Foundations

For HA ⇌ H⁺ + A⁻ in a stated solvent convention, Ka relates the equilibrium activities.

Quantitative aqueous speciation combines equilibrium relations with conservation of analytical amounts and electroneutrality.

A polyprotic acid loses protons through successive equilibria, each with its own ionization constant.

Rearranging the acid dissociation relation gives pH=pKa+log₁₀(aA⁻/aHA).

A titration equivalence point is fixed by reaction stoichiometry, whereas an observed endpoint is a measurement criterion.

A Lewis base donates an electron pair and a Lewis acid accepts it in forming an adduct.

For an ideal liquid solution in equilibrium with an ideal vapour, Raoult's law gives each component's partial pressure as its liquid mole fraction times its pure-liquid vapour pressure at the same temperature.

For an ideal dilute solution separated from pure solvent by a solvent-permeable membrane, osmotic pressure is approximately the molar concentration of osmotically active solute particles times RT.

For equilibrium among phases in a system described by independent components, the Gibbs phase rule gives F=C−P+2.

For irreversible loss of one species with constant rate coefficient, integrating −dc/dt=k cⁿ gives c=c₀−kt for n=0, c=c₀e⁻ᵏᵗ for n=1, and 1/c=1/c₀+kt for n=2.

A low-concentration intermediate can have approximately equal formation and consumption rates after a short transient, allowing its rate equation to be eliminated from a mechanism.

Transition-state theory relates an elementary rate coefficient to a constrained activated-complex equilibrium and a crossing frequency.

The Born–Oppenheimer approximation separates electronic and nuclear motion by solving an electronic problem at fixed nuclear geometry and then describing nuclear motion on the resulting energy surface.

Hartree–Fock variationally optimizes a single-determinant description including mean Coulomb and exchange interactions.

Conformations differ by rotations about bonds without changing connectivity.

For a tetrahedral stereogenic centre, rank attached groups by the Cahn–Ingold–Prelog rules: atomic number first, isotopic mass for isotopes, then the first point of difference with multiple-bond duplication.

For an alkene whose two substituents on each double-bond carbon can be distinguished, assign CIP priority independently on each carbon.

An SN2 step forms a bond to a nucleophile as the leaving group departs through one transition state.

In a simple SN1 pathway, slow substrate ionization forms a carbocation-containing intermediate before nucleophilic capture.

In an E2 step, removal of a β hydrogen, formation of an alkene bond and leaving-group departure occur together.

E1 elimination proceeds through ionization followed by loss of a proton from a carbocation intermediate.

In carbocation-mediated addition of HX to an alkene, protonation creates an intermediate that a nucleophile subsequently captures.

In the elementary Hückel description, a planar cyclic continuously conjugated π system with 4n+2 π electrons has a closed-shell aromatic pattern.

In a typical electrophilic aromatic substitution, the aromatic π system bonds to an electrophile, forming a nonaromatic σ intermediate.

A nucleophile adds to the electrophilic carbonyl carbon while the π electron pair moves toward oxygen, forming a tetrahedral intermediate.

For a carboxylic acid derivative, nucleophilic addition can form a tetrahedral intermediate whose collapse expels a leaving group and restores the carbonyl.

Removal of an α proton from a suitable carbonyl compound forms an enolate whose charge is distributed between oxygen and carbon by conjugation.

In a simple aldol pathway, an enolate or enol donor adds to another carbonyl acceptor to create a carbon–carbon bond.

A radical chain has initiation steps that generate radicals, propagation steps that transform reactants while regenerating a radical carrier, and termination steps that consume carriers.

Kinetic control favours products formed more rapidly before equilibration; thermodynamic control reflects an accessible equilibrium product distribution.