Chemistry

Analytical chemistry

Titration, spectroscopy, and chromatography — measuring what is present and how much.

Basics

Titration

A solution of known concentration is added until the equivalence point; that volume gives the unknown amount. Acid–base titrations use neutralization, redox titrations electron transfer, and chelometric titrations metal–ligand binding. An indicator’s colour change must sit near the equivalence pH, and a primary standard should be pure, stable, and of known molar mass. The inflection on a pH or potential curve marks equivalence.

Spectroscopy

Molecules absorb or emit particular wavelengths. UV–visible light probes electronic transitions, infrared probes vibrations, and NMR probes nuclear spins in a magnetic field. Quantitation is usually a calibration curve: match the instrument signal to standards, then read the unknown. Scatter, fluorescence, and background absorption can break Beer’s law, so wavelength, cell, and solvent are held fixed.

Chromatography

A mixture separates because components partition differently between a stationary phase and a mobile phase. Paper and TLC compare spots with Rf; GC uses a gas mobile phase for volatiles; HPLC pumps liquid through a column. Retention time hints at identity; peak area at amount. Resolution is how far neighbouring peaks sit apart — column, flow, and temperature set it.

Accuracy and precision

Accuracy is closeness to the true value; precision is scatter on repeat. Systematic error (a zeroed balance, impure reagent) shifts accuracy; random error spreads precision. Replicates, blanks, spike recoveries, and calibration standards help separate the two. Significant figures and units have to travel with every number or the table is decoration.

Formulas

Beer–Lambert

A = ε c ℓ

Absorbance scales with concentration and path (dilute solution, one wavelength).

Symbols

A absorbance (−log T)
ε molar absorptivity
c concentration
ℓ path length

Equivalence (1:1 acid–base)

M_a V_a = M_b V_b

Moles of acid and base match at equivalence. Multiply by stoichiometric coefficients when they are not 1:1.

Symbols

M molarity
V volume

Retention factor Rf

R_f = d_spot / d_solvent

On TLC or paper, distance of the spot over the solvent front. Between 0 and 1.

Symbols

d_spot spot travel
d_solvent solvent-front travel

Chromatographic resolution

R_s = 2 (t₂ − t₁) / (w₁ + w₂)

Neighbouring peaks. R_s ≳ 1.5 is often treated as baseline-separated.

Symbols

t retention time
w baseline peak width

Key table

Primary standard (examples)	KHP, Na₂CO₃, K₂Cr₂O₇ — dry and check purity first
UV–Vis cell	often ℓ = 1.00 cm quartz; plastic blocks UV
GC vs HPLC	GC: volatile and heat-stable. HPLC: less volatile, including aqueous