Chapter 12: Solutions and Colloids

12.1 The Dissolution Process [Go to section 12.1]

  1. How do solutions differ from compounds? From other mixtures?
  2. Which of the principal characteristics of solutions can we see in the solutions of [latex]\ce{K2Cr2O7}[/latex] shown in Figure 12.1.1?
  3. When [latex]\ce{KNO3}[/latex] is dissolved in water, the resulting solution is significantly colder than the water was originally.
    1. Is the dissolution of [latex]\ce{KNO3}[/latex] an endothermic or an exothermic process?
    2. What conclusions can you draw about the intermolecular attractions involved in the process?
    3. Is the resulting solution an ideal solution?
  4. Give an example of each of the following types of solutions:
    1. a gas in a liquid
    2. a gas in a gas
    3. a solid in a solid
  5. Heat is released when some solutions form; heat is absorbed when other solutions form. Provide a molecular explanation for the difference between these two types of spontaneous processes.
Show Selected Solutions
  1. A solution can vary in composition, while a compound cannot vary in composition. Solutions are homogeneous at the molecular level, while other mixtures are heterogeneous.
  2. The answers are as follows:
    1. Endothermic
    2. Attraction between the [latex]\ce{K+}[/latex] and [latex]\ce{NO3-}[/latex] ions is stronger than between the ions and water molecules (the ion-ion interactions have a lower, more negative energy). Therefore, the dissolution process increases the energy of the molecular interactions, and it consumes the thermal energy of the solution to make up for the difference.
    3. No
  3. Heat is released when the total intermolecular forces (IMFs) between the solute and solvent molecules are stronger than the total IMFs in the pure solute and in the pure solvent: Breaking weaker IMFs and forming stronger IMFs releases heat. Heat is absorbed when the total IMFs in the solution are weaker than the total of those in the pure solute and in the pure solvent: Breaking stronger IMFs and forming weaker IMFs absorbs heat.


