# Titration **Titration** is a quantitative method of [[Analytical_chemistry|chemical analysis]] that finds the unknown amount of a substance, the analyte, by reacting it to completion with a measured volume of a second solution, the titrant, whose [[Molar_concentration|concentration]] is known. The method rests on one idea: at the moment the reaction is exactly complete, the moles delivered and the moles present stand in the ratio written in the balanced equation, so a volume read from a burette becomes an amount of substance by [[Stoichiometry|stoichiometry]].[^af-ch7] In the microsim below the reader slides the delivered volume V_NaOH from 0 to 50 mL into 25.00 mL of 0.100 M acetic acid and a marker rides the curve computed from the charge balance `[H+] + [Na+] = [OH-] + Ca·Ka/(Ka + [H+])`, a single monotone equation solved once per volume, with the strong-acid ([[Chlorine|HCl]]) curve drawn behind it as a ghost.[^os-table142] Two labelled points carry the argument. At half-equivalence, 12.50 mL, half the acid has become its conjugate base and the [[PH|pH]] equals the acid's pKa, 4.74 for acetic acid.[^os-halfeq][^os-ka] At equivalence, 25.00 mL, all the acid is gone but the solution is not neutral: the acetate left behind is a weak base, so the pH is 8.72, not 7.00.[^os-table142] The ghost curve passes through exactly 7.00 at the same volume, which is why the two are worth drawing together.[^os-table142] On the [[Chemistry|Chemistry]] flagship's spine this page is the main article for Part VIII — Acidity and basicity, section *Titration*, and it sits downstream of [[Acid_dissociation_constant|the acid dissociation constant]] and [[Buffer_solution|buffer solutions]]: the flat middle of a weak-acid curve is a buffer, and the steep part is what a buffer stops being. [[Titration_curve|The titration curve]], [[Equivalence_point|the equivalence point]] and [[PH_indicator|pH indicators]] are the siblings that take those three parts one at a time. ## History and etymology Titration is older than the theory that explains it. The procedure needs no model of acidity: a standard solution, a burette, a visible signal at completion and the balanced equation are enough, and the bookkeeping is pure stoichiometry.[^af-ch7] The name records the purpose — to establish a *titre*, the older word for the strength of a solution, by reaction against one whose strength is already settled. [citation needed] What equilibrium theory added was not the number but the *shape*. Once [[Acid_dissociation_constant|Ka]] and the [[Self-ionization_of_water|self-ionization of water]] were available, the whole pH-against-volume curve could be computed in advance rather than merely watched, and indicator choice became a calculation instead of a tradition.[^os-indicator] That is the change this page's microsim displays. ## Procedure The analyte is measured into a flask — in the reference example, 25.00 mL of 0.100 M acid — and the titrant, 0.100 M [[Sodium_hydroxide|sodium hydroxide]], is delivered from a burette in shrinking increments as the endpoint nears.[^os-table142] Between additions the flask is swirled so the reaction stays complete; near the endpoint the titrant goes in drop by drop, because the watched property is changing fastest exactly there. The volume at which the signal changes is recorded, and the calculation is a single line of stoichiometry. The precision is limited by the burette reading and by how sharply the signal changes, not by the chemistry. This is why the reference dataset is quoted to 0.01 mL near the endpoint and to 5 mL far from it: away from equivalence a large volume moves the pH very little, while the last 0.2 mL takes the strong-acid pH from 3.70 to 10.30.[^os-table142] All figures here assume 25 °C, since the neutral point moves with [[Temperature|temperature]] — pure water is neutral at pH 6.31 at 80 °C — so a curve computed with pKw = 14 is a 25 °C object.[^os-kw] ### Preparation techniques A titration is only as good as its standard. The titrant must either be prepared from a substance pure and stable enough to weigh directly, or standardized against one before use; sodium hydroxide belongs to the second class, because it absorbs water and carbon dioxide from the air. The analyte must be dissolved completely, and a solid sample may need digestion, dilution to a known volume, or removal of an interfering species first. Where an interfering species cannot be removed it is masked — bound into an unreactive form — so that the titrant sees only the analyte. Dilution deserves its own caution, because volumes add. Adding 50 mL of titrant to 25 mL of analyte nearly triples the volume, so every concentration in the flask falls even where no reaction consumes it. That is why the charge balance behind the microsim carries the running total volume, and why the far end of the curve approaches the pH of the titrant itself.