Intermolecular Forces, Liquid Properties, and Crystal Structures

Overview of Intermolecular Forces (IMFs)

• Definition: Intermolecular forces are the attractive forces that occur between molecules. They are distinct from intramolecular forces, which are the covalent or ionic bonds holding atoms together within a single molecule.
• General Characteristics:
  • Intermolecular forces are responsible for holding liquids together.
  • Every molecule possesses some form of intermolecular interaction.
  • Van der Waals forces represent the weakest category of these interactions.

Types of Intermolecular Forces

• Van der Waals / London Dispersion Forces:

  • This force is present in every compound.
  • It arises from the constant motion of electrons, which creates temporary shifts in electron density (temporary dipoles).
  • Scale and Dispersion: The larger the compound, the stronger the dispersion forces. This is because larger molecules have more electrons and more points where electron density can shift.
  • Molecular Geometry and Contact Points:
    • Linear Structures: More linear carbon chains have more points of contact for interaction. This leads to higher dispersion forces. These points of contact occur where atoms and shifting electron densities are in closer proximity.
    • Branched Structures: Highly branched carbon chains are less linear and have fewer points of contact. Branch points may not line up easily, placing atoms too far apart for effective dispersion interactions. This leads to weaker dispersion forces compared to linear isomers.

• Dipole-Induced Dipole Interactions:

  • Occurs between a polar molecule and a nonpolar (but polarizable) molecule.
  • Polarizability: The ability of an electron cloud to move and shift around a molecule. All molecules with electrons are polarizable, though those with higher electronegativity differences often show larger shifts.
  • Mechanism: A polar molecule (like $H_2O$) with a partial negative charge (on the oxygen) or partial positive charge (on the hydrogens) approaches a nonpolar molecule (like $H_2$). The charge of the polar molecule repels or attracts the electrons in the nonpolar molecule, inducing a temporary dipole.

• Dipole-Dipole Interactions:

  • Occurs between two polar molecules that possess permanent dipole moments.
  • The partial positive end of one molecule interacts with the partial negative end of another.
  • Example: The carbon-oxygen ($C=O$) bond creates a significant dipole because oxygen is highly electronegative and pulls electron density toward itself.

• Ion-Dipole Interactions:

  • Occurs between an ion (cation or anion) and a polar molecule.
  • Strength: These are stronger than dipole-dipole interactions because the formal charge of an ion is much stronger than the partial charge of a polar molecule.
  • Coulomb's Law Application: The strength of the interaction increases with the magnitude of the charge. For example, the interaction between magnesium ($Mg^{2+}$) and water is stronger than the interaction between sodium ($Na^+$) and water because $Mg^{2+}$ has a higher positive charge.

• Hydrogen Bonding:

  • Classified as the strongest type of intermolecular force (a special case of dipole-dipole).
  • Requirements:
    • Hydrogen Bond Donor: A hydrogen atom must be directly bonded to a highly electronegative element ($ ext{Nitrogen}$, $ ext{Oxygen}$, or $ ext{Fluorine}$).
    • Hydrogen Bond Acceptor: An electronegative element ($ ext{N}$, $ ext{O}$, or $ ext{F}$) must have at least one lone pair of electrons.
  • Mechanism: The large shift in electron density toward the electronegative atom leaves the hydrogen very partially positive. This hydrogen is then attracted to the high electron density of a lone pair on a neighboring electronegative atom.
  • Biological Importance: Hydrogen bonding is crucial for life; it provides the structure for the DNA double helix and dictates how proteins fold.
  • Bond vs. IMF: Despite the name, it is not a true covalent or ionic bond.
    • Intermolecular Hydrogen Bond Energy: $10$ to $40\,kJ\,mol^{-1}$.
    • $H-O$ Covalent Bond Energy: $464\,kJ\,mol^{-1}$.
    • Covalent bonds are harder to break because they involve shared electrons that complete valence shells; IMFs are weaker because the molecules remain stable even when the interaction is broken.

Properties of Liquids

• Surface Tension:

  • Results from the collective intermolecular attractive forces within a liquid.
  • Stronger IMFs lead to higher surface tension.
  • Example: Water beads up due to high surface tension from hydrogen bonding, allowing small insects to walk on its surface.

• Capillary Action:

  • The movement of liquid up a narrow tube, driven by surface tension.
  • Cohesion: Intermolecular forces between molecules of the same substance.
  • Adhesion: Intermolecular forces between molecules and the surface of their container (different substances).
  • Stronger adhesion between the liquid and the container walls results in higher capillary action.

• Viscosity:

  • A liquid's resistance to flow.
  • Factors: High intermolecular forces and molecular entanglement lead to high viscosity.
  • Temperature Effects: Increasing temperature provides kinetic energy to overcome IMFs, typically reducing viscosity.

Unique Properties of Water ($H_2O$)

• Structure: Small size and bent shape allow for a dense network of hydrogen bonding interactions.
• Specific Heat: Water has a high specific heat, meaning it requires significant energy to raise its temperature by $1\,^{\circ}\text{C}$.
• Density of Ice: Ice is less dense than liquid water, causing it to float.
  • Temperature of Maximum Density: Water density peaks near $4\,^{\circ}\text{C}$.
  • Molecular Basis: When water freezes, it forms a hexagonal crystal structure held by hydrogen bonds. This structure creates specific gaps and empty spaces that are not present in the more freely moving liquid phase, leading to a lower density in the solid phase.

