Foundations

Nitrogen fixation converts N₂ toward biologically usable reduced nitrogen; ammonification, nitrification and denitrification transform nitrogen among distinct chemical pools.

Silicate structures organize silicon–oxygen tetrahedra as isolated units, chains, sheets or frameworks.

Metamorphism changes mineral assemblage and texture under changed pressure, temperature, fluid and deformation conditions without requiring bulk melting.

Mechanical weathering changes fragment size; chemical weathering transforms or dissolves minerals through reactions such as hydrolysis and oxidation.

A distribution coefficient relates one species' concentrations in two specified coexisting phases.

In homogeneous constant-D batch melting, mass balance and equilibrium give melt enrichment Cℓ/C₀=1/[D+F(1−D)].

Groundwater exchanges dissolved species with aquifer minerals and surfaces.

Dissolved inorganic carbon includes aqueous CO₂/carbonic-acid convention, bicarbonate and carbonate.

For a balanced reaction with signed stoichiometric coefficients νᵢ, the reaction quotient is the product of activities raised to those coefficients.

The molar Gibbs energy of a reaction at its current composition is ΔᵣG = ΔᵣG° + RT ln Q.

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.