12.2 Electrolytes [Go to section 12.2]

  1. Explain why solutions of [latex]\ce{HBr}[/latex] in benzene (a nonpolar solvent) are nonconductive, while solutions in water (a polar solvent) are conductive.
  2. Indicate the most important types of intermolecular attractions in each of the following solutions:
    1. The solution in Figure 12.1.1.
    2. [latex]\ce{O}(g)[/latex] in [latex]\ce{CO}(l)[/latex]
    3. [latex]\ce{Cl2}(g)[/latex] in [latex]\ce{Br2}(l)[/latex]
    4. [latex]\ce{HCl}(aq)[/latex] in benzene [latex]\ce{C6H6}(l)[/latex]
    5. Methanol [latex]\ce{CH3OH}(l)[/latex] in [latex]\ce{H2O}(l)[/latex]
  3. Compare the processes that occur when methanol ([latex]\ce{CH3OH}[/latex]), hydrogen chloride ([latex]\ce{HCl}[/latex]), and sodium hydroxide ([latex]\ce{NaOH}[/latex]) dissolve in water. Write equations and prepare sketches showing the form in which each of these compounds is present in its respective solution.
  4. Explain why the ions [latex]\ce{Na+}[/latex] and [latex]\ce{Cl−}[/latex] are strongly solvated in water but not in hexane, a solvent composed of nonpolar molecules.
  5. Why are most solid ionic compounds electrically nonconductive, whereas aqueous solutions of ionic compounds are good conductors? Would you expect a liquid (molten) ionic compound to be electrically conductive or nonconductive? Explain.
  6. Consider the solutions presented:
    1. Which of the following sketches best represents the ions in a solution of [latex]\ce{Fe(NO3)3}(aq)[/latex]?
    2. Write a balanced chemical equation showing the products of the dissolution of [latex]\ce{Fe(NO3)3}[/latex].
  7. What is the expected electrical conductivity of the following solutions?
    1. [latex]\ce{NaOH}(aq)[/latex]
    2. [latex]\ce{HCl}(aq)[/latex]
    3. [latex]\ce{C6H12O6}(aq)[/latex] (glucose)
    4. [latex]\ce{NH3(l)}[/latex]
  8. Indicate the most important type of intermolecular attraction responsible for solvation in each of the following solutions:
    1. the solutions in Figure 12.2.2
    2. methanol, [latex]\ce{CH3OH}[/latex], dissolved in ethanol, [latex]\ce{C2H5OH}[/latex]
    3. methane, [latex]\ce{CH4}[/latex], dissolved in benzene, [latex]\ce{C6H6}[/latex]
    4. the polar halocarbon [latex]\ce{CF2Cl2}[/latex] dissolved in the polar halocarbon [latex]\ce{CF2ClCFCl2}[/latex]
    5. [latex]\ce{O2}(l)[/latex] in [latex]\ce{N2}(l)[/latex]
Show Selected Solutions
  1. The answers are as follows:
    1. ion-dipole forces
    2. dipole-dipole forces
    3. dispersion forces
    4. dispersion forces
    5. hydrogen bonding
  2. Crystals of [latex]\ce{NaCl}[/latex] dissolve in water, a polar liquid with a very large dipole moment, and the individual ions become strongly solvated. Hexane is a nonpolar liquid with a dipole moment of zero and, therefore, does not significantly interact with the ions of the [latex]\ce{NaCl}[/latex] crystals.
  3. The answers are as follows:
    1. [latex]\ce{Fe(NO3)3}[/latex] is a strong electrolyte, thus it should completely dissociate into [latex]\ce{Fe3+}[/latex] and ions. Therefore, (z) best represents the solution.
    2. [latex]\ce{Fe(NO3)3}(s) \rightarrow \ce{Fe^{3+}}(aq) + \ce{3NO3-}(aq)[/latex]
  4. The answers are as follows:
    1. ion-dipole
    2. hydrogen bonds
    3. dispersion forces
    4. dipole-dipole attractions
    5. dispersion forces

12.3 Types of Solutions and Solubility [Go to section 12.3]

  1. Suppose you are presented with a clear solution of sodium thiosulfate, [latex]\ce{Na2S2O3}[/latex]. How could you determine whether the solution is unsaturated, saturated, or supersaturated?
  2. Supersaturated solutions of most solids in water are prepared by cooling saturated solutions. Supersaturated solutions of most gases in water are prepared by heating saturated solutions. Explain the reasons for the difference in the two procedures.
  3. Suggest an explanation for the observations that ethanol, [latex]\ce{C2H5OH}[/latex], is completely miscible with water and that ethanethiol, C2H5SH, is soluble only to the extent of 1.5 g per 100 mL of water.
  4. At 0 °C and 1.00 atm, as much as 0.70 g of O2 can dissolve in 1 L of water. At 0 °C and 4.00 atm, how many grams of O2 dissolve in 1 L of water?
  5. Which of the following gases is expected to be most soluble in water? Explain your reasoning.
    1. [latex]\ce{CH4}[/latex]
    2. [latex]\ce{CCl4}[/latex]
    3. [latex]\ce{CHCl3}[/latex]
  6. What mass of oxygen would be dissolved in a 6.604-gallon fish tank at 25 °C, at atmospheric pressure (1 atm). The partial pressure of [latex]\ce{O2}[/latex] at atmospheric pressure is about 0.21 atm. The Henry’s law constant for [latex]\ce{O2}[/latex] is 1.3 × 10-3M/atm at 25 °C.
  7. Refer to Figure 12.3.3.
    1. How did the concentration of dissolved CO2 in the beverage change when the bottle was opened?
    2. What caused this change?
    3. Is the beverage unsaturated, saturated, or supersaturated with CO2?
Show Selected Solutions
  1. The solubility of solids usually decreases upon cooling a solution, while the solubility of gases usually decreases upon heating.
  2. 2.80 g
  3. 0.22 g

