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: $\text{Mass of one particle} = \frac{\text{Molar mass (g/mol)}}{6.022 \times 10^{23}}$

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

• Density Calculation: Density is mass divided by volume.

  • Formula: $D = \frac{m}{v}$

• Length of Unit Cell: The length ($l$) of a unit cell can be calculated based on the arrangement of particles and their radii. For cubic cells:

  • BCC: $l = \frac{4r}{\sqrt{3}}$

  • FCC: $l = 2\sqrt{2}r$

  Where $r$ is the radius of the particle.

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: Low melting points, soft, poor conductors.

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

• Atomic: Metallic: variable melting points, malleable, good conductors; Covalent network: very high melting points, hard.

Identifying Types from Formulas

• Example: H2O is molecular, NaCl is ionic, Mg is atomic (metallic).

Addition Polymerization

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

• Monomer: Small molecule with a double bond (e.g., ethylene).

• Polymer: Large molecule formed by repeated addition of monomers.

• Example: Polyethylene is formed from ethylene monomers.

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 solution formation involve breaking and forming interactions.

  • $\Delta H_{\text{solution}} = \Delta H_{\text{solute}} + \Delta H_{\text{solvent}} + \Delta H_{\text{mix}}$

  • Lattice energy is the energy required to separate ions in an ionic solid.

• 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: $\text{Moles} = \frac{\text{Mass (g)}}{\text{Molar mass (g/mol)}}$

• Moles of Solute in Solution: Calculated from concentration and volume.

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

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

• 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 vapor pressure.

  • $P_{\text{solution}} = X_{\text{solvent}} \cdot P^0_{\text{solvent}}$

• Freezing Point Depression: Solute lowers the freezing point.

  • $\Delta T_f = K_f \cdot m$

  • Where $K_f$ is the freezing point depression constant, $m$ is molality.

• Boiling Point Elevation: Solute raises the boiling point.

  • $\Delta T_b = K_b \cdot m$

  • Where $K_b$ is the boiling point elevation constant.

• Osmotic Pressure: Pressure required to prevent osmosis.

  • $\Pi = MRT$

  • Where $M$ is molarity, $R$ is gas constant, $T$ is temperature in Kelvin.

Conceptual Topics

• Energetics of Solution Formation: Solution formation is favored if the overall enthalpy change is negative or small positive.

• Effect of Temperature on Solubility: 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.

• Colligative Properties: Depend on the number of dissolved particles; important for understanding solution behavior.

Summary Table: Types of Crystalline Solids

Type	Constituent Particles	Forces	Properties	Examples
Molecular	Molecules	Intermolecular	Low melting point, soft, poor conductor	H2O, CO2
Ionic	Ions	Electrostatic	High melting point, hard, brittle	NaCl, MgO
Atomic	Atoms	Metallic/Covalent	Variable melting point, malleable, conductive	Mg, Diamond

Summary Table: Solution Concentration Units

Unit	Definition	Formula
Molarity (M)	Moles of solute per liter of solution	$\frac{\text{Moles}}{\text{Liters}}$
Molality (m)	Moles of solute per kilogram of solvent	$\frac{\text{Moles}}{\text{Kilograms}}$
Mole Fraction (X)	Fraction of total moles	$\frac{\text{Moles of component}}{\text{Total moles}}$
Percent by Mass	Mass of solute per total mass	$\frac{\text{Mass of solute}}{\text{Total mass}} \times 100\%$