CHAPTER 3



DENSITY

Density is a ratio that compares the mass of an object to its volume. The units for density are often grams per cubic centimeter (g/cm3). However, since it is a ratio, it is the mass unit/volume unit.

D= m

V

Density is a characteristic physical property of the substance. It can be used to identify a substance. WHY?

Example 1: A sample of aluminum metal has a mass of 8.4 g. The volume of the sample is 3.1 cm3. Calculate the density of aluminum.

Example 2: What is the mass of the ethyl alcohol that exactly fills a 200.0 mL container? The density of ethyl alcohol is 0.789 g/mL.

Example 3: A bottle of mercury has the mass of 408 grams. The density of mercury is 13.6 g/mL. Without opening the bottle calculate how many mL of mercury are in the bottle?

Solve the following problems. SHOW YOUR WORK. Remember to record your answer using significant figure.

1. Mercury metal is poured into a graduated cylinder that holds exactly 22.5 mL. The mercury used to fill the cylinder weighs 306.0 g. From this information, calculate the density of mercury.

2. A student finds a rock on the way to school.  In the laboratory he determines that the volume of the rock by putting 53.0 mL of water in a graduated cylinder. He places the rock in the graduated cylinder and the water rises to 75.7 mL. Using a triple beam balance, he finds the mass to be 39.943 g.   What is the density of the rock?

3. A cube of aluminum has a side measuring 3.0 cm. The aluminum weighs 72.9 g. What is its density?

4. Diamond has a density of 3.26 g/cm3. What is the mass of a diamond that has a volume of 0.350 cm3?

5. What is the volume of a sample of liquid that has a mass of 76.2 g, given that the density of mercury is 13.6 g/ml?

6. A block of salt has a mass of 1.00 kg. What is its volume? Density of the salt is 2.2 g/cm3.

7. The density of pure silver is 10.5 g/cm3 at 20 (C. If 5.25 g of pure silver pellets is added to a graduated cylinder containing 11.2 mL of water, to what volume level will the water in the cylinder rise?

8. In the opening scenes of the movie Raiders of the Lost Ark, Indiana Jones tries to remove a gold idol from a booby-trapped pedestal. He replaces the idol with a bag of sand or approximately equal volume. (density of gold= 19.32 g/cm3; density of sand about 2 g/cm3)

a. Did he have a reasonable chance of not activating the mass-sensitive booby trap?

b. In a later scene he and an unscrupulous guide play catch with the idol. Assume that the volume of the idol is about

1.0 L. If it were solid gold, what mass would the idol have? Is playing catch with it plausible?

(Use density chart to solve the problems 9-11)

|DENSITIES OF SOME COMMON SUBSTANCES |

|Substance Density (g/cm3) |Substance Density (g/cm3) |

|Hydrogen |0.00009 |Aluminum |2.7 |

|Oxygen |0.0013 |Iron |7.9 |

|Corn oil |0.922 |Copper |8.9 |

|Water |1.0 |Lead |11.3 |

|Sugar |1.6 |Mercury |13.6 |

|Table Salt |2.2 |Gold |19.3 |

|Quartz |2.6 | | |

9. A block of metal is 10.0 cm long, 3.0 cm wide, and 1.0 cm high. What would its mass be if it were real gold?

10. An object has a mass of 54.6 g and a volume of 6.91 cm3. What is its density? Identify the object.

11. Equal amounts of mercury, water and corn oil are added to a beaker.

a. Sketch the arrangement of the layers in the beaker.

b. A small cube of sugar is added to the beaker. Describe its location.

c. What change will occur to the sugar cube over time?

12. Two objects are placed in a beaker of water. Object A has a density of 2.13 g/ml and Object B has a density of

0.89 g/ml. Make a sketch of the beaker with the objects and water in the beaker. Be sure to label each object.

12. Plot these data that show how the mass of sulfur increases with an increase in volume on graph paper. Determine the density of sulfur from the slope of the line.

|Mass of sulfur (g) |Volume of sulfur (cm3) |

|23.5 |11.4 |

|60.8 |29.2 |

|115 |55.5 |

|168 |81.1 |

14. What is the density in kg/m3 of a block of marble that occupies 310 cm3 and has a mass of 853 g ?

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