Titration Point Calculator

A titration converts an unknown amount of analyte into a volume reading by adding a reagent of known concentration until the reaction is stoichiometrically complete. The equivalence volume follows from the moles of analyte times the stoichiometric ratio divided by the titrant concentration, so 25 mL of 0.1 M acetic acid requires 25 mL of 0.1 M sodium hydroxide. For a weak acid the shape of the curve carries more information than the endpoint alone. Before any base is added the pH is set by the acid dissociation equilibrium and equals roughly half of pKa minus the logarithm of the concentration. Through the buffer region the Henderson-Hasselbalch expression pH = pKa + log of the conjugate base to acid ratio applies, so pH equals pKa exactly at the half-equivalence point, which is the standard experimental route to a pKa. At equivalence the solution contains only the conjugate base, which hydrolyses, so the pH lands above 7, near 8.7 for 0.05 M acetate. Several approximations underlie these numbers: water autoionisation is neglected, activity coefficients are set to unity, and dilution by the titrant is only partly accounted for. They break down for very dilute solutions below roughly 0.001 M, for acids with pKa above about 10 or below 2, and for polyprotic systems whose successive pKa values differ by less than three units, where the separate breaks merge into one. Indicator choice must match the equivalence pH, which is why phenolphthalein with its 8.2 to 10.0 transition suits weak acid titrations while methyl orange at 3.1 to 4.4 does not.

Volumetric analysis grew out of eighteenth-century industrial testing. Francois-Antoine-Henri Descroizilles built graduated glassware in the 1790s to assay bleaching liquors and potash for the French textile trade, measuring how much test solution was needed to discharge a colour. Joseph Louis Gay-Lussac put the practice on a quantitative footing in the 1820s, introducing standardised solutions and the vocabulary of titre from which titration takes its name, and applying it to silver assays for the French mint. Karl Friedrich Mohr consolidated the method in his 1855 textbook on chemical-analytical titration methods, which described the burette with a pinchcock, the pipette, and the systematic use of indicators, turning titration into a teachable laboratory routine across Europe. The theoretical layer arrived in the early twentieth century: Soren Sorensen defined the pH scale at the Carlsberg Laboratory in 1909, Lawrence Henderson derived the buffer relationship in 1908, and Karl Hasselbalch recast it in logarithmic form in 1917. Instrumental endpoint detection followed the glass electrode work of Max Cremer in 1906 and of Fritz Haber and Zygmunt Klemensiewicz in 1909, and potentiometric titration with automatic burettes eventually replaced visual indicators for most precise work.