[^os-strong] ## Titration curves A titration curve plots the monitored property against the volume delivered. For an acid–base titration that property is pH, and the curve has three regions: a slow drift while the analyte is in excess, a near-vertical jump through equivalence, and a second slow drift set by the excess titrant. The textbook builds it in stages — excess strong acid straight from concentration, the weak-acid region by an ICE table and then Henderson–Hasselbalch, hydrolysis at equivalence, and `pH = 14 + log[OH-]_excess` beyond it.[^os-strong] The microsim does not use those stage formulas, because they are discontinuous at V = 0 and at the equivalence volume. It uses the charge balance instead, `[H+] + [Na+] = [OH-] + Ca·Ka/(Ka + [H+])`, where Ca is the *total* acid concentration in the flask at that moment and `[Na+]` is the delivered base, likewise diluted. This is one monotone equation in `[H+]` per volume, solvable by bisection in log₁₀[H⁺] and valid across the whole range at once. Two lookup tables are baked from it, one per curve, 2001 points each at float16, about 5.3 KB apiece encoded, and the sim reads them rather than solving at frame rate. The bake is checked against all 19 volumes of the reference table for both acids, to ±0.01 pH. That check has one flagged exception. Solving the charge balance with Ka = 1.8 × 10⁻⁵ reproduces every entry in the reference table to within 0.01 pH except the weak acid's starting point, where it gives 2.88 against the printed 2.87, because the book computed that one value with the "x is small" approximation rather than exactly (a **derived** result of the Wikitube cross-check, not the book's).[^os-table142][^os-approx] The tolerance there is therefore ±0.02. The reader's one control is V_NaOH, from 0 to 50 mL in 0.05 mL steps. Three things move with it: the marker rides the weak-acid curve, the strong-acid ghost stays put for comparison, and the flask changes colour by the indicator ratio `pH = pKa(In) + log([In-]/[HIn])`, phenolphthalein being colourless below about pH 8.3 and pink above.[^os-indicator] The extracted source gives no pKa for phenolphthalein, so the sim centres its colour blend just above 8.3 — an **ILLUSTRATIVE** authoring choice, a display fit and not a measured constant, labelled as such in the sim. ## Types of titrations The acid–base case is worked here in full, but the argument is indifferent to the chemistry. Any reaction that is fast, complete, of known stoichiometry and accompanied by a detectable change at completion will serve; what changes between families is the equilibrium constant that shapes the curve and the signal that marks the end. ### Acid–base titration The reaction is proton transfer, and the curve's shape depends on the strength of the acid.[^os-strong] The reference dataset makes the contrast concrete: for 25.00 mL of 0.100 M HCl the pH runs 1.00, 1.95, 2.69, 7.00, 11.29, 12.52 at 0, 20, 24, 25, 26 and 50 mL; for the same volume of 0.100 M acetic acid it runs 2.87, 5.35, 6.13, 8.72 at 0, 20, 24 and 25 mL, and from 25.1 mL onward the two coincide exactly, because past equivalence the pH is set by excess base alone.[^os-table142] The weak acid starts higher, flattens through its buffer region and ends above pH 7 — differences that all follow from a single Ka. ### Redox titration Here the titrant oxidizes or reduces the analyte, and the property that jumps at equivalence is the electrode potential rather than the pH.[^ball-redox] The bookkeeping is the same stoichiometry applied to electrons instead of protons, the balanced half-reactions fixing the ratio.[^af-ch7] Some systems are self-indicating, the titrant's own colour appearing once it stops being consumed; others use a redox indicator or an electrode whose response follows [[Nernst_equation|the Nernst equation]] about the couple's [[Standard_electrode_potential|standard potential]].[^os-electro] ### Gas phase titration Nothing in the argument requires a solvent. If analyte and titrant are gases, the "volume delivered" becomes a metered flow and the amount present is read through partial pressures: in a mixture each gas contributes independently, so consuming one component changes the total by a calculable amount.