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The institutional experiment The Potentiometric Titration of an Acid Mixture, from Massachusetts Institute of Technology's 5.310 Laboratory Chemistry, determines hydrochloric acid and phosphoric acid inventories. Dried potassium hydrogen phthalate standardizes sodium hydroxide. A volumetric pipette selects an acid aliquot, diluted with water in a beaker. A burette feeds a stirred sample beside a glass electrode; the apparatus isolates the sample from stirrer warming. The burette is conditioned with titrant and its tip freed of bubbles. Stable pH and added volume are recorded, with smaller additions near the transition. Controls include replicate standardizations, a consistent pale-pink phenolphthalein endpoint, and a standard buffer solution check between sample runs. The readout supports inventory estimates through known stoichiometry; it does not directly count molecules.^[ref]

The same protocol requires drainage time for burette readings and warns that an undelivered hanging drop spoils the association between volume and pH. Its color-persistence wording differs between the main paragraph and footnote, so a reproducible titration endpoint needs an explicitly chosen criterion. Its acid mixture is not the single-strong acid ideal model above.^[ref]

A distinct control appears in Process Measurement Procedures: Sulfuric Acid Emissions, §1.4.4.2: the phenolphthalein standardization is repeated with water replacing the acid, matching the sample aliquot and indicator quantity. The volume needed for the same pink endpoint is subtracted from the sample reading.^[ref]

The independent bookkeeping for such a matched blank is $n_A=c_B(V_{\mathrm{sample}}-V_{\mathrm{blank}})$, assuming one-to-one neutralization and equal background consumption. A blank cannot correct an unmatched chemical reaction or guarantee exact coincidence of endpoint and equivalence point. Subtracting pH readings would not give this inventory correction, because pH is a logarithm. Repeatability constrains scatter; an independently known check sample also tests systematic bias. Carbon dioxide uptake, incomplete mixing, electrode drift, and uncertain titrant concentration limit the inference.

A pipette transfers a measured portion of a chemical solution.

For an acid-base titration, a volumetric pipette selects an aliquot whose amount of substance is $n=cV$ from a homogeneous sample. The delivered volume depends on the instrument's calibration and drainage convention; the residual liquid of a gravity-draining volumetric pipette is allowed for in that calibration. Its mark is read using the liquid meniscus. A volume calibration alone does not establish that the sampled chemical solution has the intended concentration.^[ref]

Let $m$ be the transferred sample mass, $p$ the known mass fraction of the intended chemical compound, and $M$ its molar mass. In a model with complete dissolution and chemically inactive impurities,The purity fraction is dimensionless: $99.95\%$ would mean $p=0.9995$, not $99.95$. These equations assume that the impurity contributes no titrant demand; an impurity that also reacts needs its own inventory equation. The value of $p$ must refer to the same preparation state as $m$, for example the specified dry material. A mass fraction assigned before unaccounted uptake of water cannot simply be used after it.

For an original worked example, stipulate pure potassium hydrogen phthalate, abbreviated KHP, so $p=1$, a selected mass $m=0.51055\mathrm{g}$, and rounded molar mass $M=204.22\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$. The NIST Chemistry WebBook lists formula ${\mathrm{C}}_8{\mathrm{H}}_5\mathrm{K}{\mathrm{O}}_4$ and molecular weight $204.2212$, consistent with the rounded molar mass used here.^[ref] The selected mass, purity assumption and volumes in this example are chosen inputs, not measured results or a claim about a real batch's purity.

The acid-bearing anion of potassium hydrogen phthalate loses one proton to hydroxide. The net chemical equation isThus sodium hydroxide has one-to-one stoichiometry with potassium hydrogen phthalate in this neutralization, givingChoose a delivered endpoint titre of $24.85\mathrm{mL}$ and matched titration blank of $0.05\mathrm{mL}$. ThenThe extra displayed digits show the arithmetic of the stipulated model; they do not establish experimental accuracy. A compact rounded result is $0.1008\mathrm{mol}{\mathrm{L}}^{-1}$.