12.4 Solution Concentration [Go to section 12.4]

  1. How many liters of [latex]\ce{HCl}[/latex] gas, measured at 30.0 °C and 745 torr, are required to prepare 1.25 L of a 3.20-M solution of hydrochloric acid?
  2. Solutions of hydrogen in palladium may be formed by exposing [latex]\ce{Pd}[/latex] metal to [latex]\ce{H2}[/latex] gas. The concentration of hydrogen in the palladium depends on the pressure of [latex]\ce{H2}[/latex] gas applied, but in a more complex fashion than can be described by Henry’s law. Under certain conditions, 0.94 g of hydrogen gas is dissolved in 215 g of palladium metal.
    1. Determine the molarity of this solution (solution density = 1.8 g/cm3).
    2. Determine the molality of this solution (solution density = 1.8 g/cm3).
    3. Determine the percent by mass of hydrogen atoms in this solution (solution density = 1.8 g/cm3).
  3. Calculate the percent by mass of [latex]\ce{KBr}[/latex] in a saturated solution of [latex]\ce{KBr}[/latex] in water at 10 °C. See Figure 12.3.8 for useful data, and report the computed percentage to one significant digit.
  4. What are the mole fractions of [latex]\ce{H3PO4}[/latex] and water in a solution of 14.5 g of [latex]\ce{H3PO4}[/latex] in 125 g of water?
    1. Outline the steps necessary to answer the question.
    2. Answer the question.
  5. What are the mole fractions of [latex]\ce{HNO3}[/latex] and water in a concentrated solution of nitric acid (68.0% [latex]\ce{HNO3}[/latex] by mass)?
    1. Outline the steps necessary to answer the question.
    2. Answer the question.
  6. Calculate the mole fraction of each solute and solvent:
    1. 583 g of [latex]\ce{H2SO4}[/latex] in 1.50 kg of water—the acid solution used in an automobile battery
    2. 0.86 g of [latex]\ce{NaCl}[/latex] in 1.00 × 102 g of water—a solution of sodium chloride for intravenous injection
    3. 46.85 g of codeine, [latex]\ce{C18H21NO3}[/latex], in 125.5 g of ethanol, [latex]\ce{C2H5OH}[/latex]
    4. 25 g of I2 in 125 g of ethanol, [latex]\ce{C2H5OH}[/latex]
  7. What is the difference between a 1 M solution and a 1 m solution?
  8. Calculate the mole fractions of methanol, [latex]\ce{CH3OH}[/latex]; ethanol, [latex]\ce{C2H5OH}[/latex]; and water in a solution that is 40% methanol, 40% ethanol, and 20% water by mass. (Assume the data are good to two significant figures.)
  9. What is the molality of nitric acid in a concentrated solution of nitric acid (68.0% [latex]\ce{HNO3}[/latex] by mass)?
    1. Outline the steps necessary to answer the question.
    2. Answer the question.
  10. The concentration of glucose, [latex]\ce{C6H12O6}[/latex], in normal spinal fluid is [latex]\frac{75\text{mg}}{100\text{g}}[/latex]. What is the molality of the solution?
  11. A 13.0% solution of [latex]\ce{K2CO3}[/latex] by mass has a density of 1.09 g/cm3. Calculate the molality of the solution.
  12. Calculate the molality of each of the following solutions:
    1. 583 g of [latex]\ce{H2SO4}[/latex] in 1.50 kg of water—the acid solution used in an automobile battery
    2. 0.86 g of [latex]\ce{NaCl}[/latex] in 1.00 × 102 g of water—a solution of sodium chloride for intravenous injection
    3. 46.85 g of codeine, [latex]\ce{C18H21NO3}[/latex], in 125.5 g of ethanol, [latex]\ce{C2H5OH}[/latex]
    4. 25 g of [latex]\ce{I2}[/latex] in 125 g of ethanol, [latex]\ce{C2H5OH}[/latex]
  13. What is the molality of sulfuric acid, [latex]\ce{H2SO4}[/latex], in a solution containing10.2 g of [latex]\ce{H2SO4}[/latex] in 135 g of water?
Show Selected Solutions
  1. 102 L [latex]\ce{HCl}[/latex]
  2. 40%
  3. The answers are as follows:
    1. Determine the number of moles of each component. Then add the number of moles of components and divide that number into the moles of the component whose percentage is desired
    2. [latex]\ce{X_{H3PO4}}[/latex] = 0.0209, [latex]\ce{X_{H2O}}[/latex] = 0.979
  4. In a 1 M solution, the mole is contained in exactly 1 L of solution. In a 1 m solution, the mole is contained in exactly 1 kg of solvent.
  5. The answers are as follows:
    1. Determine the molar mass of [latex]\ce{HNO3}[/latex]. Determine the number of moles of acid in the solution. From the number of moles and the mass of solvent, determine the molality.
    2. 33.7 m
  6. 1.08 m
  7. 0.771 m

