Chapter 13 & 14 Study Guide: Solids, Solutions, and Colligative Properties

Chapter 13: Crystalline Solids and Unit Cell Calculations

Unit Cell Calculations

Understanding the structure and properties of crystalline solids requires calculations involving unit cells, which are the smallest repeating units in a crystal lattice.

• Mass of One Particle in a Unit Cell: To find the mass of a single particle (atom, ion, or molecule), divide the molar mass by Avogadro’s number ($6.022 \times 10^{23}$).

• Formula: $\text{Mass of one particle} = \frac{\text{Molar mass}}{6.022 \times 10^{23}}$

• Mass of a Unit Cell: Multiply the mass of one particle by the number of particles in the unit cell.

  • Body-centered cubic (BCC): 2 particles per unit cell

  • Face-centered cubic (FCC): 4 particles per unit cell

• Formula: $\text{Mass of unit cell} = \text{Mass of one particle} \times \text{Number of particles per unit cell}$

• Calculating Unit Cell Length: The length ($l$) of a unit cell can be determined using geometric relationships based on the type of unit cell (BCC or FCC).

• Density Calculation: Density ($D$) is calculated as mass divided by volume.

  • Formula: $D = \frac{m}{v}$

Classification of Crystalline Solids

Crystalline solids are classified based on the nature of their constituent particles and the forces holding them together.

• Molecular Solids: Composed of molecules held together by intermolecular forces (e.g., H2O, CO2).

• Ionic Solids: Composed of ions held together by electrostatic forces (e.g., NaCl, MgO).

• Atomic Solids: Composed of atoms; can be metallic (e.g., Mg), covalent network (e.g., diamond), or noble gas solids.

Properties of Crystalline Solids

• Molecular Solids: Low melting points, poor conductors, soft.

• Ionic Solids: High melting points, brittle, conduct electricity when molten or dissolved.

• Atomic Solids: Properties vary; metallic solids are malleable and conductive, covalent network solids are hard and have high melting points.

Addition Polymerization

Addition polymerization is a process where monomers join together to form a polymer without the loss of any small molecule.

• Monomer: A small molecule that can join with others to form a polymer (e.g., ethylene).

• Polymer: A large molecule made from repeating monomer units (e.g., polyethylene).

• Example: Ethylene ($\text{CH}_2=\text{CH}_2$) polymerizes to form polyethylene.

Chapter 14: Solutions and Colligative Properties

Solution Calculations

Solutions are homogeneous mixtures, and their properties depend on the concentration and nature of solute and solvent.

• Heats of Solution, Hydration, and Lattice Energy: The energetics of dissolving a solute involve breaking lattice energy and forming hydration energy.

  • $\Delta H_{\text{solution}} = \Delta H_{\text{lattice}} + \Delta H_{\text{hydration}}$

• Solubility and Partial Pressure: For gases, solubility increases with partial pressure (Henry’s Law).

  • $C = k_P \cdot P$

  • Where $C$ is concentration, $k_P$ is Henry’s constant, $P$ is partial pressure.

• Number of Moles: $\text{Moles} = \frac{\text{Mass}}{\text{Molar mass}}$

• Moles of Solute in Solution: Calculated using molarity or other concentration units.

• Molarity ($M$): $M = \frac{\text{Moles of solute}}{\text{Liters of solution}}$

• Molality ($m$): $m = \frac{\text{Moles of solute}}{\text{Kilograms of solvent}}$

• Mole Fraction ($X$): $X = \frac{\text{Moles of component}}{\text{Total moles in solution}}$

• Percent by Mass: $\text{Percent by mass} = \frac{\text{Mass of solute}}{\text{Total mass of solution}} \times 100\%$

Colligative Properties

Colligative properties depend on the number of solute particles, not their identity.

• Vapor Pressure Lowering: Addition of solute lowers the vapor pressure of the solvent.

  • Raoult’s Law: $P_{\text{solution}} = X_{\text{solvent}} \cdot P^0_{\text{solvent}}$

• Freezing Point Depression: Solute lowers the freezing point.

  • $\Delta T_f = K_f \cdot m$

• Boiling Point Elevation: Solute raises the boiling point.

  • $\Delta T_b = K_b \cdot m$

• Osmotic Pressure: Pressure required to prevent osmosis.

  • $\Pi = MRT$

  • Where $\Pi$ is osmotic pressure, $M$ is molarity, $R$ is gas constant, $T$ is temperature in Kelvin.

Energetics and Factors Affecting Solubility

The formation of a solution involves energy changes and is influenced by temperature and intermolecular forces.

• Energetics of Solution Formation: The process involves breaking solute and solvent interactions and forming new interactions.

• Effect of Temperature:

  • Solubility of solids generally increases with temperature.

  • Solubility of gases decreases with temperature.

• Factors Affecting Solubility: Nature of solute and solvent, temperature, and pressure (for gases).

• Intermolecular Forces: "Like dissolves like"; polar solutes dissolve in polar solvents, nonpolar in nonpolar.

Identifying Solubility and Colligative Properties

Determining whether a solute will dissolve in a solvent depends on the types of intermolecular forces present.

• Colligative Properties: Include vapor pressure lowering, freezing point depression, boiling point elevation, and osmotic pressure.

• Example: Adding salt to water lowers its freezing point and raises its boiling point.

Table: Classification and Properties of Crystalline Solids

Type	Constituent Particles	Forces	Properties	Examples
Molecular	Molecules	Intermolecular forces	Low melting point, soft, poor conductor	H2O, CO2
Ionic	Ions	Electrostatic forces	High melting point, brittle, conducts when molten	NaCl, MgO
Atomic	Atoms	Metallic, covalent, or dispersion	Varies: metallic (conductive), covalent (hard), noble gas (soft)	Mg, Diamond, Ar

Table: Colligative Properties and Their Formulas

Property	Formula	Description
Vapor Pressure Lowering	$P_{\text{solution}} = X_{\text{solvent}} \cdot P^0_{\text{solvent}}$	Decrease in vapor pressure due to solute
Freezing Point Depression	$\Delta T_f = K_f \cdot m$	Lowering of freezing point
Boiling Point Elevation	$\Delta T_b = K_b \cdot m$	Increase in boiling point
Osmotic Pressure	$\Pi = MRT$	Pressure to stop osmosis