Chapter 12: Solutions 279
chapter 12
Solutions
Chapter Terms and Definitions
Numbers in parentheses after definitions give the text sections in which the terms are explained. Starred terms are italicized in the text. Where a term does not fall directly under a text section heading, additional information is given for you to locate it.
solution* homogeneous mixture of two or more substances, consisting of ions or molecules (12.1, introductory section)
solute gas or solid dissolved in a liquid or the solution component in smaller amount (12.1)
solvent liquid that dissolves a gas or solid or the solution component in greater amount (12.1)
miscible fluids fluids that mix with or dissolve in each other in all proportions (12.1)
immiscible* said of two fluids that do not mix but form two layers (12.1)
dynamic equilibrium* equilibrium in which the forward and reverse processes, such as the dissolving and depositing of crystals, are always occurring and at the same rate (12.2)
saturated solution solution that is in equilibrium with respect to a given dissolved substance (12.2)
solubility amount that dissolves in a given quantity of liquid at a given temperature to give a saturated solution (12.2)
unsaturated solution solution not in equilibrium with respect to a given dissolved substance and in which more of the substance can dissolve (12.2)
supersaturated solution solution that contains more dissolved substance than a saturated solution (12.2)
entropy* measure of disorder (12.2, marginal note)
ion–dipole force* attraction between an ion and a polar molecule (12.2)
hydration (of ions) attraction of ions for water molecules (12.2)
lattice energy* energy holding ions together in a crystal lattice (12.2)
heat of solution* heat that is released or absorbed when a substance dissolves in a solvent (12.3)
Le Châtelier’s principle when a system in equilibrium is altered by a change of temperature, pressure, or concentration variable, the system shifts in equilibrium composition in a way that tends to counteract this change of variable (12.3)
Henry’s law the solubility of a gas is directly proportional to the partial pressure of the gas above the solution; S = kHP (12.3)
colligative properties properties of solutions that depend on the concentration of solute particles (molecules or ions) in solution but not on the chemical identity of the solute (12.4, introductory section)
concentration* amount of solute dissolved in a given quantity of solvent or solution (12.4)
molarity (M)* number of moles of solute per liter of solution (12.4)
mass percentage of solute percentage by mass of solute contained in a solution (12.4)
molality (m) number of moles of solute per kilogram of solvent (12.4)
mole fraction (X) number of moles of a substance divided by the total number of moles of solution (12.4)
mole percent* mole fraction times 100 (12.4)
vapor-pressure lowering colligative property of a solution; equal to the vapor pressure of the pure solvent minus the vapor pressure of the solution (12.5)
Raoult’s law the partial pressure of solvent PA over a solution is equal to the vapor pressure of the pure solventmultiplied by the mole fraction of solvent in the solution: PA = XA (12.5)
ideal solution* solution in which both substances follow Raoult’s law for all values of mole fractions (12.5)
normal (boiling point of a liquid)* temperature at which the vapor pressure of the liquid equals 1 atm (12.6)
boiling-point elevation (DTb) colligative property of a solution; equal to the boiling point of the solution minus the boiling point of the pure solvent (12.6)
boiling-point-elevation constant (Kb)* proportionality constant between the boiling-point elevation and the molality of a solution (12.6)
freezing-point depression (DTf) colligative property of a solution; equal to the freezing point of the pure solvent minus the freezing point of the solution (12.6)
freezing-point-depression constant (Kf)* proportionality constant between the freezing-point lowering and the molality of a solution (12.6)
semipermeable* describes a membrane that allows solvent molecules but not solute molecules to pass through (12.7)
osmosis phenomenon of solvent flow through a semipermeable membrane from lower solute concentration to higher concentration to equalize concentrations on both sides of the membrane (12.7)
osmotic pressure colligative property of a solution; equal to the pressure that, when applied to the solution, just stops osmosis (12.7)
reverse osmosis* reversing the osmosis process by applying greater pressure to the more concentrated solution so that solvent flows from the concentrated solution through a membrane to the more dilute solution (12.7)
desalinate* to remove salts from seawater to make it usable for drinking or industrial uses (12.7)
activities* effective concentrations of ions in solution (12.8)
Debye–Hückel theory* describes the distribution of ions in a salt solution and enables us to calculate ionic activities (12.8)
colloid dispersion of particles of one substance (the dispersed phase) throughout another substance or solution (the continuous phase) (12.9)
Tyndall effect scattering of light by colloidal-sized particles (12.9)
aerosols colloidal dispersions of liquid droplets or solid particles throughout a gas (12.9)
emulsion colloidal dispersion of liquid droplets throughout another liquid (12.9)
sol colloidal dispersion of solid particles in a liquid (12.9)
hydrophilic colloid colloid in which there is a strong attraction between the dispersed phase and the continuous phase (water) (12.9)
hydrophobic colloid colloid in which there is a lack of attraction between the dispersed phase and the continuous phase (water) (12.9)
nuclei (in crystallization)* centers about which crystallization occur (12.9)
coagulation process by which the dispersed phase of a colloid is made to aggregate and thereby separate from the continuous phase (12.9)
micelle colloidal-sized particle formed in water by the association of molecules or ions that each have a hydrophobic and a hydrophilic end (12.9)
association colloid colloid in which the dispersed phase consists of micelles (12.9)
Chapter Diagnostic Test
1. When Solid A dissolves in water, there occurs a corresponding decrease in temperature. Therefore, heating a mixture of Solid A and water should ______the solubility of A in water. (decrease/increase)
