Liquids and Solids — Comprehensive Notes (Sections 12.1, 12.3–12.5)

Section 12.1 Intermolecular Forces

• Condensed states are held together by forces called intermolecular forces (IMFs).

• IMFs are weaker than intramolecular (chemical) bonds but govern physical properties (melting/boiling points, solubility, etc.).

• Four types of intermolecular forces:

  • Ion–dipole attractions

  • Electrostatic interactions between ions and polar molecules.

  • Hydrated ions form by ion–dipole attractions.

  • Strongest type of IMF.

  • Example: salt water where ionic compounds dissolve in water.

  • Hydrogen bonds

  • Require two components:

    • A molecule with a partially positive hydrogen atom (a hydrogen donor).

    • A molecule with a partially negative N, O, or F atom (a hydrogen acceptor).

  • An attraction between the partially positive H in one molecule and the lone pair on N, O, or F in another molecule.

  • Dipole–dipole interactions (permanent dipole–dipole)

  • Polar molecules interact with other polar molecules via electrostatic attractions between oppositely charged ends.

  • London dispersion forces (dispersion forces)

  • Result from instantaneous dipoles due to random electron motion.

  • Induced dipoles in neighboring molecules lead to short-lived attractions.

• Intramolecular vs Intermolecular Forces

  • Intramolecular forces occur within a molecule (covalent or ionic bonds); relatively strong and remain after physical processes.

  • Intermolecular forces occur between molecules; relatively weaker and are affected by physical processes (e.g., heating, phase changes).

• Polar vs. non-polar molecules

  • Polar molecules have a permanent dipole moment (uneven charge distribution).

  • Non-polar molecules have no permanent dipole moment (even charge distribution).

• Halogen size and polarizability (data related to IMFs)

  • Atomic Radius (pm) and Boiling Point (K) for halogens:

  • Fluorine: $ext{Radius} = 60 ext{ pm}, ext{ BP} = 85 ext{ K}$

  • Chlorine: $ext{Radius} = 100 ext{ pm}, ext{ BP} = 239 ext{ K}$

  • Bromine: $ext{Radius} = 117 ext{ pm}, ext{ BP} = 332 ext{ K}$

  • Iodine: $ext{Radius} = 136 ext{ pm}, ext{ BP} = 457 ext{ K}$

• Types of Intermolecular Forces (Summary)

  • Strongest → Weakest order (conceptual):

  • Ion–dipole attractions (present in mixtures of ionic and polar compounds, e.g., NaCl dissolved in water).

  • Hydrogen bonding (between molecules containing H–donor and H–acceptor N, O, or F).

  • Dipole–dipole attractions (polar molecules, e.g., H2O, HCl).

  • London dispersion forces (all molecular substances and inert gases; e.g., H2O, HCl, Cl2, He, Ne).

Section 12.3 Phase Changes and Heating Curves

• Phase changes and related terms:

  • Melting (fusion): solid → liquid

  • Freezing (solidification): liquid → solid

  • Vaporization (evaporation): liquid → gas

  • Condensation: gas → liquid

  • Sublimation: solid → gas

  • Deposition: gas → solid

• Enthalpies associated with phase changes (per mole):

  • $<br>\Delta H_{ ext{vap}}\,\text{(enthalpy of vaporization)}: \text{ energy to vaporize 1 mol of a liquid}<br>$

  • $\Delta H_{ ext{fus}}\,\text{(enthalpy of fusion)}: \text{ energy to melt 1 mol of a solid}<br>$

  • $\Delta H_{ ext{sub}}\,\text{(enthalpy of sublimation)}: \text{ energy to sublime 1 mol of a solid}<br>$

• Heating curve (for a pure substance)

  • Temperature versus time as a substance is heated.

  • Plateaus occur at phase changes due to latent heat (no temperature change while changing phase).

• Examples and calculations:

  • Problem: Identify the phase change for each equation:

  • (a) \ce{C{18}H{38}(s) -> C{18}H{38}(l)}

    • Melting (fusion).

  • (b) \ce{CO2(g) -> CO2(s)}

    • Deposition.

  • (c) \ce{NH3(l) -> NH3(g)}

    • Vaporization (boiling/evaporation).

  • Example: Energy required to melt 16.4 g of ice at 0°C with $\Delta H_{\text{fus}} = 6.01\ \text{kJ}\,\text{mol}^{-1}$

  • Molar mass of water: M_{\ce{H2O}} = 18.015\ \text{g}\,\text{mol}^{-1}

  • Moles melted: $n = \frac{m}{M} = \frac{16.4\ \text{g}}{18.015\ \text{g mol}^{-1}} \approx 0.9105\ \text{mol}$

  • Energy: $q = n \Delta H_{\text{fus}} = (0.9105) (6.01\ \text{kJ mol}^{-1}) \approx 5.47\ \text{kJ}$

Section 12.4 Vapor Pressure, Boiling Point, and the Clausius–Clapeyron Equation

• Vapor pressure ( Pvap )

  • The equilibrium pressure of a vapor above its liquid or solid in a closed container.

