London dispersion forces Knowledge-Based Study

Study notes

1. What Are London Dispersion Forces?

   London dispersion forces (often simply called dispersion forces or London forces) are weak intermolecular attractions that arise from temporary fluctuations in electron density within atoms or molecules. Named after the physicist Fritz London, they represent the weakest class of van der Waals forces, yet they are ubiquitous—occurring between all atoms and molecules, whether polar or nonpolar.

   In nonpolar substances such as noble gases (e.g., He, Ne, Ar) or symmetric diatomic molecules (e.g., $N_2$, $O_2$), dispersion forces are the sole intermolecular force holding particles together in the liquid and solid states.

   The Mechanism: Instantaneous and Induced Dipoles

   • Instantaneous Dipole: Electrons are in constant, probabilistic motion around atomic nuclei. At any given instant, electron distribution may become uneven, generating a momentary, asymmetrical charge distribution known as an instantaneous dipole.
   • Induced Dipole: The momentary partial negative charge ($\delta-$) on one atom repels the electron cloud of an adjacent neighbor, shifting its electrons and inducing a complementary dipole ($\delta+$ next to $\delta-$).
   • Attractive Interaction: The temporary electrostatic attraction between these complementary poles constitutes the dispersion force. Although each individual dipole lasts only a fraction of a second, the continuous formation and collapse across vast numbers of particles produce a persistent net attraction.

   Key Determinants of Dispersion Force Strength

   The magnitude of London dispersion forces varies widely and depends primarily on two physical factors: polarizability (associated with electron count and size) and molecular shape.

   1. Polarizability and Molecular Size

   Polarizability is the ease with which an electron cloud can be distorted by an external electric field or a neighboring charge.

   • Number of Electrons: Atoms and molecules with more electrons possess larger electron clouds held less tightly by the nucleus. Larger clouds are more readily deformed, leading to stronger instantaneous dipoles and stronger dispersion forces.
   • Periodic Trends: Down a group in the periodic table, atomic radii increase and electron counts grow, markedly increasing polarizability. For example, down Group 18, boiling points steadily rise from helium to xenon:
     • Helium ($He$): 2 electrons, boiling point = $4.2\text{ K}$
     • Neon ($Ne$): 10 electrons, boiling point = $27.1\text{ K}$
     • Argon ($Ar$): 18 electrons, boiling point = $87.3\text{ K}$
     • Krypton ($Kr$): 36 electrons, boiling point = $119.9\text{ K}$
     • Xenon ($Xe$): 54 electrons, boiling point = $165.0\text{ K}$

   2. Molecular Shape and Surface Area

   When molecules have identical chemical formulas and molecular weights (isomers), molecular geometry dictates the degree of surface contact:

   • Linear / Elongated Molecules: Extended chains have greater surface area accessible for intermolecular contact. More contact points allow additive dispersion attractions along the length of the molecule.
   • Spherical / Branched Molecules: Compact or highly branched structures minimize surface area per unit volume, reducing the contact area between neighboring molecules and weakening dispersion attractions.
   • Example: Pentane ($n$-pentane) and 2,2-dimethylpropane (neopentane) both have the formula $C_5H_{12}$. Pentane is an elongated chain and boils at $36.1\text{ }^\circ\text{C}$, whereas spherical neopentane boils at only $9.5\text{ }^\circ\text{C}$.

   Impact on Physical Properties

   London dispersion forces directly govern macroscopic phase-change properties such as melting point, boiling point, and enthalpy of vaporization in nonpolar and predominantly covalent substances.

   The Halogen Group Demonstration

   The Group 17 halogens clearly illustrate how increasing molar mass and electron count strengthen dispersion forces at room temperature ($25\text{ }^\circ\text{C}$):

   • Fluorine ($F_2$): 18 total electrons; very weak dispersion forces; gas at room temperature.
   • Chlorine ($Cl_2$): 34 total electrons; moderate dispersion forces; gas at room temperature.
   • Bromine ($Br_2$): 70 total electrons; substantial dispersion forces; reddish-brown liquid at room temperature.
   • Iodine ($I_2$): 106 total electrons; strong dispersion forces; dark violet solid at room temperature.

   Dispersion in Polar and Large Molecules

   A common misconception is that dispersion forces are always the weakest intermolecular forces in a given system. While an individual instantaneous dipole-induced dipole interaction is weak, dispersion forces are cumulative.

   In large or high-molar-mass molecules, the sum of all dispersion interactions can exceed dipole-dipole attractions and even hydrogen bonding. For instance, nonpolar hydrocarbon polymers (such as polyethylene) or high-mass nonpolar oils exist as liquids or solids strictly due to extensive dispersion forces.

   Key Concept Summary

   • London dispersion forces are electrostatic attractions between temporary (instantaneous) dipoles and complementary induced dipoles.
   • They exist in all substances, regardless of polarity.
   • The magnitude of dispersion forces increases with greater polarizability (more electrons, larger molecular mass, larger atomic radius) and greater molecular surface area (elongated versus branched shapes).
   • Nonpolar substances rely entirely on dispersion forces for condensation into liquids and freezing into solids.

   Check Your Understanding

   Consider the following pairs and identify which substance exhibits stronger London dispersion forces:

   1. $CH_4$ vs. $CCl_4$: $CCl_4$ has 74 electrons compared to 10 in $CH_4$. The significantly larger electron cloud of $CCl_4$ confers higher polarizability, giving it far stronger dispersion forces and a much higher boiling point ($76.7\text{ }^\circ\text{C}$ vs. $-161.5\text{ }^\circ\text{C}$).
   2. Hexane vs. 2,2-Dimethylbutane: Both share the formula $C_6H_{14}$. Hexane has a linear zigzag carbon chain, providing a larger surface area of contact than the compact, branched 2,2-dimethylbutane. Consequently, hexane has stronger dispersion forces and a higher boiling point.