11.5 Phase Diagrams [Go to section 11.5]

  1. Why does 1 mol of sodium chloride depress the freezing point of 1 kg of water almost twice as much as 1 mol of glycerin?
  2. Assuming ideal solution behavior, what is the boiling point of a solution of 115.0 g of nonvolatile sucrose, [latex]\ce{C12H22O11}[/latex], in 350.0 g of water?
    1. Outline the steps necessary to answer the question
    2. Answer the question
  3. Assuming ideal solution behavior, what is the boiling point of a solution of 9.04 g of [latex]\ce{I2}[/latex] in 75.5 g of benzene, assuming the [latex]\ce{I2}[/latex] is nonvolatile?
    1. Outline the steps necessary to answer the question.
    2. Answer the question.
  4. Assuming ideal solution behavior, what is the freezing temperature of a solution of 115.0 g of sucrose, [latex]\ce{C12H22O11}[/latex], in 350.0 g of water?
    1. Outline the steps necessary to answer the question.
    2. Answer the question.
  5. Assuming ideal solution behavior, what is the freezing point of a solution of 9.04 g of [latex]\ce{I2}[/latex] in 75.5 g of benzene?
    1. Outline the steps necessary to answer the following question.
    2. Answer the question.
  6. Assuming ideal solution behavior, what is the osmotic pressure of an aqueous solution of 1.64 g of [latex]\ce{Ca(NO3)2}[/latex] in water at 25 °C? The volume of the solution is 275 mL.
    1. Outline the steps necessary to answer the question.
    2. Answer the question.
  7. Assuming ideal solution behavior, what is osmotic pressure of a solution of bovine insulin (molar mass, 5700 g mol–1) at 18 °C if 100.0 mL of the solution contains 0.103 g of the insulin?
    1. Outline the steps necessary to answer the question.
    2. Answer the question.
  8. Assuming ideal solution behavior, what is the molar mass of a solution of 5.00 g of a compound in 25.00 g of carbon tetrachloride (bp 76.8 °C; Kb = 5.02 °C/m) that boils at 81.5 °C at 1 atm?
    1. Outline the steps necessary to answer the question.
    2. Solve the problem.
  9. A sample of an organic compound (a nonelectrolyte) weighing 1.35 g lowered the freezing point of 10.0 g of benzene by 3.66 °C. Assuming ideal solution behavior, calculate the molar mass of the compound.
  10. A 1.0 m solution of [latex]\ce{HCl}[/latex] in benzene has a freezing point of 0.4 °C. Is [latex]\ce{HCl}[/latex] an electrolyte in benzene? Explain.
  11. A solution contains 5.00 g of urea, [latex]\ce{CO(NH2)2}[/latex], a nonvolatile compound, dissolved in 0.100 kg of water. If the vapor pressure of pure water at 25 °C is 23.7 torr, what is the vapor pressure of the solution (assuming ideal solution behavior)?
  12. A 12.0-g sample of a nonelectrolyte is dissolved in 80.0 g of water. The solution freezes at –1.94 °C. Assuming ideal solution behavior, calculate the molar mass of the substance.
