Intermolecular Forces, Gas Solubility, and Phase Equilibria Notes

Intermolecular vs. Intramolecular Forces

• Intramolecular Forces:

  • Forces that operate directly between atoms within a single molecule.

  • Significantly stronger than intermolecular forces.

• Intermolecular Forces:

  • Forces that exist between neighboring atoms or separate molecules (e.g., interaction between a water molecule $H_2O$ and another water molecule $H_2O$).

  • Generally much weaker than intramolecular chemical bonds.

Types of Intermolecular Forces

• Dispersion (London) Forces:

  • The weakest type of intermolecular force.

  • Arises due to rapid, instantaneous fluctuations in electron density within non-polar molecules.

  • This is the only type of intermolecular force present in purely non-polar molecules.

  • Polarizability:

    • Refers to how easily the electron cloud of a molecule, ion, or atom can be distorted by an external electric field or nearby particle.

    • Larger atoms and molecules possess greater polarizability than smaller ones.

    • Higher polarizability leads to stronger London dispersion forces, which results in higher boiling points.

  • Surface Area Influence:

    • An increased molecular surface area allows for increased intermolecular contact points.

    • Greater surface area produces stronger dispersion interactions compared to molecules of smaller surface area or more compact geometries.

• Dipole-Induced Dipole Interactions:

  • Comparable in strength to London dispersion forces.

  • Occurs when a polar molecule approaches a non-polar molecule, inducing a temporary dipole moment in the non-polar species.

  • This force is responsible for enabling non-polar gases (such as oxygen gas, $O_2$) to dissolve in polar solvents (such as liquid water, $H_2O$).

• Dipole-Dipole Interactions:

  • Occurs exclusively between polar molecules containing permanent dipoles.

  • Note: Non-polar molecules can still contain polar covalent bonds if the molecular geometry cancels out the individual bond dipoles.

  • Dipole Moment ($\mu$): A quantitative value indicating the degree of polarity of a molecule.

Determining Molecular Polarity and Hydrogen Bonding

• Determining Polarity:

  • Molecular polarity is determined by evaluating both the molecular geometry via Valence Shell Electron Pair Repulsion (VSEPR) theory and the individual bond polarities derived from electronegativity differences.

• Hydrogen Bonding:

  • The strongest specific type of dipole-dipole interaction.

  • Requirements: Hydrogen must be directly covalently bonded to a highly electronegative atom—specifically Oxygen ($\text{O}$), Nitrogen ($\text{N}$), or Fluorine ($\text{F}$)—or actively interacting with one of these electronegative atoms in an adjacent molecule.

Comparative Boiling Points and Physical Properties

• Relative Strength and Boiling Point Trends:

  • Propane ($CH_3-CH_2-CH_3$): Possesses only London dispersion forces; exhibits the weakest intermolecular interactions and consequently the lowest boiling point ($BP$).

  • Methoxyethane ($CH_3-O-CH_2-CH_3$): Possesses permanent dipole-dipole forces; exhibits an intermediate boiling point higher than non-polar alkanes.

  • Methanol ($CH_3OH$): Features strong hydrogen bonding, resulting in a high boiling point.

  • Ethanol ($CH_3CH_2OH$): Contains hydrogen bonding as well as a larger chain with more total chemical bonds and surface area, requiring more thermal energy to disrupt interactions, thereby yielding a higher overall boiling point.

Ion-Dipole Interactions and General Consequences of Intermolecular Forces

• Ion-Dipole Interactions:

  • Electrostatic attractions between an ionic species (charge $Q_1$) and a polar molecule with a permanent dipole (charge $Q_2$).

  • Extremely strong interactions, proportional to charge magnitude and dielectric/permittivity factors ($\frac{Q_1 Q_2}{E \times K}$).

• Consequences of Intermolecular Forces:

  • Melting Points and Boiling Points: Both increase systematically as the overall strength of intermolecular forces increases.

  • Solubility: Dictates the mechanism and extent to which substances dissolve in one another.

    • Caveat: The presence of hydrogen bonding capability does not automatically guarantee complete solubility in water.

  • Density: Influences relative density and buoyancy behaviors (whether a substance floats or sinks).

Gas Solubility and Henry's Law

• Henry's Law:

  • Relates the equilibrium concentration of a dissolved gas in a liquid to the partial pressure of that gas above the liquid.

  • Equation:         $C_{\text{gas}} = k_H \times P_{\text{gas}}$

    • $C_{\text{gas}}$: Concentration of the dissolved gas ($\text{mol/L}$).

    • $k_H$: Henry's Law constant ($\text{mol/L/atm}$).

