= Weak acid dissociation measurement
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 <Analytical Electrochemistry: Potentiometry/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 (thermodynamics)> 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 (thermodynamics)> 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 (thermodynamics)>. For one-to-one <neutralization>, standardized <sodium hydroxide> <concentration> times equivalence <volume (thermodynamics)> estimates the initial <amount of substance> of acid. Half that <volume (thermodynamics)> gives approximately equal $[\mathrm{HA}]$ and $[\mathrm A^-]$ only when subsequent <chemical equilibrium> redistribution is small. The <Henderson-Hasselbalch equation> then gives $\mathrm{pH}\approx\mathrm pK_a$. 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.
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