  13. Arrange the following solutions in order by their decreasing freezing points: 0.1 m [latex]\ce{Na3PO4}[/latex], 0.1 m [latex]\ce{C2H5OH}[/latex], 0.01 m [latex]\ce{CO2}[/latex], 0.15 m [latex]\ce{NaCl}[/latex], and 0.2 m [latex]\ce{CaCl2}[/latex].
  14. Calculate the boiling point elevation of 0.100 kg of water containing 0.010 mol of [latex]\ce{NaCl}[/latex], 0.020 mol of [latex]\ce{Na2SO4}[/latex], and 0.030 mol of [latex]\ce{MgCl2}[/latex], assuming complete dissociation of these electrolytes and ideal solution behavior.
  15. How could you prepare a 3.08 m aqueous solution of glycerin, [latex]\ce{C3H8O3}[/latex]? Assuming ideal solution behavior, what is the freezing point of this solution?
  16. A sample of sulfur weighing 0.210 g was dissolved in 17.8 g of carbon disulfide, [latex]\ce{CS2}[/latex] (Kb = 2.34 °C/m). If the boiling point elevation was 0.107 °C, what is the formula of a sulfur molecule in carbon disulfide (assuming ideal solution behavior)?
Show Selected Solutions
  1. The answers are as follows:
    1. Determine the molar mass of sucrose; determine the number of moles of sucrose in the solution; convert the mass of solvent to units of kilograms; from the number of moles and the mass of solvent, determine the molality; determine the difference between the boiling point of water and the boiling point of the solution; determine the new boiling point.
    2. 100.5 °C
  2. The answers are as follows:
    1. Determine the molar mass of sucrose; determine the number of moles of sucrose in the solution; convert the mass of solvent to units of kilograms; from the number of moles and the mass of solvent, determine the molality; determine the difference between the freezing temperature of water and the freezing temperature of the solution; determine the new freezing temperature.
    2. -1.8 °C
  3. The answers are as follows:
    1. Determine the molar mass of [latex]\ce{Ca(NO3)2}[/latex]; determine the number of moles of [latex]\ce{Ca(NO3)2}[/latex] in the solution; determine the number of moles of ions in the solution; determine the molarity of ions, then the osmotic pressure.
    2. 2.67 atm
  4. The answers are as follows:
    1. Determine the molal concentration from the change in boiling point and Kb; determine the moles of solute in the solution from the molal concentration and mass of solvent; determine the molar mass from the number of moles and the mass of solute
    2. Molecular mass = 2.1 102 amu
  5. No. Pure benzene freezes at 5.5 °C, and so the observed freezing point of this solution is depressed by [latex]\Delta T_{f}[/latex] = 5.5 – 0.4 = 5.1 °C. The value computed, assuming no ionization of [latex]\ce{HCl}[/latex], is [latex]\Delta T_{f}[/latex] = (1.0 m)(5.14 °C/m) = 5.1 °C. Agreement of these values supports the assumption that [latex]\ce{HCl}[/latex] is not ionized.
  6. Molecular mass = 144 amu
  7. 0.870 °C
  8. S8

