AP Chemistry Notes: Intermolecular Forces and Properties of Substances (Comprehensive)
3.1 Intermolecular Forces
Van der Waals forces overview
London Dispersion Forces (LDF): temporary dipole → induced dipole attractions present in all substances; usually the weakest, often negligible when stronger forces exist; strength increases with larger electron clouds and shorter interatomic distance; represented by F = q1 q2 / r^2, noting that larger partial charges (q1 q2) and shorter distance (r^2) strengthen the interaction. In larger atoms, outer shells are farther from the nucleus, wobble more, and create larger partial charges, leading to stronger LDFs.
Dependence on molecular size and shape: LDFs increase with molecular size; branched alkanes have smaller surface areas than their chain isomers, leading to weaker LDFs; π-bond electrons can also wobble to increase LDFs.
Nonpolar substances rely on LDFs as their primary intermolecular attraction.
Permanent dipole–dipole interactions
Occur when molecules have significant electronegativity differences and shapes allow dipoles to align; typically stronger than LDFs in equivalent molecules.
Example: butane vs acetone; acetone has a stronger dipole-dipole interaction contributing to higher mp due to permanent dipoles.
Hydrogen bonding (special dipole–dipole interaction)
Enhanced dipole–dipole attraction when H is bonded to N, O, or F, producing a highly polar bond.
Hydrogen bond forms between molecules with δ+ H (on X–H) and a lone pair on another electronegative atom (N, O, F) in a neighboring molecule; often shown as a linear arrangement with H bridging two electronegative atoms.
Hydrogen bonding markedly raises boiling points (e.g., HF, H2O, NH3, etc.).
Relative strengths and examples
LDFs < Dipole–Dipole < Hydrogen bonding (in many cases for comparable molecules).
Additional points
The charges in ions (q1, q2) are full elementary charges; partial charges δ+ and δ− arise from electron distribution and are harder to quantify but still obey Coulombic principles.
3.2 Properties of Solids
General solid features
Solids can be crystalline (regular three-dimensional order) or amorphous (no long-range order).
In all solids, particle motion is limited to vibration; interparticle interactions and packing influence structure.
Ionic lattices
Strong interactions at short distances; high melting/boiling points; solids at standard conditions.
Coulomb force: F = \frac{q1 q2}{r^2}; lattice enthalpies depend on ion charges (|q1 q2|) and ion–ion distances (r).
Melting/boiling points high; vapour pressures very low; brittle due to lattice distortion causing repulsion.
Distance approximated as the sum of ionic radii; same charge with smaller radii → stronger lattice enthalpy.
Covalent networks
Very strong, extensive covalent bonding across a network; high mp; electrons largely immobile; poor electrical conductivity.
Most networks are tetrahedral (sp^3) with strong bonds; e.g., diamonds have extremely high mp (~3500 °C) under normal pressure; graphite is an exception due to layered structure with delocalised electrons, giving conductivity along layers.
Graphite: each carbon forms 3 σ bonds in a plane with delocalised π electrons, enabling conductivity; layers held together by weaker London dispersion forces; layers can slide, making graphite soft and a lubricant.
Metallic lattices
Delocalised electrons form a ‘sea’ around metal cations; good electrical and thermal conductivity; malleable and ductile.
Melting points vary across metals (Hg liquid at room temp; Cs melts near 28.4 °C; W ≈ 3680 °C).
Alloys: substitutional and interstitial; properties can be tuned (e.g., brass, steel). Interstitial carbon atoms in iron increase hardness but reduce malleability.
Covalent molecular solids
Intermolecular forces (LDFs, dipole–dipole, and hydrogen bonding) hold molecules together; many are liquids or gases at s.p.t. but some can be solids with relatively low mp.
I2 is an example of a covalent molecular solid with significant LDFs.
Summary points
Ionic lattices: strong electrostatic interactions, high mp; brittle.
Covalent networks: very high mp, non-conductors (except graphite).
Metals/alloys: mobile electrons, high conductivity, malleable/ductile.
Covalent molecular solids: weaker overall attractions, mp moderate to low unless strong hydrogen bonding or highly polar molecules present.
3.3 Solids, Liquids & Gases
Solids
Crystalline vs amorphous; particles fixed in position; vibration only.
Packing and interparticle forces determine the exact structure.
Liquids
Closely packed particles that can flow; definite volume but no definite shape; density and melting points depend on intermolecular forces.
Water is anomalous: ice expands upon freezing due to extensive hydrogen bonding, creating a hexagonal lattice which holds molecules further apart; this makes solid water (ice) less dense than liquid water, so ice floats.