    • $P_{\text{gas}}$: Partial pressure of the gas above the solution ($\text{atm}$).

  • Key Relationships:

    • A larger $k_H$ constant denotes a substantially more soluble gas.

    • Increasing the partial pressure $P_{\text{gas}}$ raises the frequency of gas-liquid molecular collisions, thereby increasing gas solubility.

  • Calculation Example:

    • Given $k_H = 6.7 \times 10^{-4}\,\text{mol/L/atm}$, $P_{\text{gas}} = 0.78\,\text{atm}$, and molar mass $M = 28.014\,\text{g/mol}$:

    • Molar concentration: $C_{\text{gas}} = (6.7 \times 10^{-4}\,\text{mol/L/atm}) \times 0.78\,\text{atm} = 5.226 \times 10^{-4}\,\text{mol/L}$.

    • Mass basis calculation yields $7.8 \times 10^{-3}\,\text{g}$.

Vapor Pressure of Pure Liquids

• Vapor Pressure ($VP$):

  • The pressure exerted by a vapor in dynamic equilibrium with its liquid phase inside a closed system.

  • Temperature Dependence: Increasing temperature ($\uparrow T$) results in a non-linear exponential increase in vapor pressure ($\uparrow VP$).

• Boiling Point Relationship:

  • A liquid boils when its internal vapor pressure equals the surrounding ambient atmospheric pressure.

  • The boiling point of a liquid varies based on external pressure. For example, at the high altitude of Mount Everest where ambient atmospheric pressure is significantly lower, water boils at approximately $70\,^\circ\text{C}$.

The Clausius-Clapeyron Equation and Quantitative Calculations

• Standard Clausius-Clapeyron Form (for $1\,\text{mol}$ of liquid transitioning to vapor at normal boiling point):     $\ln(P_{\text{vap}}) = \left(-\frac{\Delta H_{\text{vap}}}{R}\right) \times \left(\frac{1}{T}\right) + C$

  • Plotting $\ln(P_{\text{vap}})$ versus $\frac{1}{T}$ yields a straight line where:

    • $\text{Slope} = -\frac{\Delta H_{\text{vap}}}{R}$

    • $\text{Y-intercept} = C$

• Two-Point Clausius-Clapeyron Equation:     $\ln\left(\frac{P_{\text{vap},1}}{P_{\text{vap},2}}\right) = \left(\frac{\Delta H_{\text{vap}}}{R}\right) \times \left(\frac{1}{T_2} - \frac{1}{T_1}\right)$     (Derived from $\ln(x) - \ln(y) = \ln\left(\frac{x}{y}\right)$)

• Quantitative Problem Example:

  • Given Parameters:

    • $\Delta H_{\text{vap}} = 19.04\,\text{kJ/mol} = 19,040\,\text{J/mol}$

    • $R = 8.314\,\text{J/mol} \cdot \text{K}$

    • $T_1 = -42\,^\circ\text{C} = 231\,\text{K}$

    • $T_2 = 25\,^\circ\text{C} = 298\,\text{K}$

    • $P_{\text{vap},1} = 1\,\text{atm}$ at $T_1 = 231\,\text{K}$

  • Execution:         $\ln\left(\frac{1}{P_{\text{vap},2}}\right) = \left(\frac{19,040\,\text{J/mol}}{8.314\,\text{J/mol} \cdot \text{K}}\right) \times \left(\frac{1}{298\,\text{K}} - \frac{1}{231\,\text{K}}\right)$         $\ln\left(\frac{1}{P_{\text{vap},2}}\right) = 2290.112 \times (-0.0009733) = -2.228$         $\frac{1}{P_{\text{vap},2}} = e^{-2.228} = 0.108$         $P_{\text{vap},2} = 9.3\,\text{atm}\text{ at } 25\,^\circ\text{C}$

Phase Diagrams and Unique Physical Properties of Water

• Phase Diagram:

  • A graphical representation displaying the physical states of matter (solid, liquid, gas) and their phase transitions as a function of temperature ($T$) and pressure ($P$).

• Unique Properties of Water ($H_2O$):

  • Density Anomaly: Solid ice is less dense than liquid water, causing ice to float (noted as sinking in comparison to higher density anomalies); this unique density behavior is singular to $H_2O$ among common liquids.

  • Surface Tension: Directly proportional to intermolecular forces ($\uparrow \text{intermolecular forces} \rightarrow \uparrow \text{surface tension}$).

  • Viscosity: Defined as a liquid's internal resistance to flow or its degree of liquid thickness.

  • Meniscus: The characteristic curvature of a liquid column surface in a tube, displaying either a convex or concave ($\text{U}$-shaped) profile depending on adhesive versus cohesive forces.