Chapter 11: Solutions: Properties and Behavior

Learning Objectives 11.1: Interactions between Ions • Be able to estimate changes in lattice energy from the potential energy form of Coulomb’s Law, Q Q Cation Anion , in which is lattice energy, is a proportionality constant, is the charge on E = k E k QCation r the cation, Q is the charge on the anion, and r is the distance between the centers of the ions. Anion

11.2: Energy Changes during Formation and Dissolution of Ionic Compounds • Understand the concept of lattice energy and how it is a quantitative measure of stability for any ionic solid. As lattice energy increases, the stability of the ionic solid increases. • Be able to estimate changes in lattice energy from the potential energy form of Coulomb’s Law, Q Q Cation Anion , in which is lattice energy, is a proportionality constant, is the charge on E = k E k QCation r the cation, Q is the charge on the anion, and r is the distance between the centers of the ions. Anion • Be able to determine lattice energies using a Born-Haber cycle, which is a Hess’s Law process using ionization energies, electron affinities, and enthalpies for other atomic and molecular properties. • Be able to describe a molecular view of the solution process using Hess’s Law:

1. Solvent → Solvent Particles where ∆Hsolvent separation is endothermic.

2. Solute → Solute Particles where ∆Hsolute separation is endothermic.

3. Solvent Particles + Solute Particles → Solution where ∆Hsolvation can be endo- or exothermic.

4. ∆Hsolution = ∆Hsolvent separation + ∆Hsolute separation + ∆Hsolvation This is a Hess’s Law thinking process, and ∆Hsolvation is called the ∆Hhydration when the solvent is water.

11.3: Vapor Pressure of Solutions • Be able to perform calculations with Raoult’s Law: � = �� which states that the vapor pressure of a solvent over a solution, �, is given by the mole fraction of the solvent, �, multiplied by the vapor pressure of the pure solvent, � . • Recall that if both components of a solution are volatile (ex. two solvents are present), then: � = � + � = � � + � � • If the gases behave ideally, Raoult’s Law is strictly followed, and we get a diagram like Fig. 12.7: • Case 1: If the respective solvent molecules are more attracted to molecules of the same solvent, there will be positive deviations from Raoult’s Law. (See Fig. 12.8a) • Case 2: If the respective solvent molecules are more attracted to molecules of the other solvent, there will be negative deviations from Raoult’s Law. (See Fig. 12.8b)

11.4: Mixtures of Volatile Solutes • Be able to recognize all types of solutions. • Be able to distinguish between solute, solvent, solution, and solubility. • Be able to use both words and graphs to compare and contrast saturated, unsaturated, and supersaturated solutions. • Be able to draw and explain heating curves. Be able to perform related calculations starting at any point on the curve and ending at any other point on the curve. Chapter 11: Solutions: Properties and Behavior, Page 2

11.5: Colligative Properties of Solutions • Be able to compare, contrast, and perform calculations for percent by mass, mole fraction, molarity, and molality concentrations.

Types of Concentration Units Concentration Unit Calculation Comment(s)

Percent by Mass: �� Independent of temperature % �� = (100) ��

Mole Fraction: �� Used to calculate gas pressures �� = � = ��

Molarity (M): �� Since volume is temperature �� = �� dependent, then molarity is temperature dependent

Molality (m): �� Independent of temperature �� = ��

• Be able to compare and contrast the four colligative properties vapor-pressure lowering, boiling-point elevation, freezing-point depression, and osmotic pressure. Recall that colligative properties depend only on the number of solute particles in solution and not on the nature of the solute particles. A table of colligative properties for nonelectrolyte solutions appears below. • Be able to compare and contrast volatile and nonvolatile solutes. As you will recall, nonvolatile solutes have no measurable vapor pressure and they are generally used when discussing colligative properties.

Colligative Properties of Nonelectrolyte Solutes Colligative Property Equation Comments

Vapor-Pressure Lowering: ∆� = �� ∆� is the vapor pressure (V.P.) lowering, � is the mole fraction (This equation is derived from of the solute, � is the V.P. of the Raoult’s Law, � = �� ) pure solvent, � is the V.P. of the solvent over the solution, and � is the mole fraction of the solvent.

Boiling-Point Elevation: ∆� = �� ∆� is the boiling point (b.p.) o elevation in C, � is the b.p. elevation constant in oC/m from Table 12.2, and � is the concentration in molality.

Freezing-Point Depression: ∆� = �� ∆� is the freezing point (f.p.) o depression in C, � is the f.p. depression constant in oC/m from Chapter 11: Solutions: Properties and Behavior, Page 3

Table 12.2, and � is the concentration in molality.

Osmotic Pressure: � = �� is osmotic pressure in atm, � is the concentration in molarity, � = 0.0821 L-atm/mole-K, and � is the Kelvin temperature.

• Recall that osmosis is the selective passage of solvent molecules through a semipermeable membrane from a more dilute solution (hypotonic solution) to a more concentrated one (hypertonic solution). The driving force for this process is nature attempting to equalize the concentrations (make isotonic solutions) on both sides of the semipermeable membrane. Osmotic pressure is the pressure required to stop osmosis. • Be able to perform colligative property calculations for both electrolyte and nonelectrolyte solutions. • Recall that colligative properties depend on the number of solute particles. Nonelectrolytes will not dissociate, but electrolytes will, which will increase the number of solute particles. This means that the van’t Hoff factor must be included in calculations. • Van’t Hoff factor: � =

Colligative Properties of Electrolyte Solutes Colligative Property Equation Comments

Boiling-Point Elevation: ∆� = �� ∆� is the boiling point (b.p.) elevation in oC, � is the van’t Hoff factor, � is the b.p. elevation constant in oC/m from Table 12.2, and � is the concentration in molality.

Freezing-Point Depression: ∆� = �� ∆� is the freezing point (f.p.) depression in oC, � is the van’t

Hoff factor, � is the f.p. depression constant in oC/m from Table 12.2, and � is the concentration in molality.

Osmotic Pressure: � = �� is osmotic pressure in atm, � is the van’t Hoff factor, � is the concentration in molarity, � = 0.0821 L-atm/mole-K, and � is the Kelvin temperature.

11.6: Measuring the Molar Mass of a Solute by Using Colligative Properties • Be able to use colligative properties to calculate molar masses. Recall that freezing-point depression and osmotic pressure are commonly used for this purpose because they give the largest changes.