and then the heat given off when the temperature of the water is lowered to 0.0 C . to heat the ice cm g cm J g C C C J = 54 0.917 1 2.01 0 + 25.0 = 2.5 10 3 3 1 1 3 b g 3 1 1 3 3 0.998 g to cool the water = 400.0 cm 4.18 J g C 0 C 32.0 C = 53.4 10 J 1 cm Mass of ice = 3 3 0.917 g 54 cm 1 cm = 49.5 g = 50. g ice
Chapter 12: Liquids, Solids, and Intermolecular Forces 530 Mass of water = 3 3 0.998 g 400.0 cm 1 cm = 399 g water Thus, at 0 C , we have 50. g ice, 399 g water, and 53.4 2.5 10 = 50.9 3 b g J kJ of heat available. Since 50.0 g of ice is a bit less than 3 moles of ice and 50.9 kJ is enough heat to melt at least 8 moles of ice, all of the ice will melt. The heat needed to melt the ice is 2 2 1 mol H O 6.01 kJ 50. g ice =17 kJ 18.0 g H O 1 mol ice We now have 50.9 17 = 34 kJ kJ kJ of heat, and 399 +50. = 449 g g g of water at 0 C . We compute the temperature change that is produced by adding the heat to the water. 3 1 1 34 10 J = =18 C The final temperature is 18 C. 449 g 4.18 J g C T 59. (E) The liquid in the can is supercooled. When the can is opened, gas bubbles released from the carbonated beverage serve as sites for the formation of ice crystals. The condition of supercooling is destroyed and the liquid reverts to the solid phase. An alternative explanation follows. The process of the gas coming out of solution is endothermic (heat is required). (We know this to be true because the reaction solution of gas in water gas + liquid water proceeds to the right as the temperature is raised, a characteristic direction of an endothermic reaction.) The required heat is taken from the cooled liquid, causing it to freeze. 60. (E) Both the melting point of ice and the boiling point of water are temperatures that vary as the pressure changes, and the boiling point changes more substantially than the melting point. The triple point, however, does not vary with pressure. Solid, liquid, and vapor coexist only at one fixed temperature and pressure. Network Covalent Solids 61. (E) One would expect diamond to have a greater density than graphite. Although the bond distance in graphite, “one-and-a-half” bonds, would be expected to be shorter than the single bonds in diamond, the large spacing between the layers of C atoms in graphite makes its crystals much less dense than those of diamond. 62. (E) Diamond works well in glass cutters because of its extreme hardness. Its hardness is due to the crystal being held together entirely by covalent bonds. Graphite will not function effectively in a glass cutter, since it is quite soft, soft enough to flake off in microscopic pieces when used in pencils. The bonding in between layers of graphite is weak, which leads to it being a softer material. In fact, graphite is so soft that pure graphite is rarely used in common wooden pencils. Often clay or some other substance is mixed with the graphite to produce a mechanically strong pencil “lead.”
Chapter 12: Liquids, Solids, and Intermolecular Forces 531 63.