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A pH measurement becomes evidence for a weak acid chemical equilibrium when paired with a known analytical concentration and a calibrated glass electrode. For the pure-weak acid model, measured pH estimates $h=10^{-\mathrm{pH}}$ only in the ideal thermodynamic activity approximation. Then $o=K_w/h$, $x=h-o$, $y=c-x$, and $K_a=hx/y$. Require $0<x<c$; values outside that range signal inconsistent measurements or an inadequate model. Repeating this reconstruction across a dilution series tests whether one acid dissociation constant describes the data, rather than merely fitting one point.

The Analytical Sciences Digital Library's Potentiometric Titration of an Unknown Weak Monoprotic Acid provides a complementary acid-base titration experiment. Its apparatus includes a glass electrode and meter, a stirring magnet, a volumetric flask, pipettes, and a burette containing standardized sodium hydroxide. Prepare an aqueous acid stock of known analytical concentration, transfer a measured portion, and stir gently with the glass electrode clear of the magnet. Record added volume and stable pH after each addition; use a preliminary run to locate the steep region and smaller additions there on a fresh portion. The readout is the pH versus added volume curve, not a visual count of dissociated molecules.

Calibrate with fresh standard buffer solutions bracketing the pH range being interpreted. Use their assigned values at the actual temperature; a pair near pH $4$ and $7$ can cover the midpoint of many weak acid examples, but does not cover an entire alkaline endpoint region. Rinse between standards and samples to limit carryover, keep the sensing bulb and reference electrode junction immersed, and wait for a stable reading. These instrument practices are documented in HI5221 & HI5222 Instruction Manual: pH and mV and ISE and Temperature Bench Meters by Hanna Instruments (pp. 45–47, 49–50 and 73–74: calibration, measurement, rinsing and electrode conditioning).

Locate the acid-base titration equivalence region from the steepest change of pH with added volume. For one-to-one neutralization, standardized sodium hydroxide concentration times equivalence volume estimates the initial amount of substance of acid. Half that volume gives approximately equal $[\mathrm{HA}]$ and $[{\mathrm{A}}^{-}]$ only when subsequent chemical equilibrium redistribution is small. The Henderson-Hasselbalch equation then gives $\mathrm{pH}\approx \mathrm{p}{K}_a$. Unequal activity coefficients or appreciable hydronium or hydroxide inventories can shift this estimate. The full chemical equilibrium curve supplies a stronger consistency check than its midpoint alone.

Useful controls for this model test are a fresh independently prepared acid portion, a water blank, a check standard after measurement to detect instrument drift, and fixed recorded temperature. A blank diagnoses contamination but should not be subtracted directly from pH, which is a logarithm. Keep exposure to atmospheric carbon dioxide comparable, especially at high dilution, and record any background salt that changes ionic strength. These are experimental-design controls suggested by the model's assumptions. The observed curve and its uncertainty determine whether the model is adequate; the diagrams here contain no experimental readouts. An aqueous acid dissociation constant cannot be inferred unchanged from a sample requiring a different solvent mixture, and a nearly neutral dilute sample makes the difference $h-K_w/h$ particularly sensitive to pH error.

Yeasts are fungi whose growth is predominantly unicellular, commonly through budding or division into two cells. The word describes a growth form across different fungal lineages, rather than one species or an exclusive clade; some fungi can switch between unicellular and filamentous growth. Thus Saccharomyces cerevisiae is a yeast, but yeast is not another name for that one species. See Kurtzman, Fell and Boekhout, The Yeasts, chapter 1 (2011): definition and classification.

A yeast cell has eukaryotic organization, including a cell nucleus, mitochondria and a cell wall. Small size and a unicellular lifestyle do not make it a member of bacteria. These compartments let an experimentally accessible biological cell retain much of the organization shared with other eukaryotes. See Clark, Douglas and Choi, Biology 2e, 24.1: fungal cells and yeast growth.

A motivating experiment: can fermentation continue without intact yeast cells? In 1897, Eduard Buchner ground brewers' yeast with quartz sand and diatomite, added water, and pressed out a liquid extract. Adding concentrated cane sugar produced carbon dioxide after 15–60 minutes. A cell-retaining filter still yielded an active filtrate: with sterilized cane sugar in an icebox, fermentation began after about a day. Saturated lactose gave no observed fermentation. These are reported observations, not invented control results. See Buchner, Alcoholic fermentation without yeast cells (1897), translated excerpt hosted by Carmen Giunta.

The filtration comparison addresses the objection that surviving intact yeast cells caused the activity. The lactose comparison tests substrate dependence; it is not a no-sugar blank, nor a comparison at matched sugar concentrations. A proposed modern follow-up would also compare the same extract with and without added sugar, accounting for material already in the extract. That is an experimental suggestion, not a result attributed to Buchner. His report specifies brewers' yeast; it does not identify the preparation here as a pure Saccharomyces cerevisiae strain.

Heat treatment asks a different question: does destroying activity in the extract stop fermentation? Buchner's preliminary report described weak or absent activity after heating and filtration, rather than one clean universal threshold. Harden's 1914 account of the subsequent work summarized loss of activity on heating the juice to $50{}^{\circ }\mathrm{C}$. Harden also described requirements for both enzymes and coenzymes. Cell-free therefore means neither chemical-free nor a preparation containing one purified enzyme. See Arthur Harden, Alcoholic Fermentation (1914), chapters II and VI: cell-free activity and the fermenting complex.

The inference is that extracted cellular machinery can sustain these chemical reactions without an intact living biological cell. This does not show that the extract reproduces, grows or maintains itself like a yeast. Moreover, gas evolution alone does not identify ethanol: cellular respiration can also release carbon dioxide. Product identification is a separate measurement; Harden's account describes both ethanol and carbon dioxide as products of cell-free alcoholic fermentation. The beautiful separation is between the organism that produces and maintains the machinery and the machinery that catalyzes a particular transformation.