Intermolecular Forces and Properties of Liquids – Chapter 11

States of Matter and the Ubiquity of Intermolecular Forces

Under normal conditions, gases obey PV=nRT reasonably well because the model assumes molecules do not attract each other. In the condensed phases (liquids and solids) molecules lie close together; attractive forces are no longer negligible and dominate physical behaviour. For instance, 300\ \text{mL} of liquid N_2 expands to more than 200\ \text{L} of gas at 25\ ^\circ\text{C} and 1.0\ \text{atm} because the intermolecular separations change dramatically on vaporisation, whereas liquid and solid benzene occupy almost the same volume because their molecules are already tightly packed.

Electrostatic Principles: Coulomb’s Law and Ionic vs. Molecular Solids

Whenever positive and negative charges approach one another an electrostatic attraction results; like charges repel. The magnitude of the force is determined by Coulomb’s law:

F=-k\frac{q1q2}{d^2}

Here d is the centre‐to‐centre distance and k is a proportionality constant. Ionic crystals (e.g. NaCl) are held together by such forces, accounting for their very high melting and boiling points. Molecular substances possess much weaker non-covalent forces; nevertheless these van der Waals interactions are strong enough to permit condensation and solidification.

Catalogue of van der Waals Intermolecular Forces

All non-covalent attractive forces between discrete species are grouped as van der Waals interactions.

1. Dipole–Dipole (between two permanent dipoles).
2. Dipole–Induced Dipole (Debye) – a permanent dipole polarises a non-polar neighbour.
3. Induced Dipole–Induced Dipole (London dispersion) – instantaneous correlations in the electron clouds of any two particles.

Although individually weak (typically (<15\%) of a covalent bond) these forces decisively influence melting/boiling points, heats of phase change, solubility, and the shapes of biomolecules such as DNA and proteins.

Ion–Dipole Interactions and Hydration Phenomena

A polar molecule approaches an ion with the favourable orientation: the negative pole faces the cation and the positive pole the anion. Strength depends on (i) ion–dipole separation, (ii) ionic charge, and (iii) dipole magnitude. The standard enthalpy of hydration for Na^+ is \Delta_{\text{hydr}}H^\circ=-405\ \text{kJ\,mol}^{-1}; values become less exothermic down the alkali-metal column as ionic radius (and thus d) increases, but become much more exothermic for ions of higher charge (e.g. Mg^{2+}:\ -1922\ \text{kJ\,mol}^{-1}).

Hydrated salts such as BaCl2\cdot2H2O or [Cr(H2O)4Cl2]Cl\cdot2H2O form when lattice sites or coordination spheres incorporate water via ion–dipole forces.

Dipole–Dipole Forces, Volatility and “Like Dissolves Like”

When two polar molecules meet, the partially positive end of one aligns with the partially negative end of the other. The stronger these interactions, the higher the boiling point, the larger the enthalpy of vaporisation \left(\Delta{\text{vap}}H^\circ\right) and the lower the equilibrium vapour pressure. Table-based comparisons show that polar ICl (molar mass 162\ \text{g\,mol}^{-1}) boils at 97\ ^\circ\text{C}, well above non-polar Br2 of almost identical mass. Solubility mirrors this: polar ethanol mixes completely with polar water, whereas non-polar hydrocarbons (e.g. octane) do not disrupt the hydrogen-bonded water network and hence separate.

Hydrogen Bonding: Origin, Energetics and Consequences

Extraordinary boiling points of HF, H2O and NH3 (deviating sharply from group trends) arise because an X–H bond where X=\text{N,O,F} is highly polar. The very small hydrogen, bearing a concentrated partial positive charge, bridges to the lone pair of a neighbouring electronegative atom forming an X–H···Y hydrogen bond (typical energies 5–30\ \text{kJ\,mol}^{-1}).

Water is a textbook exemplar: each molecule can engage in four hydrogen bonds (two as donor, two as acceptor) producing an open tetrahedral network in ice. Consequently ice is about 10\% less dense than liquid water – hence it floats. As ice melts, hydrogen-bonded cages collapse and density increases until a maximum at 4\ ^\circ\text{C}; this anomaly prevents lakes from freezing solid and drives seasonal turnover. Extensive hydrogen bonding also yields water’s high specific heat capacity 4.184\ \text{J\,g}^{-1}\,\text{K}^{-1} and large \Delta_{\text{vap}}H^\circ=40.7\ \text{kJ\,mol}^{-1}.

Debye Forces and London Dispersion in Non-Polar Systems

A permanent dipole (e.g. H2O) can polarise a large, soft electron cloud (e.g. I2), inducing a complementary dipole that attracts – accounting for the solubility trend O2 < N2 < Cl2 < Br2 < I_2 in water. Polarizability rises with molar mass and volume: heavier atoms/molecules are easier to distort.