When the entire weighed portion is titrated, added water changes concentration and the pH path but preserves the initial acid inventory. The dissolution volume therefore does not appear in $n_s=mp/M$. If instead a volumetric flask prepares a stock and a volumetric pipette selects an aliquot, the selected inventory is $n_s{V}_a/V_f$ for homogeneous stock, with delivered aliquot volume $V_a$ and final stock volume $V_f$. The same bookkeeping explains why complete transfer matters even when the amount of dissolution water is approximate.

How can an invisible dissolved inventory be measured? The unsigned laboratory handout Solubility Product Constant, Ksp, for Calcium Hydroxide by Acid-Base Titration, Procedure, starts with saturated calcium hydroxide, supplied by the teacher or prepared from calcium and water. Its apparatus includes filter paper, a funnel, stoppered flasks, a volumetric pipette, a volumetric flask and a burette. Two successive rounds of filtration remove particles. The filtrate is stoppered to reduce carbon dioxide exposure. A $10.00\mathrm{mL}$ aliquot is diluted with deionized water and titrated with standardized hydrochloric acid; bromothymol blue gives a pale-green titration endpoint. The readout is the difference between final and initial burette readings; four consistent trials are required.^[ref]

Unlike AB, calcium hydroxide has one-to-two dissolution stoichiometry:For molar solubility $s$ in the ideal model with no background calcium or hydroxide, no additional chemical reactions, and negligible self-ionization of water, $[{\mathrm{Ca}}^{2+}]=s$ and $[{\mathrm{OH}}^{-}]=2s$. Hence $K_{\mathrm{sp},c}=4s^3$, with units ${\mathrm{M}}^3$; it is not the AB constant used in the figures. The neutralization chemical equation is ${\mathrm{H}}^{+}+{\mathrm{OH}}^{-}⟶{\mathrm{H}}_2\mathrm{O}$. Let $C_H$ be the known titrant molar concentration, $v$ its delivered volume at the equivalence point, and $V_a$ the original aliquot volume. Then the inventory calculation isDilution of the aliquot changes its concentration during the acid-base titration, but preserves its initial amount of substance of hydroxide. Therefore $V_a$, rather than the diluted flask volume, belongs in the denominator.

The handout identifies two biases: carried-over calcium hydroxide solid dissolves during acid-base titration, consuming extra titrant; carbon dioxide consumes hydroxide and forms calcium carbonate. Filtration and stoppering address these effects, while repeat trials test consistency. Its review questions also ask about dissolved ion pairs, which filtration cannot remove.^[ref]

Further controls would compare a water blank, independently verify titrant standardization, and record the saturation temperature; these are proposed checks, not reported measurements. A titration endpoint estimates the equivalence point and may introduce a systematic offset. Even perfect inventory measurement does not determine activity coefficients. Recovering the dimensionless thermodynamic solubility product additionally requiresThis explains both the power and the limit of the experiment: acid-base titration measures a dissolved inventory, while the link from that inventory to a thermodynamic equilibrium constant still depends on a chemical model.

A volumetric flask prepares a chemical solution at a specified total volume, using a calibration mark.

Its mark specifies contained volume under its calibration conditions. In contrast, a volumetric pipette specifies a delivered portion. The narrow neck makes a small change of volume visible as a larger change of liquid height. The final chemical solution volume includes the solute; “dilute to $100\mathrm{mL}$” does not mean “add $100\mathrm{mL}$ of water”.^[ref]

For an original dilution example, a fully transferred $10.00\mathrm{mL}$ aliquot of $0.100\mathrm{mol}{\mathrm{L}}^{-1}$ acid contains $1.000\mathrm{mmol}$. Making the final total $100.0\mathrm{mL}$ gives analytical concentration $0.0100\mathrm{mol}{\mathrm{L}}^{-1}$. A subsequent $10.00\mathrm{mL}$ aliquot contains $0.1000\mathrm{mmol}$ and needs $1.000\mathrm{mL}$ of $0.100\mathrm{mol}{\mathrm{L}}^{-1}$ base for one-to-one neutralization. The entire diluted flask still needs $10.00\mathrm{mL}$ of that base: dilution preserves the selected inventory but sampling selects a fraction of it.

Overfilling lowers the intended molar concentration. Removing some well-mixed chemical solution to restore the mark also removes solute, so it does not recover the intended inventory. Full transfer, known final volume, and mixing are separate requirements.

A volumetric pipette transfers one nominal volume of chemical solution according to its marked calibration and drainage convention.