Solids and Crystal Structures

• Crystalline Solids: Rigid structures with molecules or atoms at specific, repeating locations.
• Unit Cells: The smallest repeating unit of a crystal lattice.
  • Simple Cubic Cell: Contains $1$ total atom ($8\text{ corners} \times \frac{1}{8}\text{ atom per corner}$).
  • Body-Centered Cubic ($BCC$): Contains $2$ total atoms ($8\text{ corners} \times \frac{1}{8} + 1\text{ center atom}$).
  • Face-Centered Cubic ($FCC$): Contains $4$ total atoms ($8\text{ corners} \times \frac{1}{8} + 6\text{ faces} \times \frac{1}{2}\text{ atom per face}$).
• Coordination Number: A value used to identify the specific geometry of a structure based on neighboring atoms.
• Common Lattice Shapes: Simple cubic, tetragonal, orthorhombic, rhombohedral, and hexagonal.

Types of Crystals and Applications

• Ionic Crystals: Held by electrostatic attraction between ions (e.g., Table Salt/$NaCl$). Optimized to maximize attraction and minimize repulsion.
• Covalent Crystals: Held by covalent bonds (e.g., Diamond and Graphite, which are different allotropes of carbon).
• Molecular Crystals: Held by IMFs (e.g., Protein crystals).
  • X-ray Diffraction: A technique where X-rays are shone on a crystal to produce a diffraction pattern, allowing scientists to determine the three-dimensional structure of the molecule.
  • Case Study (MRSA): In drug development, researchers crystallize proteins essential to the survival of $MRSA$ to visualize where inhibitors bind, informing antibiotic design.
• Metallic Crystals: Held by metallic bonds (e.g., Tungsten, Copper, Iron). Characterized by a "sea of electrons" that move freely, making them excellent conductors of heat and electricity.
• Amorphous Solids: Lack a regular, three-dimensional repeating structure. They are often less transparent and may have multiple compositions. Glass is the most common example.

Phase Changes and Energetics

• Phase Change Terminology:
  • Solid to Liquid: Melting or Fusion.
  • Liquid to Gas: Vaporization.
  • Solid to Gas: Sublimation.
  • Gas to Solid: Deposition.
  • Gas to Liquid: Condensation.
  • Liquid to Solid: Freezing.
• Vapor Pressure: The pressure exerted by a vapor in equilibrium with its liquid phase in a closed container. As temperature increases, kinetic energy increases, allowing more molecules to enter the gas phase, thereby increasing vapor pressure.
• Dynamic Equilibrium: Occurs when the rate of evaporation equals the rate of condensation.

The Clausius-Clapeyron Equation

• Definition: Relates the vapor pressure of a liquid to its temperature and its molar heat of vaporization ($\Delta H_{vap}$).
• Variable Constants:
  • $R$ (Gas Constant): $8.314\,J\,mol^{-1}\,K^{-1}$.
  • Temperature must be in Kelvin ($K$).
  • $\Delta H_{vap}$ must often be converted from $kJ\,mol^{-1}$ to $J\,mol^{-1}$ to match the units of $R$.
• Mathematical Form (Two-Point):     $\ln\left(\frac{P_2}{P_1}\right) = \frac{\Delta H_{vap}}{R} \left(\frac{1}{T_1} - \frac{1}{T_2}\right)$
• Logarithmic Rules:
  • $\ln\left(\frac{A}{B}\right) = \ln(A) - \ln(B)$.
  • To undo a natural log: If $\ln(x) = y$, then $x = e^y$.

Example Problem: Diethyl Ether

• Given Data:
  • $P_1 = 401\,mmHg$
  • $T_1 = 291\,K$
  • $T_2 = 305\,K$
  • $\Delta H_{vap} = 26\,kJ\,mol^{-1} = 26000\,J\,mol^{-1}$
  • $R = 8.314\,J\,mol^{-1}\,K^{-1}$
• Calculation Steps:
  1. Substitute variables: $\ln\left(\frac{P_2}{401}\right) = \frac{26000}{8.314} \left(\frac{1}{291} - \frac{1}{305}\right)$.
  2. Simplify thermal constant term: $\frac{26000}{8.314} \approx 3127.26$.
  3. Simplify temperature difference: $\left(\frac{1}{291} - \frac{1}{305}\right) \approx 0.0001577$.
  4. Multiply terms to find the log value: $\ln\left(\frac{P_2}{401}\right) \approx 0.49329$.
  5. Convert to log subtraction: $\ln(P_2) - \ln(401) = 0.49329$.
  6. Solve for $\ln(P_2)$: $\ln(P_2) = 0.49329 + 5.994 = 6.4873$.
  7. Remove natural log: $P_2 = e^{6.4873}$.
• Final Result: $P_2 = 657\,mmHg$.

Questions & Discussion

• Q: Do metals with loose electrons have stronger Van der Waals forces?
  • A: You could say so. In some systems, these interactions move into the territory of ion or dipole interactions. However, because metals have many electrons, there is more possibility for significant dispersion, making those interactions stronger.
• Q: Is there an example of strong vs. weak adhesion?
  • A: Water and glass show strong adhesion. Different wines show weak adhesion; you can see "legs" or droplets trial down the glass as you swirl it.
• Q: Would soda show strong adhesion?
  • A: Soda contains carbon dioxide ($CO_2$) bubbles. The gas molecules escaping might disrupt the capillary behavior. If the soda were flat, it should behave similarly to water and show strong adhesion to the glass.
• Q: Why is there a difference between the energy of a hydrogen bond and a covalent bond?
  • A: Covalent bonds share electron density at short distances to complete valence octets, creating high stability. Breaking them leaves atoms with incomplete shells. Hydrogen bonds are intermolecular attractions at greater distances; even when they break, the individual molecules retain their internal covalent bonds and remain stable, thus requiring less energy to disrupt.
• Q: Is glass actually moving over time?
  • A: There is a theory that old glass is thicker at the bottom due to flow, but it is likely actually due to historical manufacturing techniques where glass was not made perfectly flat and was simply installed with the thicker side down.