CHE 140 Final Exam Study Guide: Liquids, Solids, and Intermolecular Forces

Liquids, Solids, and Intermolecular Forces

Freezing Point Depression

The freezing point of a solution is lowered when a solute is dissolved in a solvent. This phenomenon is called freezing point depression and is a colligative property, meaning it depends on the number of solute particles, not their identity.

• Key Equation: The change in freezing point is calculated as: $\Delta T_f = i K_f m$ where:

  • $\Delta T_f$ = freezing point depression (°C)

  • $i$ = van 't Hoff factor (number of particles the solute dissociates into)

  • $K_f$ = freezing point depression constant (°C·kg/mol)

  • $m$ = molality of the solution (mol solute/kg solvent)

• Calculating the New Freezing Point: $T_{f,solution} = T_{f,solvent} - \Delta T_f$

• Example: If 10 g of NaCl (molar mass = 58.44 g/mol) is dissolved in 100 g of water ($K_f = 1.86$ °C·kg/mol), calculate the freezing point of the solution.

  • Find moles of NaCl: $10 \text{ g} / 58.44 \text{ g/mol} = 0.171 \text{ mol}$

  • Molality: $0.171 \text{ mol} / 0.100 \text{ kg} = 1.71 \text{ m}$

  • For NaCl, $i = 2$ (Na+ and Cl-)

  • $\Delta T_f = 2 \times 1.86 \times 1.71 = 6.36$ °C

  • Water's freezing point: $0.00$ °C, so $T_{f,solution} = 0.00 - 6.36 = -6.36$ °C

Heating and Cooling Curves & Phase Changes

When a substance is heated or cooled, it may undergo temperature changes and phase transitions (solid ↔ liquid ↔ gas). The energy required depends on the specific heat capacities and enthalpies of phase changes.

• Key Equations:

  • For temperature change (no phase change): $q = m c \Delta T$

  • For melting/freezing: $q = n \Delta H_{fus}$

  • For vaporization/condensation: $q = n \Delta H_{vap}$

• Heating/Cooling Curve: A plot of temperature vs. heat added shows plateaus during phase changes (where temperature remains constant).

• Example: Calculate the energy to heat 50 g of ice at -10°C to steam at 110°C (using provided values for $c_{solid}$, $c_{liquid}$, $c_{gas}$, $\Delta H_{fus}$, $\Delta H_{vap}$).

Unit Cells and Chemical Formulas

Solids have repeating patterns called unit cells. The arrangement and number of atoms in a unit cell determine the empirical formula of the solid.

• Types of Unit Cells: Simple cubic, body-centered cubic, face-centered cubic.

• Counting Atoms:

  • Corner atom: shared by 8 cells (1/8 per cell)

  • Edge atom: shared by 4 cells (1/4 per cell)

  • Face atom: shared by 2 cells (1/2 per cell)

  • Center atom: belongs entirely to one cell

• Example: In a face-centered cubic cell, there are 8 corners and 6 faces:

  • Corner: $8 \times 1/8 = 1$ atom

  • Face: $6 \times 1/2 = 3$ atoms

  • Total: 4 atoms per unit cell

Vapor Pressure and Clausius-Clapeyron Equation

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid at a given temperature. The Clausius-Clapeyron equation relates vapor pressure and temperature.

• Key Equation: $\ln \left( \frac{P_2}{P_1} \right) = -\frac{\Delta H_{vap}}{R} \left( \frac{1}{T_2} - \frac{1}{T_1} \right)$ where:

  • $P_1$, $P_2$ = vapor pressures at $T_1$, $T_2$ (in Kelvin)

  • $\Delta H_{vap}$ = enthalpy of vaporization (J/mol)

  • $R$ = gas constant ($8.314$ J/mol·K)

• Example: Given $P_1$ at $T_1$ and $\Delta H_{vap}$, solve for $P_2$ at $T_2$.

Liquid Properties and Intermolecular Forces

The physical properties of liquids depend on the types and strengths of intermolecular forces (IMFs) present.

• Key Properties:

  • Surface tension: Energy required to increase surface area of a liquid

  • Viscosity: Resistance to flow

  • Capillary action: Movement of liquid in narrow tubes

  • Vapor pressure: Tendency to evaporate

  • Cohesion: Attraction between like molecules

  • Adhesion: Attraction between unlike molecules

• Types of IMFs:

  • London dispersion forces: Present in all molecules, especially nonpolar

  • Dipole-dipole forces: Between polar molecules

  • Hydrogen bonding: Special dipole-dipole interaction (H with N, O, or F)

  • Ion-dipole forces: Between ions and polar molecules

• Comparing Properties:

  • Stronger IMFs → higher surface tension, viscosity, boiling point; lower vapor pressure

  • "Like dissolves like": Polar solvents dissolve polar solutes; nonpolar solvents dissolve nonpolar solutes

• Example: Rank H2O, CH3OH, CH4, and CCl4 by boiling point based on IMFs.

Effect of Temperature on Liquid Properties

Temperature changes affect the physical properties of liquids by influencing the kinetic energy of molecules and the strength of intermolecular forces.

• As temperature increases:

  • Surface tension and viscosity decrease (molecules move more freely)

  • Vapor pressure increases (more molecules escape to vapor phase)

  • Capillary action may decrease due to lower cohesion

• Example: Water at 90°C has lower surface tension and higher vapor pressure than at 25°C.

Solubility and "Like Dissolves Like"

Solubility depends on the similarity of intermolecular forces between solute and solvent. Polar solutes dissolve best in polar solvents, and nonpolar solutes in nonpolar solvents.

• Example: NaCl (ionic, polar) dissolves well in water (polar), but not in hexane (nonpolar).

Boiling Points and Intermolecular Forces

The boiling point of a substance is determined by the strength of its intermolecular forces. Stronger IMFs require more energy (higher temperature) to separate molecules.

• Order of increasing boiling point (for similar molar mass):

  • London dispersion < dipole-dipole < hydrogen bonding

• Example: Compare boiling points of CH4 (dispersion), CH3F (dipole-dipole), and H2O (hydrogen bonding).

Phase Diagrams

A phase diagram shows the state of a substance (solid, liquid, gas) at various temperatures and pressures. Key features include phase boundaries, triple point, and critical point.

• Key Features:

  • Phase boundaries: Lines separating solid, liquid, and gas regions

  • Triple point: All three phases coexist

  • Critical point: End of liquid-gas boundary; above this, no distinction between liquid and gas

  • Normal freezing/boiling point: Temperature at which phase change occurs at 1 atm

• Example Table:

Feature	Description
Phase Boundary	Line separating two phases (e.g., solid-liquid)
Triple Point	All three phases in equilibrium
Critical Point	Highest T/P where liquid and gas are distinct
Normal Boiling Point	Boiling at 1 atm pressure
Normal Freezing Point	Freezing at 1 atm pressure

• Example: On a phase diagram, identify the region for liquid water, the triple point, and what happens when pressure is increased at constant temperature.