Gases
Particles are in continuous, random motion with negligible intermolecular forces at typical conditions; no definite volume or shape; highly compressible.
Key comparisons
Similar molar volumes for solids and liquids due to close particle spacing, except water’s anomaly.
3.4 Ideal Gas Law
Foundational gas laws
Boyle’s Law: for constant n and T, V ∝ 1/P; expressed as PV = ext{constant}.
Charles’s Law: for constant n and P, V ∝ T; expressed as V = kT or \frac{V}{T} = \text{constant}.
Avogadro’s Law: for constant P and T, V ∝ n; expressed as V = k n.
Ideal gas equation
Combined gas law: PV = nRT where R is the gas constant.
Common SI value: R = 0.08206\ \mathrm{L\,atm\,mol^{-1}\,K^{-1}}
Temperature must be in Kelvin; amount in moles; pressure in atm (or convert units accordingly).
STP: 1 mole occupies 22.4 L at standard temperature and pressure (0 °C, 1 atm) depending on convention; many experiments use 22.4 L (STP) or 24.0 L (some modern definitions).
Examples from the notes
Example 1: SF6 in a 5.43 L vessel at 69.58 °C with 1.82 mol:
Convert T to Kelvin: T = 342.5\ \text{K}
Use P = \dfrac{nRT}{V} to find P \approx 9.42\ \text{atm}.
Calculation shown: P = \dfrac{(1.82\ \text{mol})(0.08206\ \mathrm{L\,atm\,mol^{-1}\,K^{-1}})(342.5\ \text{K})}{5.43\ \text{L}} = 9.42\ \text{atm}.
Example 2: NO, 2.12 mol, at 6.54 atm and 768 °C in a certain volume.
Temperature in K: T = 1041\ \text{K}
Volume: V = \dfrac{nRT}{P} = \dfrac{(2.12)(0.08206)(1041)}{6.54} \approx 27.69\ \text{L}
Assumptions of the kinetic molecular theory and ideal gas behavior
Two key assumptions for ideal behavior (not perfectly true in real gases):
Molecules have negligible volume
No intermolecular attractions
In reality, gas molecules do have volume and weak attractions; under many conditions (not too high P or too low T) the ideal gas equation provides accurate predictions.
Gas mixtures and Dalton’s law
For mixtures, partial pressures add: P{\text{total}} = P1 + P_2 + \cdots
Each gas contributes proportionally to its mole fraction: Pi = P{\text{total}} \times Xi\quad\text{where}\quad Xi = \dfrac{ni}{n{\text{total}}}
Still governed by PV = nRT for each component with the same T and V.
3.5 Kinetic Molecular Model
Five postulates of the theory
1) Gases consist of large numbers of molecules in continuous, random motion.
2) The combined volume of all gas molecules is negligible relative to the container volume.
3) Attractive and repulsive forces between gas molecules are negligible.
4) Energy can be transferred between molecules during collisions, but at constant temperature the average kinetic energy remains constant.
5) The average kinetic energy is proportional to the absolute temperature: \text{KE} = \tfrac{1}{2} m v^2,\quad \text{and at a given T, all gases have the same average KE.}Consequences of mass and speed
Heavier molecules move more slowly at the same temperature than lighter ones.
The speed distribution depends on mass: lighter molecules diffuse and effuse faster than heavier ones (e.g., HCl (36.5 amu) vs NH3 (17 amu)).
Effusion and diffusion
Rate of effusion and diffusion increases as molecular mass decreases.
3.6 Deviation from Ideal Gas Law
When do real gases diverge from ideal behavior?
Temperature effects: lowering temperature reduces kinetic energy, increasing the likelihood of intermolecular attractions; deviations increase as gases are cooled.
Pressure effects: at low pressure (< about 10 atm) deviations are small; at high pressure (> 10 atm) deviations are larger and gas-specific.
Generally, at very high pressures or very low temperatures, real gases deviate significantly from ideal behavior.
3.7 Solutions & Mixtures
Pure substances vs mixtures
Pure substances: elements or compounds; can write a chemical formula.
Mixtures: two or more components; can be homogeneous (solutions) or heterogeneous.
Solutions (a homogeneous mixture)
In a solution, solute particles disperse throughout the solvent.
The ease of solute dissolution depends on three central interactions:
Solute–solute interactions to be overcome to disperse solute.
Solvent–solvent interactions to be overcome to make room for solute.
Solvent–solute interactions that occur as particles mix.
Solvent and solute roles
The component in greater quantity is the solvent; the other is the solute.
