Molecular Orbitals and Intermolecular Forces – Comprehensive Study Notes
Molecular Orbitals and Bonding in the Second Row Diatomics (Homonuclear)
Key idea: compare sigma (σ) and pi (π) orbitals from s–p mixing in second-row diatomics; energy ordering changes across the row due to mixing magnitude.
s–p mixing affects the σ2p and π2p energies:
On the left (e.g., B to N region), strong mixing pushes the σ2p orbital up in energy (and the σ*2p up as well), while the π2p orbitals remain relatively at their expected energy. This can lead to σ2p > π2p for early elements.
On the right (e.g., O to F), mixing is reduced; σ2p is less affected and can sit below π2p, giving σ2p < π2p.
Crossover point highlighted: for oxygen, σ2p is lower in energy than π2p; at nitrogen, σ2p is higher than π2p.
Summary electron configurations and bond orders for the second-row homonuclear diatomics (molecule-to-molecule):
Li₂: bond order BO = 1. Adding electrons can go into antibonding orbital, raising BO toward 0.
Be₂: essentially nonexistent (only under special conditions).
B₂: single bond in practice; electrons are unpaired in the SOMO, so paramagnetic.
C₂: double bond; electrons paired in the bonding orbitals; diamagnetic.
N₂: extra electrons occupy σ bonding orbitals; bond order increases to a triple bond (BO = 3).
O₂: some electrons occupy π* antibonding orbitals; ends with two unpaired electrons in π*; BO effectively 2; paramagnetic.
F₂: electrons paired; BO = 1; diamagnetic.
Ne₂: bond order 0 (no stable bond under normal conditions).
Key orbital terms:
HOMO: highest occupied molecular orbital (the highest energy MO that contains electrons).
LUMO: lowest unoccupied molecular orbital (the next available higher-energy MO).
SOMO: singly occupied molecular orbital. When a molecule has one unpaired electron, the HOMO and SOMO are the same; oftentimes the LUMO is the SOMO’s counterpart for radical species.
In many discussions, the SOMO and the HOMO/LUMO designation can merge when there is an unpaired electron.
Heteronuclear diatomics (e.g., CO): energy levels are different due to differing atomic energies; diagrams get skewed; the same MO principles apply, but you typically won’t be asked to draw the diagram for this course—focus on interpretation.
Beyond diatomics: polyatomic molecules
MO theory extends over the entire molecule, giving very large, often delocalized orbitals.
Some MOs are localized on a few atoms; others spread over the whole molecule.
Practical MO calculations for large molecules require computers; exact solutions are computationally heavy.
For practical purposes, Lewis structures with valence-bond insights often explain chemistry well enough.
Guiding wisdom: molecular orbital theory at near-perfect accuracy becomes too complex to be useful for large systems; use simpler models when appropriate.
Interlude on bonding models and evaluation
You should be able to: describe delocalization with MOs, represent with Lewis structures and resonance, draw/interpret MO diagrams for homonuclear diatomics (electron configurations, bond order), and interpret heteronuclear diatomic MO diagrams without drawing them.
Compare strengths/weaknesses of MO vs Lewis/valence approaches; know when to prefer which model (often Lewis + valence concepts suffice).
Intermolecular Forces and States of Matter
Additional intermolecular forces (beyond dipole–dipole and dispersion): blue-box forces
Ion–Dipole: dominant when dissolving ionic salts; strong interaction between ions and solvent dipoles; crucial for solubility of salts in water.
Ion–Induced Dipole: a nearby ion distorts the electron cloud of a molecule, creating a dipole; weaker than permanent dipole interactions; can occur with large ions allowing some dissolution in nonpolar media.
Dipole–Induced Dipole: a polar molecule induces a dipole in a nonpolar neighbor; weaker still; important for life processes (e.g., oxygen solubility in water is aided by polar environments).
Life-relevant examples and context
Water is polar; oxygen is nonpolar and dissolves in water mainly via dipole-induced dipole interactions.
Hydration and dissolution depend on both permanent dipoles and induced dipoles; interactions enable biological processes and transport (e.g., oxygen transport in blood requires dissolution through these weak interactions).
Comparative solubilities (illustrative values):
NaCl in water: high solubility due to strong ion–dipole interactions; ≈ 6 mol/kg H₂O.
I₂ in water: very low solubility; dominated by dispersion and induced-dipole forces; ≈ 0.003 mol/kg.
O₂ in water: very limited solubility; dispersive/induced interactions dominate.
Sucrose in water: high solubility due to extensive hydrogen bonding; ≈ 2 mol/kg; effectively large mass dissolving.