11.6 The Solid State of Matter [Go to section 11.6]

  1. At very low temperatures oxygen, O2, freezes and forms a crystalline solid. Which best describes these crystals?
    1. ionic
    2. covalent network
    3. metallic
    4. amorphous
    5. molecular crystals
  2. What types of liquids typically form amorphous solids?
  3. Explain why ice, which is a crystalline solid, has a melting temperature of 0 °C, whereas butter, which is an amorphous solid, softens over a range of temperatures.
  4. As it cools, olive oil slowly solidifies and forms a solid over a range of temperatures. Which best describes the solid?
    1. ionic
    2. covalent network
    3. metallic
    4. amorphous
    5. molecular crystals
  5. Identify the type of crystalline solid (metallic, network covalent, ionic, or molecular) formed by each of the following substances:
    1. [latex]\ce{CaCl2}[/latex]
    2. [latex]\ce{SiC}[/latex]
    3. [latex]\ce{N2}[/latex]
    4. [latex]\ce{Fe}[/latex]
    5. [latex]\ce{C}[/latex] (graphite)
    6. [latex]\ce{CH3CH2CH2CH3}[/latex]
    7. [latex]\ce{HCl}[/latex]
    8. [latex]\ce{NH4NO3}[/latex]
    9. [latex]\ce{K3PO4}[/latex]
  6. Substance B is hard, does not conduct electricity, and melts at 1200 °C. Substance B is likely a(n):
    1. ionic solid
    2. metallic solid
    3. molecular solid
    4. covalent network solid
  7. Classify each substance in the table as either a metallic, ionic, molecular, or covalent network solid:
    Substance Appearance Melting Point Electrical Conductivity Solubility in Water
    X brittle, white 800 °C only if melted/dissolved soluble
    Y shiny, malleable 1100 °C high insoluble
    Z hard, colorless 3550 °C none insoluble
  8. Classify each substance in the table as either a metallic, ionic, molecular, or covalent network solid:
    Substance Appearance Melting Point Electrical Conductivity Solubility in Water
    X lustrous, malleable 1500 °C high insoluble
    Y soft, yellow 113 °C none insoluble
    Z hard, white 800 °C only if melted/dissolved soluble
  9. Substance A is shiny, conducts electricity well, and melts at 975 °C. Substance A is likely a(n):
    1. ionic solid
    2. metallic solid
    3. molecular solid
    4. covalent network solid
  10. Identify the following substances as ionic, metallic, covalent network, or molecular solids:Substance A is malleable, ductile, conducts electricity well, and has a melting point of 1135 °C. Substance B is brittle, does not conduct electricity as a solid but does when molten, and has a melting point of 2072 °C. Substance C is very hard, does not conduct electricity, and has a melting point of 3440 °C. Substance D is soft, does not conduct electricity, and has a melting point of 185 °C.
Show Selected Solutions
  1. The answers are as follows:
    1. molecular crystals
  2. Ice has a crystalline structure stabilized by hydrogen bonding. These intermolecular forces are of comparable strength and thus require the same amount of energy to overcome. As a result, ice melts at a single temperature and not over a range of temperatures. The various, very large molecules that compose butter experience varied van der Waals attractions of various strengths that are overcome at various temperatures, and so the melting process occurs over a wide temperature range.
  3. The answers are as follows:
    1. CaCl2, ionic
    2. SiC, covalent network
    3. N2, molecular
    4. Fe, metallic
    5. C (graphite), covalent network
    6. CH3CH2CH2CH3, molecular
    7. HCl, molecular
    8. NH4NO3, ionic
    9. K3PO4, ionic
  4. X = ionic; Y = metallic; Z = covalent network
  5. (b) metallic solid