Even between two ostensibly non-polar partners a fleeting charge asymmetry can instantaneously arise; this induces a corresponding dipole in the neighbour, giving London dispersion forces. They act between all particles but are the only forces available to noble gases and homonuclear diatomics. Their magnitude scales with molar mass and shape: compare \Delta{\text{vap}}H^\circ for N2:5.6\ \text{kJ\,mol}^{-1} versus I_2:41.9\ \text{kJ\,mol}^{-1}.

Synthesis: Comparative Overview of Intermolecular Forces

Gecko Adhesion: A Macroscopic Exploitation of van der Waals Forces

Gecko toes are covered with millions of microscopic setae and even finer spatulae, generating enormous cumulative surface area. At very short distances London forces between the spatulae and wall enable the lizard to adhere and run up vertical surfaces; a single seta can support an ant’s weight, a dime-sized patch could hold a 20\ \text{kg} child.

Properties of Liquids and the Impact of Intermolecular Attractions

Vaporisation, Condensation and \Delta_{\text{vap}}H

Molecules in a liquid exhibit a Boltzmann-type energy distribution. Those at the surface possessing kinetic energy E \ge E{\text{escape}} overcome cohesive forces and enter the gas phase (vaporisation, endothermic). The molar enthalpy of vaporisation for water at its boiling point is +40.7\ \text{kJ\,mol}^{-1}; condensation is the exothermic reverse (-\Delta{\text{vap}}H). Evaporative cooling of sweat and latent-heat release in rainfall (an inch over an acre liberates >2\times10^8\ \text{kJ}) both stem from these large enthalpies.

Equilibrium Vapour Pressure and Volatility

In a closed vessel liquid and vapour reach a dynamic equilibrium; the pressure exerted is the equilibrium vapour pressure P{\text{vap}}, a direct measure of volatility. Stronger intermolecular forces ⇒ lower P{\text{vap}} at the same T. Plotting \ln P versus 1/T yields a straight line (Clausius–Clapeyron):

\ln P = -\frac{\Delta_{\text{vap}}H}{R}\left(\frac{1}{T}\right)+C

Two-point form:
\ln\frac{P2}{P1} = -\frac{\Delta{\text{vap}}H}{R}\left( \frac{1}{T2}-\frac{1}{T_1} \right)

Example: using vapour‐pressure data for ethylene glycol at T1=373\ \text{K} and T2=398\ \text{K} gives \Delta_{\text{vap}}H\approx59\ \text{kJ\,mol}^{-1}.

Boiling Point and External Pressure

A liquid boils when P{\text{vap}}=P{\text{ext}}. The normal boiling point is referenced to 760\ \text{mm Hg}; water’s is 100\ ^\circ\text{C}, but at Denver’s (650\ \text{mm Hg}) it boils near 95\ ^\circ\text{C}, lengthening cooking times.

Critical Temperature, Pressure and Supercritical Fluids

As T rises P{\text{vap}} climbs until liquid–vapour distinction disappears at the critical point (Tc,Pc). For CO2, Tc=30.99\ ^\circ\text{C} and Pc=72.8\ \text{atm}. Above these, supercritical CO_2, with liquid-like density but gas-like viscosity, is exploited as a green solvent for decaffeinating coffee, extracting hop oils, and processing algae.

Surface Tension, Capillarity and Viscosity

Surface molecules experience a net inward pull, contracting the surface and generating surface tension (energy per unit area) – hence water droplets adopt spherical shapes. Capillary action arises from competition between adhesive (liquid–solid) and cohesive (liquid–liquid) forces: water climbs glass (concave meniscus) whereas mercury, whose cohesion outweighs adhesion to glass, forms a convex meniscus. Viscosity (resistance to flow) increases with stronger intermolecular attractions and with molecular length/branching; olive oil is about 70\times more viscous than ethanol, honey even more so because numerous O–H groups engage in hydrogen bonding.

Applications: Chromatographic Separations and the 2007 Pet-Food Crisis

Chromatography exploits differential intermolecular interactions. In liquid partition chromatography a polar methanol–water mobile phase carries solutes through a non-polar C-18 stationary phase; components that hydrogen-bond or dipole-interact with the mobile phase elute fastest.

In 2007 melamine and cyanuric acid were fraudulently added to pet-food wheat gluten. Individually harmless, together they form an insoluble hydrogen-bonded complex (melamine cyanurate) that precipitates in animal kidneys, causing failure. This tragedy illustrates the real-world consequences of seemingly subtle intermolecular chemistry.

Epilogue: Intermolecular Forces as the Hidden Architects of Matter

From the anomalous density of ice to the double helix of DNA, from geckos scuttling upside-down to supercritical fluids that revolutionise green chemistry, it is the sum of myriad weak, non-covalent forces that shapes the macroscopic world. Mastery of their origins, magnitudes and manifestations enables prediction of physical properties, design of new materials, and understanding of biological function.