Source: https://guthlabs.ai/docs/instruments/titration-curve-plotter/mechanism/

instrument mechanism / verified-with-binding-errata

# Titration Curve Plotter mechanism

The inspectable method record for Titration Curve Plotter, kept separate from implementation and qualification.

Status: **VERIFIED_WITH_ERRATA**Lifecycle: **verified-with-binding-errata**

## Model scope

The supplied formulas are directionally standard for a monoprotic weak acid titrated by a strong base, but they do not fully specify the advertised instrument. The exact ambiguity requiring review is the unsupported meaning of 'strong/weak combinations' and the absence of a defined treatment for weak-base/strong-acid and weak/weak titrations. One arithmetic correction is important in the weak-acid and weak-base vectors: the exact initial quadratic result is 0.00133267 M, giving pH 2.87528 for the weak acid and pH 11.1247 for the weak base.

- The piecewise description is incomplete for the claimed strong/weak acid-base combinations: it does not specify separate charge-balance formulas for strong acid/strong base, weak base/strong acid, or weak acid/weak base titrations.

- At equivalence, using Kb of the conjugate is correct for a weak acid titrated by strong base, but a weak base titrated by strong acid requires Ka of the conjugate acid; weak/weak equivalence requires a different equilibrium treatment.

- The statement half-equivalence pH=pKa is valid only for a monoprotic weak acid titrated by a strong base. For a weak base titrated by strong acid, pOH=pKb and pH=pKw-pKb. It is not generally valid for strong/strong or weak/weak systems.

- The pre-equivalence Henderson-Hasselbalch approximation is not valid at the initial zero-titrant point and can be inaccurate when dissociation is not negligible compared with neutralized analyte.

- The specification does not state stoichiometry assumptions such as monoprotic acid/base behavior; equivalence volume and the piecewise equations change for polyprotic systems.

- A full pH curve requires explicit water autoionization and charge-balance handling near neutrality and at very low concentrations; the listed formulas do not define those cases.

## Units and conventions

- All concentrations are mol/L (M), all solution volumes are converted to liters before mole calculations, and titrant/analyte concentrations are analytical concentrations.

- Calculations assume 25 degrees C, with Kw=1.00e-14, pH=-log10[H+], and pOH=-log10[OH-].

- Solutions are treated as ideal: activities are approximated by concentrations and volume additivity is assumed.

- The test vectors use monoprotic acids/bases and 1:1 neutralization stoichiometry.

- Strong acid/base pH values assume complete dissociation; weak-species values use the stated Ka or Kb.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "analyte": {
      "type": "strong_acid",
      "formula": "HCl",
      "concentration_M": 0.1,
      "volume_mL": 25
    },
    "titrant": {
      "type": "strong_base",
      "formula": "NaOH",
      "concentration_M": 0.1
    },
    "sampled_volumes_mL": [
      0,
      12.5,
      25,
      30
    ]
  },
  "expected_outputs": {
    "curve_points": [
      {
        "volume_mL": 0,
        "pH": 1
      },
      {
        "volume_mL": 12.5,
        "pH": 1.477121
      },
      {
        "volume_mL": 25,
        "pH": 7
      },
      {
        "volume_mL": 30,
        "pH": 11.958607
      }
    ],
    "equivalence_volume_mL": 25,
    "half_equivalence_volume_mL": 12.5,
    "half_equivalence_pH": 1.477121,
    "key_features": {
      "equivalence_point": "pH 7.000000 under the 25 C ideal strong/strong assumption",
      "half_equivalence_note": "pH is not pKa; the analyte is a strong acid"
    }
  },
  "working": "Initial acid moles = 0.100 mol/L * 0.0250 L = 0.002500 mol. Equivalence volume = 0.002500 mol / 0.100 mol/L = 0.0250 L = 25.0 mL. At 0 mL: [H+]=0.100, so pH=-log10(0.100)=1.000000. At 12.5 mL: OH- moles=0.100*0.0125=0.001250 mol; remaining H+ moles=0.002500-0.001250=0.001250 mol; total volume=0.0375 L; [H+]=0.001250/0.0375=0.0333333; pH=-log10(0.0333333)=1.477121. At 25.0 mL, strong acid and strong base exactly neutralize, so pH=7.000000. At 30.0 mL: excess OH- moles=0.100*0.0300-0.002500=0.000500 mol; total volume=0.0550 L; [OH-]=0.000500/0.0550=0.00909091; pOH=-log10(0.00909091)=2.041393; pH=14.000000-2.041393=11.958607."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The zero-concentration titrant case creates a genuine division-by-zero in equivalence-volume calculation and must be rejected. The zero-volume boundary also exposes a likely log10(0) failure if the pre-equivalence Henderson-Hasselbalch formula is applied at the initial point. Volume-direction conventions require explicit handling.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/titration-curve-plotter/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/titration-curve-plotter/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/titration-curve-plotter/qualification/>)

## 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`