11.7 Lattice Structures in Crystalline Solids [Go to section 11.7]

  1. Describe the crystal structure of iron, which crystallizes with two equivalent metal atoms in a cubic unit cell.
  2. Describe the crystal structure of [latex]\ce{Pt}[/latex], which crystallizes with four equivalent metal atoms in a cubic unit cell.
  3. What is the coordination number of a chromium atom in the body-centered cubic structure of chromium?
  4. What is the coordination number of an aluminum atom in the face-centered cubic structure of aluminum?
  5. Cobalt metal crystallizes in a hexagonal closest packed structure. What is the coordination number of a cobalt atom?
  6. Nickel metal crystallizes in a cubic closest packed structure. What is the coordination number of a nickel atom?
  7. Barium crystallizes in a body-centered cubic unit cell with an edge length of 5.025 Å
    1. What is the atomic radius of barium in this structure?
    2. Calculate the density of barium.
  8. Aluminum (atomic radius = 1.43 Å) crystallizes in a cubic closely packed structure. Calculate the edge length of the face-centered cubic unit cell and the density of aluminum.
  9. The density of aluminum is 2.7 g/cm3; that of silicon is 2.3 g/cm3. Explain why [latex]\ce{Si}[/latex] has the lower density even though it has heavier atoms.
  10. The free space in a metal may be found by subtracting the volume of the atoms in a unit cell from the volume of the cell. Calculate the percentage of free space in each of the three cubic lattices if all atoms in each are of equal size and touch their nearest neighbors. Which of these structures represents the most efficient packing? That is, which packs with the least amount of unused space?
  11. Cadmium sulfide, sometimes used as a yellow pigment by artists, crystallizes with cadmium, occupying one-half of the tetrahedral holes in a closest packed array of sulfide ions. What is the formula of cadmium sulfide? Explain your answer.
  12. A compound of cadmium, tin, and phosphorus is used in the fabrication of some semiconductors. It crystallizes with cadmium occupying one-fourth of the tetrahedral holes and tin occupying one-fourth of the tetrahedral holes in a closest packed array of phosphide ions. What is the formula of the compound? Explain your answer.
  13. What is the formula of the magnetic oxide of cobalt, used in recording tapes, that crystallizes with cobalt atoms occupying one-eighth of the tetrahedral holes and one-half of the octahedral holes in a closely packed array of oxide ions?
  14. A compound containing zinc, aluminum, and sulfur crystallizes with a closest-packed array of sulfide ions. Zinc ions are found in one-eighth of the tetrahedral holes and aluminum ions in one-half of the octahedral holes. What is the empirical formula of the compound?
  15. A compound of thallium and iodine crystallizes in a simple cubic array of iodide ions with thallium ions in all of the cubic holes. What is the formula of this iodide? Explain your answer.
  16. Which of the following elements reacts with sulfur to form a solid in which the sulfur atoms form a closest-packed array with all of the octahedral holes occupied: [latex]\ce{Li}[/latex], [latex]\ce{Na}[/latex], [latex]\ce{Be}[/latex], [latex]\ce{Ca}[/latex], or [latex]\ce{Al}[/latex]?
  17. What is the percent by mass of titanium in rutile, a mineral that contains titanium and oxygen, if structure can be described as a closest packed array of oxide ions with titanium ions in one-half of the octahedral holes? What is the oxidation number of titanium?
  18. Explain why the chemically similar alkali metal chlorides [latex]\ce{NaCl}[/latex] and [latex]\ce{CsCl}[/latex] have different structures, whereas the chemically different [latex]\ce{NaCl}[/latex] and [latex]\ce{MnS}[/latex] have the same structure.
  19. As minerals were formed from the molten magma, different ions occupied the same cites in the crystals. Lithium often occurs along with magnesium in minerals despite the difference in the charge on their ions. Suggest an explanation.
  20. Rubidium iodide crystallizes with a cubic unit cell that contains iodide ions at the corners and a rubidium ion in the center. What is the formula of the compound?
  21. One of the various manganese oxides crystallizes with a cubic unit cell that contains manganese ions at the corners and in the center. Oxide ions are located at the center of each edge of the unit cell. What is the formula of the compound?
