg = 0.614 kg </li></ul><ul><li>Problem 1 mL 1000 g </li></ul><ul><li> density metric </li></ul><ul><li> factor factor </li></ul>Solution
16. 16. <ul><li>If olive oil has a density of 0.92 g/mL, how many liters of olive oil are in 285 g of olive oil? </li></ul><ul><li>1) 0.26 L </li></ul><ul><li>2) 0.31 L </li></ul><ul><li>3) 310 L </li></ul>Learning Check
17. 17. <ul><li>2) 0.31 L </li></ul><ul><li>Given: D = 0.92 g/mL mass = 285 g </li></ul><ul><li>Need: volume in liters </li></ul><ul><li>Plan: g mL L </li></ul><ul><li>Equalities: 1 mL = 0.92 g 1 L = 1000 mL </li></ul><ul><li>Set Up Problem: </li></ul><ul><li>285 g x 1 mL x 1 L = 0.31 L </li></ul><ul><li> 0.92 g 1000 mL </li></ul><ul><li>density metric </li></ul><ul><li> factor factor </li></ul>Solution
18. 18. <ul><li>A group of students collected 125 empty aluminum cans to take to the recycling center. If 21 cans make 1.0 lb aluminum, how many liters of aluminum (D=2.70 g/cm 3 ) are obtained from the cans? </li></ul><ul><li>1) 1.0 L 2) 2.0 L 3) 4.0 L </li></ul>Learning Check
19. 19. <ul><li>1) 1.0 L </li></ul><ul><li>125 cans x 1.0 lb x 454 g x 1 cm 3 x 1 mL x 1 L </li></ul><ul><li> 21 cans 1 lb 2.70 g 1 cm 3 1000 mL </li></ul><ul><li> = 1.0 L </li></ul>Solution
20. 20. <ul><li>Which of the following samples of metals will displace the greatest volume of water? </li></ul><ul><li>1 2 3 </li></ul><ul><li> </li></ul>Learning Check 25 g of aluminum 2.70 g/mL 45 g of gold 19.3 g/mL 75 g of lead 11.3 g/mL
21. 21. <ul><li>1) </li></ul><ul><li>Plan: Calculate the volume for each metal and select </li></ul><ul><li>the metal sample with the greatest volume. </li></ul><ul><li>1) 25g x 1 mL = 9.3 mL aluminum 2.70 g </li></ul><ul><li>2) 45 g x 1 mL = 2.3 mL gold 19.3 g </li></ul><ul><li>3) 75 g x 1 mL = 6.6 mL lead 11.3 g </li></ul>Solution 25 g of aluminum 2.70 g/mL