[^ae-dalton] The endpoint must then be read from a physical signal rather than a dissolved dye — the only part of the method that has to be redesigned. ### Complexometric titration The titrant here is a [[Ligand|ligand]] that binds the analyte metal ion into a [[Coordination_complex|coordination complex]], and the reaction runs to completion because the formation constant is very large. Those constants are tabulated alongside the acid constants used above, and their size is what makes a sharp endpoint possible.[^os-complex] Multidentate ligands, which grip a metal at several points at once, are preferred because the resulting chelate is far more stable than the same number of separate bonds would suggest.[^os-coord] ### Zeta potential titration Some analytes are suspended particles rather than dissolved molecules, and the property followed is then electrokinetic: the titrant shifts the zeta potential of the particles, and the endpoint is where that potential crosses zero. [citation needed] The logic is unchanged — reagent is added until a monitored property reaches a known value — and only the [[Sensor|sensor]] differs from the burette-and-flask picture. ### Assay An assay asks how much of a named substance a sample contains, and titration is the classic answer where that substance has a clean reaction. Because the calculation returns an [[Amount_of_substance|amount of substance]] rather than a signal intensity, it needs no calibration curve — its lasting advantage over comparative methods such as [[Spectrophotometry|spectrophotometry]].[^af-ch7] The limitation is the mirror image: it measures only what reacts, so two components that both react report as their sum unless one is masked. ## Measuring the endpoint of a titration The reaction finishes at one volume; the observer notices at another. Every real titration therefore has two distinct points, and the quality of the method is the distance between them. Everything in this section is an attempt to make that distance small, or at least to know how large it is. ### Endpoint and equivalence point The **equivalence point** is the volume at which the delivered titrant exactly matches the analyte by the balanced equation. The **endpoint** is where the observer sees the signal change. An indicator is itself a weak acid whose two forms differ in colour, so it obeys `pH = pKa(In) + log([In-]/[HIn])` and changes visibly over roughly pKa ± 1.[^os-indicator] A good indicator has that range inside the vertical part of the curve, so the pH sweeps through the whole colour change within a drop or two. This is why indicator choice is a calculation. Phenolphthalein, colourless below about 8.3 and pink above, straddles the weak acid's equivalence pH of 8.72 and is correct there.[^os-indicator][^os-table142] Methyl orange, which changes far lower, is explicitly wrong for a weak acid titrated with a strong base: its colour change is over long before equivalence arrives.[^os-methylorange] With a strong acid, whose jump spans 3.70 to 10.30 across 0.2 mL, both fall inside the vertical section and either will do.[^os-table142] ### Back titration When the direct reaction is too slow, or the analyte is a solid that dissolves only as it reacts, the reagent is added in known excess and the *leftover* is titrated instead. The analyte is then the difference between what was added and what was found — the limiting-reagent argument run backwards, on the same bookkeeping as the direct case.[^af-ch7] The cost is two standardized solutions instead of one, with the uncertainties of both entering the answer. ## Graphical methods Reading an endpoint from a colour is a human judgement; reading it from the curve is not. Because equivalence is where the curve is steepest, plotting the first derivative ΔpH/ΔV against volume replaces "where did it turn pink" with "where is the peak", and the second derivative locates the same volume as a zero crossing. The reference data show why that is worth doing even when an indicator exists: for HCl the pH rises from 3.70 at 24.9 mL to 10.30 at 25.1 mL, 6.60 units across 0.2 mL, while for acetic acid the same 0.2 mL gives only 7.14 to 10.30, or 3.16 units — a peak less than half as tall (**derived** from the reference table).