  • At equilibrium, rate of evaporation equals rate of condensation.

  • Pvap increases with temperature; it is a function of intermolecular forces.

• Boiling point (BP)

  • The temperature at which Pvap equals the ambient atmospheric pressure (P_{ ext{atm}}).

  • Example reference points for water at various elevations:

  • Sea level: BP = $100^ ext{°}C$

  • Everest: BP ≈ $69.9^ ext{°}C$

• Relationship among Pvap, BP, and IMFs

  • Substances with stronger IMFs tend to have lower Pvap at a given temperature and higher BP.

  • The Pvap–T curves differ for substances (e.g., diethyl ether, ethanol, water) due to IMF strength.

• Clausius–Clapeyron equation (to relate Pvap at two temperatures)

  • General form (two states):
    $\ln\left(\frac{P<em>2}{P</em>1}\right) = -\frac{\Delta H<em>{ ext{vap}}}{R}\left( \frac{1}{T</em>2} - \frac{1}{T_1} \right)$

  • Alternative linear form: $\ln P = -\frac{\Delta H_{ ext{vap}}}{R}\frac{1}{T} + C$ where C is a constant.

  • Universal gas constant: $R = 8.314\ \text{J mol}^{-1} \text{K}^{-1}$

  • In practice, use Pvap data at known temperatures to solve for $\Delta H_{ ext{vap}}$ or to predict Pvap at another temperature.

• Example: Methanol

  • Given: Normal boiling point $T<em>1 = 64.60^{\circ}\text{C} = 337.75\ \text{K}$; $\Delta H</em>{\text{vap}} = 35.2\ \text{kJ mol}^{-1} = 35200\ \text{J mol}^{-1}$; Measured vapor pressure at $T<em>2 = 25.00^{\circ}\text{C} = 298.15\ \text{K}$; Assume $P</em>1 = 1\ \text{atm} = 760\ \text{torr}$.

  • Calculation steps:

  • $\ln\left(\frac{P<em>2}{P</em>1}\right) = -\frac{\Delta H<em>{\text{vap}}}{R}\left( \frac{1}{T</em>2} - \frac{1}{T_1} \right)$

  • Compute: $\frac{\Delta H_{\text{vap}}}{R} = \frac{35200}{8.314} \approx 4237.5$

  • $\frac{1}{T<em>2} - \frac{1}{T</em>1} = \frac{1}{298.15} - \frac{1}{337.75} \approx 0.000391\ \text{K}^{-1}$

  • Product: $4237.5 \times 0.000391 \approx 1.656$

  • $\ln\left(\frac{P_2}{760}\right) \approx -1.656$

  • $\frac{P_2}{760} \approx e^{-1.656} \approx 0.191$

  • $P_2 \approx 0.191 \times 760 \approx 145\ \text{torr}$

  • Result: The vapor pressure of methanol at $25^{\circ}\text{C}$ is approximately $P_2 \approx 1.45\times 10^{2}\ \text{torr}$.

• Applications and notes

  • The Clausius–Clapeyron equation enables extraction of enthalpies from Pvap data and vice versa.

  • Pvap data and BP are practical indicators of how substances will behave under heating, cooling, or reduced/augmented pressure conditions.

Section 12.5 Phase Diagrams

• Phase diagrams show the phase (solid, liquid, gas) of a substance under all possible pressure–temperature (P–T) combinations.

• Key features of a generic phase diagram:

  • Regions corresponding to solid, liquid, and gas phases.

  • Lines separating phases depict equilibria between phases (fusion/melting line, vaporization/condensation line, sublimation/deposition line).

  • Points of interest:

  • Triple point: the single point where all three phases are in equilibrium; lines intersect there.

  • Critical point: above this P–T location, the substance no longer exists as a distinct liquid; liquid and gas become indistinguishable (supercritical fluid).

  • Normal melting point: the temperature at which the solid melts at 1 atm.

  • Normal boiling point: the temperature at which the vapor pressure equals 1 atm.

• Reading and interpreting phase diagrams

  • Identify phase in each region (solid, liquid, gas).

  • Determine the phase boundary for solid–gas equilibrium (sublimation/deposition line).

  • Locate the normal boiling point on the temperature axis by finding the point where Pvap equals 1 atm.

• Conceptual use

  • Phase diagrams predict phase changes when changing temperature or pressure (
    e.g., heating/cooling at constant pressure or compression/expansion at constant temperature).

• Example interpretation task (from slides)

  • a) Identify the phase(s) in regions A, B, and C.

  • b) Identify the line where the solid and gas phases are in equilibrium (sublimation line).

  • c) Identify the point indicating the normal boiling point (where Pvap = 1 atm).

  • Note: The exact labels A, B, C depend on the specific diagram provided, but the concepts remain the same.