Ethanol and water: miscible in all compositions (broad H-bonding).
Hexane in water: immiscible due to nonpolar nature.
Big molecules and phase behavior
Large biomolecules/molecules with distinct polar and nonpolar ends may be polar in one region and nonpolar in another; e.g., surfactants can self-assemble in water to form micelles, vesicles, liposomes, etc.
Micelle: spherical assembly with a hydrophobic interior and hydrophilic exterior; hydrophobic tails cluster inside, polar heads face outward toward water.
Vesicle: elongated micelle-like structure; liposome: vesicle with hydrophilic interior; lipid bilayers form most cell membranes.
Amphipathic molecules
Amphoteric term: molecules with both polar (hydrophilic) and nonpolar (hydrophobic) regions; behavior in water depends on balance of interactions.
Surfaces and wetting
Water tends to adhere to polar surfaces (e.g., glass) due to hydrogen bonding; coating surfaces with hydrophobic groups (alkyl chains) reduces adhesion and causes water to bead up and roll off.
Capillary action: rise of liquid in a narrow tube due to cohesive vs adhesive forces; concave vs convex menisci depend on relative strengths.
Surface tension and contact angles
Surface tension results from molecules at surface experiencing a net inward cohesive force.
If adhesive forces to a surface are strong, you get a concave meniscus (water climbs a glass surface).
If cohesive forces dominate (surface is nonpolar/hydrophobic), you get a convex meniscus (water beads).
Viscosity and flow
Viscosity: resistance to flow; higher viscosity means slower flow.
Factors: intermolecular forces, molecular size/shape, temperature; larger, long-chain molecules tend to be more viscous due to entanglements.
For liquids with similar size, stronger intermolecular forces yield higher viscosity.
Solutions, Vapor Pressure, and Real-Gas Behavior
Ideal vs real solutions and Raoult’s Law
Ideal solution assumption: gas phase behaves as if the liquid components were non-interacting; each component contributes to vapor pressure independently.
Raoult’s Law: for an ideal solution, the partial vapor pressure of component i is Pi = xi Pi^, where xi is the mole fraction of component i in the liquid and P_i^ is the vapor pressure of pure component i.
Total vapor pressure: P =
abla \, Pi = \sumi xi Pi^*.
Non-ideality and deviations from Raoult’s Law
Positive deviation: vapor pressure is higher than predicted; weaker intermolecular forces in the mixture than in pure components.
Negative deviation: vapor pressure is lower than predicted; stronger intermolecular forces in the mixture.
Azeotrope: a point where liquid and vapor compositions are identical; distillation cannot separate beyond this composition because boiling distilled mixture yields same composition in liquid and vapor.
Non-ideal mixing and Henry’s Law (gas dissolution in liquids)
Henry’s Law: for dissolution of a gas in a liquid, the concentration of dissolved gas is proportional to its partial pressure: C = kH Pg. Each gas has its own Henry’s constant k_H.
Temperature dependence: for gases, increasing temperature generally decreases gas solubility in liquids (Le Chatelier’s principle; gas prefers to escape when hotter).
Distillation and vapor-liquid equilibria
Distillation relies on differences in vapor pressures; more volatile components vaporize more readily.
Fractional distillation exploits differing partial pressures to separate components.
In mixtures with azeotropes, separation by simple distillation is limited; may require special techniques.
Practical example: acetone–water at 20°C (example calculations from lecture)
Given: acetone vapor pressure at 20°C is P^{acetone} = 21.3 ext{ kPa}; water vapor pressure at 20°C is P^{water} = 2.3 ext{ kPa}.
For an 80% water by number (mole fraction xW = 0.8, xA = 0.2):
Partial pressure of acetone: P{acetone} = xA P^*_{acetone} = 0.2 imes 21.3 = 4.26 ext{ kPa}.
Partial pressure of water: P{water} = xW P^*_{water} = 0.8 imes 2.3 = 1.84 ext{ kPa}.
Total vapor pressure: P{total} = P{acetone} + P_{water} = 6.1 ext{ kPa}.
Gas phase composition (mole fractions): Water ≈ rac{1.84}{6.1}
abla ext{, acetone}
abla rac{4.26}{6.1} ≈ 0.30 and 0.70 respectively; acetone dominates the vapor due to higher volatility.This illustrates distillation: more volatile component (acetone) is preferentially carried into the gas phase, allowing separation.
Non-ideality in solutions
If intermolecular forces between mixed components are weaker than in the pure components, vapor pressures tend to be higher (positive deviation) and components may separate more readily.