[^os-table142] Where the jump is smaller still — a very weak acid, a dilute sample — the derivative peak flattens until it is unreliable, and the remedy is to fit straight lines to a linearized form of the data on either side of equivalence and take their intersection. Fitting many points by [[Least_squares|least squares]] instead of eyeing one drop is the trade [[Chemical_kinetics|chemical kinetics]] makes when it plots an integrated rate law rather than timing a half-life. The microsim is the graphical method run in advance: the curve is computed before the titration rather than measured during it. ## Particular uses Titration survives in routine use because it is cheap, traceable to a weighed mass and a measured volume, and free of calibration drift. The three families below account for most of the working practice, and they differ only in which equilibrium constant sets the shape of the jump. ### Acid–base titrations The standard measurements of acid content in foods, soils and water are acid–base titrations, and the reference textbook's worked examples are of this type: a second case takes 50.0 mL of 0.100 M nitric acid against 0.200 M base, giving pH 1.000, 1.5111, 7 and 12.523 at 0, 15, 25 and 40 mL.[^os-strong] The matching weak-acid case, 50.0 mL of 0.100 M formic acid against 0.200 M base, gives 2.37, 3.92, 8.29 and 12.097 — again an equivalence point well above 7.[^os-weakcheck] Body fluids are the standing exception: [[Bicarbonate_buffer_system|the bicarbonate buffer]] of blood resists titration by design, and the source's own blood-buffer example is internally inconsistent, so it is reported rather than used.[^os-blood] ### Redox titrations Redox titrations measure dissolved oxygen, available chlorine in water treatment, [[Iodine|iodine]] number in fats and the strength of oxidizing agents in a process stream. The endpoint can be followed potentiometrically with an inert electrode, which makes the method easy to automate; the half-cell bookkeeping behind it is the subject of [[Electrochemistry|electrochemistry]].[^os-electro] ### Miscellaneous Two further families show the same curve arising from a different equilibrium constant. In a precipitation titration the analyte leaves solution as an insoluble salt, and the endpoint's sharpness is governed by that salt's solubility product.[^os-solub] In a complexometric assay the governing constant is a formation constant instead.[^os-complex] In every case the curve answers the microsim's question: how steep is the jump, and is there an indicator whose range sits inside it? ## See also - [[Acid–base_titration]] - [[PH_indicator]] - [[Titration_curve]] - [[Equivalence_point]] - [[Analytical_chemistry]] - [[Buffer_solution]] - [[Acid_dissociation_constant]] - [[Stoichiometry]] - [[PH]] ## References [^os-table142]: Flowers, Paul; Neth, Edward; Robinson, William; et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 14, §14.7 Acid-Base Titrations, p. 705, Table 14.2 (25.00 mL of 0.100 M acid against 0.100 M NaOH; 19 volumes per acid; HCl 1.00 → 7.00 at 25.00 mL → 12.52 at 50 mL; CH₃CO₂H 2.87 → 8.72 at 25.00 mL, identical to HCl from 25.1 mL on). Portal Book 051. https://open.umn.edu/opentextbooks/textbooks/chemistry-atoms-first [^os-strong]: Flowers, Paul; Neth, Edward; Robinson, William; et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 14, §14.7, pp. 702–704 (the stagewise construction of the curve: excess strong acid, ICE and Henderson–Hasselbalch for the weak acid, hydrolysis at equivalence and `pH = 14 + log[OH⁻]_excess` beyond it; Example 14.21 and its check problem, 50.0 mL of 0.100 M HNO₃ against 0.200 M NaOH → 1.000, 1.5111, 7, 12.523). Portal Book 051. [^os-halfeq]: Flowers, Paul; Neth, Edward; Robinson, William; et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 14, §14.7, p. 704 (at half-equivalence the acid is half converted and pH = pKa). Portal Book 051. [^os-weakcheck]: Flowers, Paul; Neth, Edward; Robinson, William; et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 14, §14.7, p. 704, check problem (50.0 mL of 0.100 M HCOOH against 0.200 M NaOH → pH 2.37, 3.92, 8.29, 12.097 at 0, 15, 25 and 30 mL). Portal Book 051. [^os-indicator]: Flowers, Paul; Neth, Edward; Robinson, William; et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 14, §14.7, pp. 706–707 (an indicator is a weak acid obeying `pH = pKa(In) + log([In⁻]/[HIn])`, with a visible change over about pKa ± 1; phenolphthalein colourless below pH 8.3 and pink above). Portal Book 051. [^os-methylorange]: Flowers, Paul; Neth, Edward; Robinson, William; et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 14, §14.7, pp. 707–708 (methyl orange is the wrong indicator for a weak acid titrated with a strong base). Portal Book 051. [^os-ka]: Flowers, Paul; Neth, Edward; Robinson, William; et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 14, p. 716 (Ka of acetic acid = 1.80 × 10⁻⁵, so pKa = 4.74). Portal Book 051. [^os-approx]: Flowers, Paul; Neth, Edward; Robinson, William; et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 14, §14.3, pp. 679–686 (the "x is small" approximation and the 5 % test that governs when it may be used). The 2.88-against-2.87 discrepancy at the weak acid's starting point was computed in the Wikitube cross-check of the charge balance against Table 14.2 and is marked derived, not a book result. Portal Book 051. [^os-kw]: Flowers, Paul; Neth, Edward; Robinson, William; et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 14, §14.1–14.2, pp. 667–670 (Kw = 1.0 × 10⁻¹⁴ at 25 °C; pH + pOH = pKw; neutral means [H₃O⁺] = [OH⁻], and pure water is neutral at pH 6.31 at 80 °C, where Kw = 2.4 × 10⁻¹³). Portal Book 051. [^os-blood]: Flowers, Paul; Neth, Edward; Robinson, William; et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 14, §14.6, pp. 700–701 (the carbonic acid/bicarbonate buffer of blood). The printed pKa was lost in extraction, and the book's own numbers (0.024 and 0.0012 mol/L at pH 7.4) require pKa ≈ 6.1 against a prose value of 7.35, so the example is reported rather than used. Portal Book 051. [^os-electro]: Flowers, Paul; Neth, Edward; Robinson, William; et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 16, "Electrochemistry", pp. 753–790 (standard electrode potentials, cell potential and the Nernst relation behind a potentiometric endpoint; page to pin). Portal Book 051. [^os-complex]: Flowers, Paul; Neth, Edward; Robinson, William; et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Appendix K, "Formation Constants for Complex Ions", pp. 1123–1124 (the tabulated constants that make a complexometric endpoint sharp; page to pin). Portal Book 051. [^os-coord]: Flowers, Paul; Neth, Edward; Robinson, William; et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 19, "Transition Metals and Coordination Chemistry", pp. 929–970 (ligands, denticity and the extra stability of chelate complexes; page to pin). Portal Book 051. [^os-solub]: Flowers, Paul; Neth, Edward; Robinson, William; et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 15, "Equilibria of Other Reaction Classes", pp. 719–752, with the solubility products of Appendix J, pp. 1117–1122 (the equilibrium constant governing a precipitation endpoint; page to pin). Portal Book 051. [^af-ch7]: Flowers, Paul; Neth, Edward; Robinson, William; et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 7, "Stoichiometry of Chemical Reactions", pp. 313–362 (titration as quantitative analysis; limiting reagents and the excess-reagent argument behind a back titration; page to pin). Portal Book 051. [^ball-redox]: Ball, David W. (2011). *Introductory Chemistry*. Chapter "Oxidation and Reduction", pp. 673–719, with the titration material of the "Acids and Bases" chapter, pp. 571–622 (page to pin). Portal Book 056. https://open.umn.edu/opentextbooks/textbooks/introductory-chemistry [^ae-dalton]: Averill, Bruce; Eldredge, Patricia (2011). *General Chemistry: Principles, Patterns, and Applications*. Chapter 10, Gases, pp. 924–925 (Dalton's law: in a gas mixture each component contributes its own partial pressure, and the total is their sum; the worked heliox cylinder gives 3.85 atm O₂ and 196 atm He for a total of 200 atm). Portal Book 050. https://open.umn.edu/opentextbooks/textbooks/general-chemistry-principles-patterns-and-applications ## External links - *Chemistry: Atoms First 2e* (OpenStax, 2019), Portal Book 051 — Open Textbook Library record: https://open.umn.edu/opentextbooks/textbooks/chemistry-atoms-first - *Introductory Chemistry* (2011), Portal Book 056 — Open Textbook Library record: https://open.umn.edu/opentextbooks/textbooks/introductory-chemistry - The Wikipedia pair's External links section lists the pair's own links. <!-- MATTERSIM:BEGIN g24 — Matter & Energy Cluster microsim (framework build, specs/sims/Titration.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework), pending deploy:** *Titration* will play here once `https://wikitube-3d-microsims.netlify.app/matter/Titration.html` is live. <!-- pending: <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Titration.html" data-title="Titration"></div> --> <!-- MATTERSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Titration) : [Wikitube](https://en.wikitube.io/wiki/Titration) · pinned revision [1371094173](https://en.wikipedia.org/w/index.php?oldid=1371094173) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. Portals: [[PORTAL_Chemistry]]. --- *Matter & Energy Cluster child articles, wave 1 · 2026-09-11 · drafted · Chemistry row K42 · sim pending (matter/Titration).*