Density Problems Honors

Zumdahl 7th ed

•53. A material will float on the surface of a liquid if the material has a density less than that of the liquid. Given that the density of water is approximately 1.0 g/mL, will a block of material having a volume of 1.2X104 in3 and weighing 350 lb float or sink when placed in a reservoir of water?

Ans 8.0X10-1 g/cm3; float

55. A star is estimated to have a mass of 2X1036

kg. Assuming it to be a sphere of average radius 7X105 km, calculate the average density of the star in units of grams per cubic centimeter. Ans 1X106g/cm3

57. Diamonds are measured in carats, and 1 carat = 0.200 g. The density of diamond is 3.51 g/cm3. What is the volume of a 5.0-caratdiamond? Ans: 2.8X10-1 cm3

59. A sample containing 33.42 g of metal pellets is poured into a graduated cylinder initially containing 12.7 mL of water, causing the water level in the cylinder to rise to 21.6 mL. Calculate the densityof the metal. Ans: 3.8 g/mL

• 61. In each of the following pairs, which has the greater mass? (See

Table 1.5.)a. 1.0 kg of feathers or 1.0 kg of leadb. 1.0 mL of mercury or 1.0 mL of waterc. 19.3 mL of water or 1.00 mL of goldd. 75 mL of copper or 1.0 L of benzeneAns: a. same; b. Hg; c. same; d. benzene

TABLE 1.5 Densities of Various Common Substances* at 20CSubstance Physical State Density (g/cm3)Oxygen Gas 0.00133Hydrogen Gas 0.000084Ethanol Liquid 0.789Benzene Liquid 0.880Water Liquid 0.9982Magnesium Solid 1.74Salt (sodium chloride) Solid 2.16Aluminum Solid 2.70Iron Solid 7.87Copper Solid 8.96Silver Solid 10.5Lead Solid 11.34Mercury Liquid 13.6Gold Solid 19.32

63. In each of the following pairs, which has the greater volume?a. 1.0 kg of feathers or 1.0 kg of leadb. 100 g of gold or 100 g of waterc. 1.0 L of copper or 1.0 L of mercuryAns: • a. feathers; • b. water; • c. same;

TABLE 1.5 Densities of Various Common Substances* at 20CSubstance Physical State Density (g/cm3)Oxygen Gas 0.00133Hydrogen Gas 0.000084Ethanol Liquid 0.789Benzene Liquid 0.880Water Liquid 0.9982Magnesium Solid 1.74Salt (sodium chloride) Solid 2.16Aluminum Solid 2.70Iron Solid 7.87Copper Solid 8.96Silver Solid 10.5Lead Solid 11.34Mercury Liquid 13.6Gold Solid 19.32

65. The density of osmium (the densest metal) is 22.57 g/cm3. If a 1.00-kg rectangular block of osmium has two dimensions of 4.00 cm 4.00 cm, calculate the third dimension of the block. Ans: 2.77 cm

54. For a material to float on the surface of water, the material must have a density less than that of water (1.0 g/mL) and must not react with the water or dissolve in it. A spherical ball has a radius of 0.50 cm and weighs 2.0 g. Will this ball float or sink whenplaced in water? (Note: Volume of a sphere 4/3 πr3.) Ans:3.8 g/cm3 sink

56. A rectangular block has dimensions 2.9 cm 3.5 cm 10.0 cm. The mass of the block is 615.0 g. What are the volume and densityof the block?•Ans: 6.1 g/cm3

58. The volume of a diamond is found to be 2.8 mL. What is the mass of the diamond in carats? (See Exercise 57.- Denisty 3.51 g/cm3)Ans: 4.9 X101 carats

60. The density of pure silver is 10.5 g/cm3 at 20C. 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?Ans: 0.500 mL, so rises 11.2+0.500=11.7 mL = 1.17X101mL