Buffer Capacity Estimator mechanism

Model scope

The core beta expression is acceptable under stated chemical assumptions, but the catalog specification must add pH as an input, define how [HA] and [A−] are derived, specify concentration units, and label the pKa±1 result as an approximate range. The output description says usable pH range shading, but no shading rule or capacity threshold is defined.

• The stated beta formula is standard for an ideal monoprotic HA/A− buffer when [HA] and [A−] are known: beta≈2.303·C_total·([HA][A−]/C_total²). However, the listed inputs omit pH and the individual species concentrations, so beta cannot be calculated from only pKa and total buffer concentration.
• The implementation must derive species fractions from pH and pKa, for example r=10^(pH−pKa), alpha_HA=1/(1+r), and alpha_A−=r/(1+r).
• The effective range pH=pKa±1 is an approximate rule of thumb, not an exact buffering-capacity boundary. It should be labeled as an approximate usable range rather than a rigorously calculated range.
• The formula assumes a monoprotic buffer, fixed total analytical concentration, ideal activities, and negligible water and other acid-base contributions. Those constraints are not stated.

Units and conventions

• pH and pKa are dimensionless base-10 quantities, and pKa refers to the same temperature, solvent, and ionic-strength conditions as the buffer.
• C_total must be a molar concentration in mol/L for beta to be reported in mol/L per pH unit. Concentration units cancel inside [HA][A−]/C_total² but not in the leading C_total factor.
• The test vectors convert mM to M before calculation.
• The numerical factor 2.303 is treated as an approximation to ln(10).

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "pKa": 4.76,
    "pH": 4.76,
    "total_buffer_concentration": 100,
    "concentration_unit": "mM"
  },
  "expected_outputs": {
    "beta_mol_L_per_pH": 0.057575,
    "effective_range_pH": {
      "lower": 3.76,
      "upper": 5.76
    }
  },
  "working": "Convert concentration: C_total=100 mM/1000=0.100 M. pH−pKa=4.76−4.76=0, so r=10^0=1. alpha_HA=1/(1+1)=0.5. alpha_A−=1/(1+1)=0.5. Species-product fraction=0.5×0.5=0.25. beta=2.303×0.100×0.25=0.057575 mol/L per pH. Range lower=4.76−1=3.76; upper=4.76+1=5.76."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

A zero total concentration produces the undefined expression 0/0, so the estimator requires explicit input rejection. The sign convention for pH-pKa is also not specified, creating a species-label ambiguity even though beta is symmetric and numerically unchanged.

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-tranche4/tranche4-results.json
• BOUNDARY_HAZARD_CATALOG.json