2. The graph in Figure A plots solubility as a function of temperature.
Figure A
Which of the following statements concerning information available from the solubility curves in Figure A is(are) incorrect?
a. At all indicated temperatures, KBr is more soluble in water than is KCl.
b. The solubility of KBr can be increased by warming the solution.
c. At 35°C, the order of solubilities is KBr > KNO3 > KCl > Ce2(SO4)3.
d. The solubility of Ce2(SO4)3 is an endothermic process.
e. The solubility of KNO3 is more affected by temperature than that of KCl.
3. The energy of hydration increases with decreasing cation size, when cationic charge is constant, because
a. a larger cation can coordinate more water molecules about it.
b. cationic charge has no effect on the coordination of water molecules.
c. electrostatic attractive forces are inversely proportional to cation size.
d. the cation size has no effect on hydration when the cationic charge changes.
e. cations are attracted to water molecules and anions are repelled by water molecules.
4. For the following chemical reaction at equilibrium,
H3PO4 + KOH KH2PO4 + H2O; ΔH is negative
the addition of water to the reaction mixture will
a. produce a larger ΔH per mole of H3PO4.
b. increase the amount of KH2PO4 when the new equilibrium is established.
c. have no effect.
d. increase the amount of H3PO4 and KOH when equilibrium is reestablished.
e. have no effect other than giving a more dilute solution of KH2PO4.
5. Which of the following carbonates would you expect to be insoluble in water?
a. Na2CO3
b. H2CO3
c. (NH4)2CO3
d. Rb2CO3
e. BaCO3
6. A solution of 132.4 g Cu(NO3)2 per liter has a density of 1.116 g/mL. The mass percent of Cu(NO3)2 in the solution is
a. 11.86.
b. 8.40.
c. 9.00.
d. 22.4.
e. Insufficient data are given to calculate mass percent.
7. Calculate the mole fraction of each component in a solution that contains 46.5 g of ethylene glycol, CH2OHCH2OH, and 236 g of methanol, CH3OH.
8. Calculate the molecular formula of a species that has the empirical formula CH3O if, when 25.1 g of the compound was added to 0.150 kg of water, the solution froze at -5.0°C. Kf = 1.86°C/m.
9. Which of the following should have the highest boiling point?
a. Pure water
b. A 0.2 m Ca(NO3)2 aqueous solution
c. A 0.2 m (CH3)2CO aqueous solution
d. A 0.1 m KBr aqueous solution
e. A 0.1 m Ba(NO3)2 aqueous solution
10. The graph in Figure B shows the effect of the addition of a nonvolatile solute on the vapor pressure of water.
Figure B
Which of the following statements is a logical deduction from this graph?
a. If a nonvolatile solute is added to water, the boiling point of the solution will be Tb.
b. The addition of a volatile solute will change the boiling point of the water.
c. Atmospheric pressure will affect the composition of the aqueous solution.
d. If a nonvolatile solute is added to water, the freezing point of the solution will be lower than that of water.
e. If a nonvolatile solute is added to water, the boiling and melting points of the solution will be greater than those of the water by DTb and DTf , respectively.
11. A liter of water at 25°C and 1.0 atm dissolves 1.45 g of carbon dioxide. If the partial pressure of CO2 is increased to 15 atm, what is its solubility in water?
12. An 8.0 M solution of KCl in water has a density of 1.218 g/mL. The density of pure water is 1.000 g/mL. Calculate the mole fraction of KCl in the solution.
