SECTION 13.1 Solutions form when one substance disperses uniformly throughout another. The attractive interaction of solvent molecules with solute is called solvation. When the solvent is water, the interaction is called hydration. The dissolution of ionic substances in water is promoted by hydration of the separated ions by the polar water molecules. The overall enthalpy change upon solution formation may be either positive or negative. Solution formation is favored both by a positive entropy change, corresponding to an increased dispersal of the components of the solution, and by a negative enthalpy change, indicating an exothermic process.

SECTION 13.2 The equilibrium between a saturated solution and undissolved solute is dynamic; the process of solution and the reverse process, crystallization, occur simultaneously. In a solution in equilibrium with undissolved solute, the two processes occur at equal rates, giving asaturated solution. If there is less solute present than is needed to saturate the solution, the solution is unsaturated. When solute concentration is greater than the equilibrium concentration value, the solution is supersaturated. This is an unstable condition, and separation of some solute from the solution will occur if the process is initiated with a solute seed crystal. The amount of solute needed to form a saturated solution at any particular temperature is the solubility of that solute at that temperature.

SECTION 13.3 The solubility of one substance in another depends on the tendency of systems to become more random, by becoming more dispersed in space, and on the relative intermolecular solute–solute and solvent–solvent energies compared with solute–solvent interactions. Polar and ionic solutes tend to dissolve in polar solvents, and nonpolar solutes tend to dissolve in nonpolar solvents (“like dissolves like”). Liquids that mix in all proportions are miscible; those that do not dissolve significantly in one another are immiscible. Hydrogen-bonding interactions between solute and solvent often play an important role in determining solubility; for example, ethanol and water, whose molecules form hydrogen bonds with each other, are miscible. The solubilities of gases in a liquid are generally proportional to the pressure of the gas over the solution, as expressed by Henry's law: Sg = kPg. The solubilities of most solid solutes in water increase as the temperature of the solution increases. In contrast, the solubilities of gases in water generally decrease with increasing temperature.

SECTION 13.4 Concentrations of solutions can be expressed quantitatively by several different measures, including mass percentage [(mass solute/mass solution) × 102], parts per million (ppm), parts per billion (ppb), and mole fraction. Molarity, M, is defined as moles of solute per liter of solution; molality, m, is defined as moles of solute per kg of solvent. Molarity can be converted to these other concentration units if the density of the solution is known.

SECTION 13.5 A physical property of a solution that depends on the concentration of solute particles present, regardless of the nature of the solute, is a colligative property. Colligative properties include vapor-pressure lowering, freezing-point lowering, boiling-point elevation, and osmotic pressure. Raoult's law expresses the lowering of vapor pressure. An ideal solution obeys Raoult's law. Differences in solvent–solute as compared with solvent–solvent and solute–solute intermolecular forces cause many solutions to depart from ideal behavior.

A solution containing a nonvolatile solute possesses a higher boiling point than the pure solvent. The molal boiling-point-elevation constant, Kb, represents the increase in boiling point for a 1 m solution of solute particles as compared with the pure solvent. Similarly, the molal freezing-point-depression constant, Kf, measures the lowering of the freezing point of a solution for a 1 m solution of solute particles. The temperature changes are given by the equations ΔTb = Kbm and ΔTf = Kfm. When NaCl dissolves in water, two moles of solute particles are formed for each mole of dissolved salt. The boiling point or freezing point is thus elevated or depressed, respectively, approximately twice as much as that of a nonelectrolyte solution of the same concentration. Similar considerations apply to other strong electrolytes.

Osmosis is the movement of solvent molecules through a semipermeable membrane from a less concentrated to a more concentrated solution. This net movement of solvent generates an osmotic pressure, Π, which can be measured in units of gas pressure, such as atm. The osmotic pressure of a solution is proportional to the solution molarity: Π = MRT. Osmosis is a very important process in living systems, in which cell walls act as semipermeable membranes, permitting the passage of water but restricting the passage of ionic and macromolecular components.

SECTION 13.6 Particles that are large on the molecular scale but still small enough to remain suspended indefinitely in a solvent system form colloids, or colloidal dispersions. Colloids, which are intermediate between solutions and heterogeneous mixtures, have many practical applications. One useful physical property of colloids, the scattering of visible light, is referred to as the Tyndall effect. Aqueous colloids are classified as hydrophilic or hydrophobic. Hydrophilic colloids are common in living organisms, in which large molecular aggregates (enzymes, antibodies) remain suspended because they have many polar, or charged, atomic groups on their surfaces that interact with water. Hydrophobic colloids, such as small droplets of oil, may remain in suspension through adsorption of charged particles on their surfaces.


• Describe how enthalpy and entropy changes affect solution formation. (Section 13.1)

• Describe the relationship between intermolecular forces and solubility, including use of the “like dissolves like” rule. (Sections 13.1 and 13.3)

• Describe the role of equilibrium in the solution process and its relationship to the solubility of a solute. (Section 13.2)

• Describe the effect of temperature on the solubility of solids and gases. (Section 13.3)

• Describe the relationship between the partial pressure of a gas and its solubility. (Section 13.3)

• Calculate the concentration of a solution in terms of molarity, molality, mole fraction, percent composition, and parts per million and be able to interconvert between them. (Section 13.4)

• Describe what a colligative property is and explain the difference between the effects of nonelectrolytes and electrolytes on colligative properties. (Section 13.5)

• Calculate the vapor pressure of a solvent over a solution. (Section 13.5)

• Calculate the boiling-point elevation and freezing-point depression of a solution. (Section 13.5)

• Calculate the osmotic pressure of a solution. Section 13.5)

• Explain the difference between a solution and a colloid. (Section 13.6)


Henry's law, relating gas solubility to partial pressure

Defining concentration in terms of mass percent

Defining concentration in terms of parts per million (ppm)

Defining concentration in terms of mole fraction

Defining concentration in terms of molarity

Defining concentration in terms of molality

Raoult's law, calculating vapor pressure of solvent above a solution

Calculating the boiling-point elevation of a solution

Calculating the freezing-point depression of a solution

Calculating the osmotic pressure of a solution