  22. [latex]\ce{NaH}[/latex] crystallizes with the same crystal structure as [latex]\ce{NaCl}[/latex]. The edge length of the cubic unit cell of [latex]\ce{NaH}[/latex] is 4.880 Å.
    1. Calculate the ionic radius of [latex]\ce{H–}[/latex]. (The ionic radius of Li+ is 0.0.95 Å.)
    2. Calculate the density of [latex]\ce{NaH}[/latex].
  23. Thallium(I) iodide crystallizes with the same structure as [latex]\ce{CsCl}[/latex]. The edge length of the unit cell of [latex]\ce{TlI}[/latex] is 4.20 Å. Calculate the ionic radius of [latex]\ce{TI+}[/latex]. (The ionic radius of [latex]\ce{I–}[/latex] is 2.16 Å.)
  24. A cubic unit cell contains manganese ions at the corners and fluoride ions at the center of each edge.
    1. What is the empirical formula of this compound? Explain your answer.
    2. What is the coordination number of the [latex]\ce{Mn3+}[/latex] ion?
    3. Calculate the edge length of the unit cell if the radius of a [latex]\ce{Mn3+}[/latex] ion is 0.65 A.
    4. Calculate the density of the compound.
Show Selected Solutions
  1. The structure of this low-temperature form of iron (below 910 °C) is body-centered cubic. There is one-eighth atom at each of the eight corners of the cube and one atom in the center of the cube.
  2. Coordination number refers to the number of nearest neighbors. A chromium atom lies at the center of a body-centered cube and has eight nearest neighbors (at the corners of the cube): four in one plane above and four in one plane below. The coordination number, therefore, is eight.
  3. Hexagonal closest packing occurs in such a way that each atom touches 12 nearest neighbors: six in its own layer and three in each adjacent layer. The coordination number is therefore 12.
  4. The answers are as follows:
    1. 2.176 Å
    2. 3.595 g/cm3
  5. The crystal structure of [latex]\ce{Si}[/latex] shows that it is less tightly packed (coordination number 4) in the solid than Al (coordination number 12).
  6. In a closest-packed array, two tetrahedral holes exist for each anion. If only half the tetrahedral holes are occupied, the numbers of anions and cations are equal. The formula for cadmium sulfide is [latex]\ce{CdS}[/latex].
  7. In a closest-packed array of oxide ions, one octahedral hole and two tetrahedral holes exist for each oxide ion. If one-half of the octahedral holes are filled, there is one [latex]\ce{Co}[/latex] ion for every two oxide ions. If one-eighth of the tetrahedral holes are filled, there is one [latex]\ce{Co}[/latex] ion for each four oxide ions. For every four oxide ions, there are two [latex]\ce{Co}[/latex] ions in octahedral holes and one [latex]\ce{Co}[/latex] in a tetrahedral hole; thus the formula is [latex]\ce{Co3O4}[/latex].
  8. In a simple cubic array, only one cubic hole can be occupied be a cation for each anion in the array. The ratio of thallium to iodide must be 1:1; therefore, the formula for thallium is [latex]\ce{TlI}[/latex].
  9. 59.95% ; +4
  10. Both ions are close in size: [latex]\ce{Mg}[/latex], 0.65; [latex]\ce{Li}[/latex], 0.60. This similarity allows the two to interchange rather easily. The difference in charge is generally compensated by the switch of [latex]\ce{Si4+}[/latex] for [latex]\ce{Al3+}[/latex].
  11. [latex]\ce{Mn2O3}[/latex]
  12. 1.48 Å

11.8 X-Ray Crystallography [Go to section 11.8]

  1. A metal with spacing between planes equal to 0.4164 nm diffracts X-rays with a wavelength of 0.2879 nm. What is the diffraction angle for the first order diffraction peak?
  2. A diffractometer using X-rays with a wavelength of 0.2287 nm produced first order diffraction peak for a crystal angle [latex]\theta[/latex] = 16.21°. Determine the spacing between the diffracting planes in this crystal.
  3. When an electron in an excited molybdenum atom falls from the L to the K shell, an X-ray is emitted. These X-rays are diffracted at an angle of 7.75° by planes with a separation of 2.64 Å. What is the difference in energy between the K shell and the L shell in molybdenum assuming a first order diffraction?
  4. Gold crystallizes in a face-centered cubic unit cell. The second-order reflection (n = 2) of X-rays for the planes that make up the tops and bottoms of the unit cells is at [latex]\theta[/latex] = 22.20°. The wavelength of the X-rays is 1.54 Å. What is the density of metallic gold?
Show Selected Solutions
  1. 20.2°
  2. 2.79 × 10-15 J = 1.74 × 104 eV

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