Titration Curve Simulator (weak acid/base biochem context) mechanism

Model scope

The stated honest label is appropriate for an idealized educational model, but the specification must explicitly choose weak acid versus weak base, monoprotic behavior, temperature, pKw, and the equations used in each volume regime. The four vectors use a weak monoprotic acid titrated by NaOH and are deterministic sampled plot points.

• The specification does not identify whether the analyte is a weak monoprotic acid or a weak monoprotic base, so one unique titration curve is not defined.
• Henderson-Hasselbalch is valid only in the buffer region, not at zero titrant, very near equivalence, or after equivalence.
• Equivalence-point stoichiometry determines the conjugate-species concentration but does not by itself determine pH; hydrolysis and water autoionization must be included.
• The formula set omits the post-equivalence strong-titrant excess calculation.
• The initial pH calculation is unspecified; for a weak acid it requires solving the weak-acid equilibrium rather than applying Henderson-Hasselbalch with zero conjugate base.
• A single-pKa model must explicitly state that the analyte is monoprotic and that additional equilibria, activity effects, precipitation, and dilution effects beyond the stated ideal model are ignored.

Units and conventions

• The test vectors assume a monoprotic weak acid HA titrated by strong base NaOH.
• Temperature is 25 °C, so Kw = 1.00000e-14 and pKw = 14.0000.
• pKa = 4.75000, so Ka = 10^-4.75 = 1.77827941e-5.
• Concentrations are mol/L, volumes are L in calculations and mL in plot coordinates, and molarity is treated as activity.
• The analyte concentration is 0.100000 mol/L and initial analyte volume is 50.0000 mL; NaOH concentration is 0.100000 mol/L.
• At pre-equivalence volumes, pH = pKa + log10(nA-/nHA), where nA- = Cbase Vbase and nHA = Canalyte Vanalyte - nA-.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "analyte": "0.100000 mol/L HA",
    "initial_volume": "50.0000 mL",
    "pKa": 4.75,
    "titrant": "0.100000 mol/L NaOH",
    "titrant_volume": "0.00000 mL",
    "temperature": "25 °C",
    "model": "exact weak-acid initial equilibrium"
  },
  "expected_outputs": {
    "sampled_point": {
      "titrant_volume_mL": 0,
      "pH": 2.8779
    },
    "key_curve_features": {
      "equivalence_point_mL": 50,
      "half_equivalence_point_mL": 25,
      "half_equivalence_pH": 4.75,
      "buffering_region_approximately_mL": "4.54545 to 45.4545",
      "pH_as_titrant_volume_increases": "approaches 14 from below after excess strong base dominates"
    }
  },
  "working": "Ka = 10^(-4.75) = 1.77827941e-5. For HA ⇌ H+ + A-, let x = [H+]. The exact weak-acid equation is x^2 + Ka*x - Ka*C = 0. Thus x = (-Ka + sqrt(Ka^2 + 4*Ka*C))/2 = (-1.77827941e-5 + sqrt((1.77827941e-5)^2 + 4*(1.77827941e-5)*(0.100000)))/2 = 0.00132466 mol/L. Therefore pH = -log10(0.00132466) = 2.87790."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The idealized formula set is not fully defined at the zero-titrant boundary, invalid negative-volume inputs produce logarithm and zero-volume failures, and unspecified volume units can change the computed pH from 4.76 to approximately 12.998.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche6/tranche6-results.json
• BOUNDARY_HAZARD_CATALOG.json