If intermolecular forces between components are stronger, vapor pressures tend to be lower (negative deviation) and components mix more thoroughly, potentially forming azeotropes.
Henry’s law vs Raoult’s law in practice
Gases in liquids often deviate from Raoult’s law; Henry’s law provides a better description for solubility of gases in liquids, with gas-specific constants that vary with temperature.
Phase diagrams and critical phenomena
Phase diagrams show solid–liquid–gas boundaries; the critical point marks the end of the liquid–gas boundary; beyond this point, the substance becomes a supercritical fluid.
Crossing phase boundaries can damage delicate materials; supercritical drying avoids crossing a liquid–gas boundary by moving through the supercritical region (high pressure, then supercritical state, then depressurize) to preserve delicate structures (e.g., SEM sample prep, aerogels).
Practical Implications and Real-World Contexts
Phase transitions and boiling points
Boiling point is the temperature at which the vapor pressure equals the ambient pressure.
Normal boiling point refers to 1 atm (one atmosphere) pressure; boiling line exists for other pressures as well.
Generally, larger molecules have higher boiling points due to greater dispersion forces; for similarly sized molecules, stronger dipole moments raise boiling points.
Hydrogen bonding often overrides size effects (e.g., HF, H2O) and can lead to unusually high boiling points; exceptions occur, especially with very large, nonpolar molecules where dispersion dominates.
Boiling points across groups and trends
Across a group: larger atoms/molecules tend to have higher boiling points due to stronger dispersion forces.
Hydrogen-bonding compounds often show elevated boiling points compared with non-H-bonded analogs, sometimes overriding size trends.
For first-row vs second-row elements, hydrogen bonding can heavily skew trends (e.g., HF, H2O).
Phase behavior of gases and vapors
Real gases deviate from ideal gas behavior, especially at high pressures; PV/(nRT) deviates from 1 due to finite molecular size (b term) and intermolecular attractions (a term).
van der Waals equation captures these deviations: igl(P + a rac{n^2}{V^2}igr)(V - nb) = nRT.
In the low-pressure, high-volume limit, real gases behave like ideal gases (a and b corrections negligible).
Applications: supercritical drying and aerogels
Supercritical drying avoids liquid–gas phase transitions by crossing through a supercritical region, preserving delicate structures (e.g., biological samples for electron microscopy) and enabling porous materials like aerogels.
Aerogels: highly porous, low-density solids formed via supercritical drying; useful for insulation and other applications.
Biological relevance of intermolecular forces
Proteins and amino acids: primary structure (peptide bonds) is covalent; secondary structure (alpha helices, beta sheets) stabilized by intramolecular hydrogen bonding; side chains (R groups) govern polarity and interactions.
Amphipathic amino acids and proteins: the balance of polar and nonpolar regions drives folding and interactions in aqueous environments.
Quick Reference: Key Equations to Know
Ideal gas law:
PV = nRTvan der Waals equation (real gases): igl(P + a rac{n^2}{V^2}igr)(V - nb) = nRT
a: strength of intermolecular attractions; larger a for stronger interactions and larger molecules.
b: volume excluded by finite molecular size; larger b for larger molecules.
Raoult’s law for ideal solutions:
Partial pressure: Pi = xi P_i^*
Total pressure: P =
ablai xi P_i^*
Henry’s law for gas solubility in liquids:
C = kH PgDistillation concept: the vapor-phase composition follows from partial pressures; fractionating depends on relative volatility.
Azeotrope: a point where liquid and vapor compositions are identical; simple distillation cannot separate beyond this composition.
Phase diagram concepts: critical point (Tc, Pc); supercritical fluid region; surface phenomena influence wetting and capillarity.
Quick Term Sketches (for exam recall)
HOMO: highest occupied MO; LUMO: lowest unoccupied MO; SOMO: singly occupied MO.
BO (bond order): an indicator of bond strength; typically BO = (number of bonding electrons − number of antibonding electrons)/2.
Amphoteric: molecule with two different functional groups, often with both acidic and basic character.
Micelle / Vesicle / Liposome: self-assembled structures from amphiphiles in water; hydrophobic cores or interiors, hydrophilic exteriors.
Critical point: end of liquid–gas boundary; above this, supercritical fluid forms.
Azeotrope: mixture with identical liquid and vapor compositions at a given T; distillation cannot achieve complete purification.
If you want, I can tailor these notes to a specific section you expect on the exam (MO theory, solution chemistry, or phase behavior) and expand any bullet into a mini-study card with a worked example.