Foundations

The mole is linked to a specified number of entities.

A reference material is sufficiently homogeneous and stable for specified properties and an intended measurement or examination use.

A detection limit depends on the measurement procedure's false-presence probability α and false-absence probability β.

An analytical result concerns the sampled material; inference to a larger population requires a defensible sampling plan.

A detection limit specifies a decision about distinguishability from an appropriate blank or background, with a stated statistical model.

Gravimetry infers analyte amount from a measured mass or mass change and a known chemical or physical relation.

Retention factor measures time spent beyond an unretained marker relative to its transit time.

Molecular infrared absorption probes transitions between vibrational states.

Nuclear magnetic resonance distinguishes magnetically responsive nuclei in different electronic environments.

Coupled nuclear spins can split resonances into multiplets.

A mass spectrometer ionizes material, separates ions by mass-to-charge ratio and detects their abundance.

For identical sample aliquots diluted to a common final volume, blank-corrected linear response satisfies S=k(c₀V₀+cstdVstd)/Vf.

A distinct internal standard added to standards and samples permits calibration of SA/SIS=K cA/cIS, where K is the relative response.

An extraction distribution ratio D compares total solute concentrations in two immiscible phases.

In a buffered capillary, an analyte's velocity combines electrophoretic migration with electroosmotic solvent motion: v=(μep+μeo)E.

Atomic absorption measures attenuation at element-specific transitions after atomization.

Potentiometry measures the potential difference between an analyte-responsive indicator electrode and a reference electrode with negligible measurement current.

A molecular internal partition function sums the Boltzmann weights and degeneracies of its internal states.

A linear rigid rotor has rotational levels proportional to J(J+1), with magnetic degeneracy 2J+1.

For one harmonic normal mode, a geometric sum gives its vibrational partition function.

In an electric-dipole description, a pure rotational transition requires a molecular permanent dipole, while a normal-mode vibrational transition requires a changing dipole along that coordinate.

An electronic transition is fast relative to nuclear motion, so its initial nuclear coordinates are approximately unchanged during the transition.

In an isotropic Fickian transport model, diffusive mass flux is proportional to the negative local mass-density gradient.

For a reversible one-to-one receptor/ligand interaction at equilibrium, the dissociation constant relates free receptor, free ligand and complex concentrations.

Ligand binding at one site can alter affinity or activity at another through coupling of protein states.

Coulometry infers reacting amount from integrated charge and electron stoichiometry.

Voltammetry records current while controlling the working-electrode potential relative to a reference; a counter electrode carries the balancing current.

Fluorescence emission follows optical excitation while competing with nonradiative relaxation.

The NIST-authored XPS guide emphasizes planning the specimen, measurement and reporting together.

XANES and EXAFS constrain absorption-edge and local-neighbor structure rather than directly determining every atom in a material.