13. Calculate the boiling point of a glucose solution consisting of 9.0 g of glucose dissolved in 100.0 g of water (glucose = C6H12O6, 180.1 g/mol, Kb for water is 0.512°C/m).
14. A solution consists of 0.100 mol of naphthalene, C10H8, and 9.90 mol of benzene, C6H6, at 25°C. Calculate the vapor pressure and vapor-pressure lowering of the solution. (The vapor pressure of pure benzene at 25°C is 2.70 ´ 102 mmHg. Assume that naphthalene is a nonvolatile, nonelectrolytic solute.)
15. Calculate the osmotic pressure of a solution that consists of 4.68 g of hemoglobin (molar mass = 6.83 ´ 104 g/mol) in 125 mL of water (molar mass = 18.0 g/mol) at 3.00 ´ 102 K.
16. Classify each of the following colloids as an aerosol, foam, emulsion, sol, or gel.
a. Cigarette smoke
b. Strawberry-flavored jello
c. Muddy water
d. Milk
e. Carbon ink
f. Pearl
g. Raised dough
Answers to Chapter Diagnostic Test
If you missed an answer, study the text section and problem-solving skill (PS Sk.) given in parentheses after the answer.
1. Increase (12.2, 12.3)
2. d (12.2, 12.3)
3. c (12.2)
4. d (12.3)
5. e (12.2)
6. a (12.3)
7. Xglycol = 9.23 ´ 10-2; = 9.08 ´ 10-1 (12.4, PS Sk. 2)
8. Molecular formula: C2H6O2 (12.6, PS Sk. 5, 6)
9. b (12.6, 12.8)
10. d (12.5, 12.6)
11. 22 g CO2/L H2O (12.3, PS Sk. 1)
12. Mole fraction KCl = 0.19 (12.4, PS Sk. 3)
13. b.p. = 100.26°C (12.4, 12.6, PS Sk. 2, 5)
14. Vapor pressure = 267 mmHg; vapor-pressure lowering = 2.70 mmHg (12.5, PS Sk. 4)
15. 0.0135 atm (12.7, PS Sk. 7)
16.
a. Aerosol
b. Gel
c. Sol
d. Emulsion
e. Sol
f. Gel
g. Foam (12.9)
Summary of Chapter Topics
12.1 Types of Solutions
Learning Objectives
· Define solute and solvent.
· Define miscible fluid.
· Provide examples of gaseous solutions, liquid solutions, and solid solutions.
Whether we call a mixture of one or more substances in another a suspension, a colloid, or a solution depends on the size of the particles, particularly of those we are adding. To illustrate, assume that we have water as the solvent. If the particles we add are large and heavy, they will sink to the bottom. If we stir the mixture vigorously, we will have a suspension, wherein the added particles are momentarily suspended in the continuous phase, the water. If the particles are small and light, they may stay suspended; light passing through this suspension, or colloid, will be scattered. If the particles are the size of molecules and ions, they are so small that we cannot discern them unless they color the solution, as does the Cu2+ ion in CuSO4.
The definitions of the key terms in this chapter are of particular importance. Memorize them as soon as possible. Your ability to do the exercises and problems will depend on knowing them.
Exercise 12.1
Give an example of a solid solution prepared from a liquid and a solid.
Solution: The dental-filling alloy mentioned in the text has liquid mercury in silver (and other metals), which gives a solid solution.
12.2 Solubility and the Solution Process
Learning Objectives
· List the conditions that must be present to have a saturated solution, to have an unsaturated solution, and to have a supersaturated solution.
· Describe the factors that make one substance soluble in another.
· Determine when a molecular solution will form when substances are mixed.
· Learn what conditions must be met in order to create an ionic solution.
The solubility of one substance in another at a given temperature and pressure is a function of two factors: the attraction the substance has for its own species and the attraction the substance has for the other species. When we dissolve a solid in water, we can measure these attractions in terms of lattice energy and energy of hydration, respectively.
Exercise 12.2
Which of the following compounds is likely to be more soluble in water: C4H9OH or C4H9SH? Explain.
Known: The molecules differ only in S and O; oxygen can hydrogen bond, whereas sulfur cannot.
Solution: C4H9OH is the more soluble because it can hydrogen bond with water.
Exercise 12.3
Which ion has the larger hydration energy, Na+ or K+?
Known: Hydration energy is inversely proportional to ionic radius and proportional to charge; K+ has the same charge as Na+ and is below it on the periodic table, so it is larger.