3.8 Representations of Solutions
Primary standards and standard solutions
A primary standard is a pure, stable substance weighed accurately (2–3 decimal places) and dissolved to prepare a standard solution for calibration or titration.
Concentration formula: M = \dfrac{n}{V} \quad\text{(mol L}^{-1}\text{)}
Weighing by difference can minimize errors.
Standardization and secondary standards
Many acids/bases cannot be prepared directly from solids due to moisture or reaction with air; they are standardized against primary standards.
Dilution and stock solutions
Dilution rule: M{\text{stock}} \times V{\text{stock}} = M{\text{new}} \times V{\text{new}}
Example: 25 mL of 0.25 M solution diluted to 500 mL gives a new concentration of 0.0125 M.
Calibration and spectrophotometry
Calibration curves relate absorbance to concentration; preparation of multiple known concentrations for a linear relationship is common.
Important practical notes
Use consistent cuvettes, avoid contamination, and ensure linear response by staying within the working concentration range.
3.9 Separation of Solutions & Mixtures
Filtration
Effective when precipitating a solute selectively via chemical reaction or temperature differences; not always practical for complete recovery.
Distillation and evaporation
Distillation separates components by differing boiling points; useful for separating a solute from solvent (e.g., salt from water).
Desalination uses distillation/evaporation to obtain fresh water.
Fractional distillation
Uses a tall column to separate miscible liquids with different volatilities; vapors rise, condense at different heights, and are collected sequentially.
Solvent extraction
Uses two immiscible solvents; solutes partition according to differential solubilities; practical for separating a solute from a mixture; typically multiple extractions improve yield.
Chromatography
Mobile phase (solvent) and stationary phase (often paper or resin) separate components by differing affinities.
Retention factor (Rf): ratio of distance moved by compound to distance moved by solvent; TLC and column chromatography are common forms.
Gas-layer chromatography (gas chromatography)
Carried out in a column with a carrier gas; separation depends on interactions with stationary phase.
3.10 Solubility
General solubility principles
Solute–solvent interactions must be at least as strong as solute–solute or solvent–solvent interactions for dissolution to occur readily.
“Like dissolves like” is a useful rule of thumb, though not absolute; polar solvents dissolve polar solutes best, nonpolar solvents dissolve nonpolar solutes best.
Examples: hydrocarbons dissolve in each other; short-chain alcohols dissolve in water due to hydrogen bonding; solubility of larger alcohols decreases with increasing hydrocarbon chain length due to dominating LDFs.
Ionic solubility and Ksp (solubility product)
Water is highly polar and can dissolve many ionic substances; dissolution is often treated as a reversible equilibrium: dissolution ⇄ solid ⇌ ions in solution.
Ksp expresses the equilibrium level of dissolution; e.g., NaCl is effectively soluble (highly dissociated), often described as complete dissolution in water, while PbI2 has a very small Ksp (~1.4 × 10^−8), indicating very low solubility.
Thermodynamic and environmental considerations
Enthalpy and entropy changes influence dissolution; dissolution may be endothermic or exothermic depending on solute/solvent pairs.
Temperature can affect solubility; many ionic solids become more soluble with increasing temperature, but not universally (e.g., some salts). Gas solubility in water generally decreases with increasing temperature.
Environmental note: oceanic oxygen solubility decreases as sea temperature rises, affecting aquatic life; rising CO2 in seawater and temperature changes can influence buffering and climate effects.
3.11 Spectroscopy & Electromagnetic Spectrum
Electromagnetic spectrum basics
Energy of radiation relates to frequency by \Delta E = h\nu, where h is Planck’s constant; visibility spans roughly 400–800 nm; energy can be absorbed or emitted when electrons transition between energy levels.
Wavelength–frequency–energy relations: c = \lambda \nu and \Delta E = \dfrac{hc}{\lambda}.
Spectroscopic techniques and uses
NMR spectroscopy (nuclear magnetic resonance): uses nuclear spin states to deduce structure; relies on magnetic environments around nuclei (e.g., 1H, 13C).
Microwave spectroscopy: rotational transitions probe molecular rotations.
Infrared (IR) spectroscopy: molecular vibrations; identifies functional groups (C–H, C=O, C–O, etc.).
UV-Vis spectroscopy: electronic transitions; color and absorption bands in visible light; used to infer conjugation and presence of chromophores.
X-ray photoelectron spectroscopy (PES): measures binding energies and electronic structure by removing electrons.
Practical example notes
Indigo carmine dye absorbs in red-orange-yellow, transmitting blue-purple; strongest absorbance around a particular wavelength; measurement often performed near 615 nm due to instrument practicality.
Rotational, vibrational, and electronic transitions provide distinct spectral fingerprints for molecules.
3.12 Properties of Photons
Photon energy and its relation to electromagnetic radiation
Photon energy: \Delta E = h\nu; frequency–energy relation via \nu = c/\lambda and \Delta E = \dfrac{hc}{\lambda}.
Practical calculations
Balmer series example: energy of n=6 → n=2 transition with \lambda = 410\,\text{nm}:
Convert to meters: \lambda = 410\times 10^{-9} \text{ m}
\Delta E = \dfrac{hc}{\lambda} = \dfrac{(6.626\times 10^{-34}\ \mathrm{J\,s})(3.00\times 10^{8}\ \mathrm{m\,s^{-1}})}{410\times 10^{-9}\ \mathrm{m}} \approx 4.85\times 10^{-19}\ \mathrm{J} per photon.
For one mole of photons: \Delta E{mol} = \Delta E \times NA = 4.85\times 10^{-19}\ \mathrm{J} \times 6.023\times 10^{23}\ \mathrm{mol^{-1}} \approx 2.92\times 10^{5}\ \mathrm{J\,mol^{-1}} = 2.92\ \mathrm{kJ\,mol^{-1}}.
Another example uses PES data: if 1.31 MJ mol^−1 is the energy needed to remove an electron, compute the corresponding wavelength via \lambda = \dfrac{h c}{\Delta E} with Avogadro’s number for conversion to per-mole values.
General note
Lyman, Balmer, and other spectral series provide lines corresponding to electronic transitions; visible lines contribute to color, while UV/VIS spectroscopy informs about electronic structure.
3.13 Beer–Lambert Law
Colorimetry fundamentals
Absorbance (A) is related to concentration (c) and path length (b) via the Beer–Lambert law:A = \varepsilon b c where \varepsilon is the molar absorptivity (units: M^−1 cm^−1).
The law assumes constant conditions: same wavelength, cuvette, temperature, and solvent.
Practical aspects
Absorbance is proportional to concentration and path length; the slope of a plot of A vs. c yields ε; the linear region provides a reliable calibration curve.
Non-ideal behaviors can occur at high concentrations due to inter-molecular interactions; instrument calibration and using suitable cuvette geometry are crucial.
3.1–3.13 recap: core relations and constants to remember
Coulombic interactions (broad): F = \dfrac{q1 q2}{r^2} (for point charges) and the role of partial charges in intermolecular attractions.
Ideal gas law and constants:
PV = nRT with R = 0.08206\ \mathrm{L\,atm\,mol^{-1}\,K^{-1}}, temperatures in K, volumes in L, P in atm.
For mole quantities: V = \dfrac{nRT}{P}; for n in moles and P in atm.
1 mol of any gas at STP occupies 22.4 L (conventional value; note that some definitions use 24.0 L depending on the standard).
Molar absorptivity and Beer–Lambert principles are used to connect spectrophotometry data to concentrations.
Ksp (solubility product) concepts explain why some ionic solids dissolve little in water (e.g., PbI2 with Ksp ~ 1.4×10^−8).
Basic climate-relevant solubility considerations emphasize how temperature affects gas solubility in water and how oceanic chemistry interacts with climate changes.
Key formulas (for quick reference):
PV = nRT
V = \dfrac{nRT}{P}
V = kT or \dfrac{V}{T} = \text{constant} (Charles’s Law)
V = kn (Avogadro’s Law)
Pi = P{\text{total}} \cdot Xi = P{\text{total}} \cdot \dfrac{ni}{n{\text{total}}}
A = \varepsilon b c (Beer–Lambert Law)
\Delta E = h\nu = \dfrac{hc}{\lambda}
E_{\text{photon}} = \dfrac{hc}{\lambda}
\text{KE} = \tfrac{1}{2} m v^2
F = \dfrac{q1 q2}{r^2} (Coulomb’s law as presented in these notes)
Note on units and practice
Ensure temperature is always in Kelvin when using the ideal gas law.
When performing dilution, maintain consistent units for volumes (any unit works as long as it is the same on both sides of the equation).
Always consider whether a system truly behaves ideally before applying the ideal gas law at extreme P/T conditions.
Real-world relevance
Solubility and phase behavior influence environmental processes (e.g., ocean chemistry, climate-related changes in gas solubility, and solubility of minerals).
Spectroscopy and Beer–Lambert law underpin many analytical techniques across chemistry and biology, including quantitative colorimetric assays and spectrophotometric calibration.