Graham's Law Effusion/Diffusion Calculator mechanism

Model scope

NEEDS_REVIEW because the exact ambiguity is that the spec does not identify which rate or time is known, does not state the equal-quantity assumption for time calculations, and uses diffusion as though Graham's effusion relationship were universally exact. The instrument should honestly label the result as a Graham-law estimate for effusion and an approximation for diffusion, and should document the atomic-weight table and unit-normalization rules.

• rate1/rate2 = sqrt(M2/M1) is the standard Graham-law relationship for effusion when rates are measured under comparable conditions and molar masses use the same units.
• For diffusion, the relationship is an approximation and may not apply exactly when gases have different intermolecular interactions, concentrations, pressures, or transport conditions; labeling the result simply as a diffusion rate may be misleading.
• The specification does not explicitly provide the time relationship needed for time outputs: for equal amounts of gas, t1/t2 = sqrt(M1/M2), equivalently t2 = t1*sqrt(M2/M1).
• The inputs do not specify which rate or time is known, so the direction of the calculation is ambiguous.

Units and conventions

• M1 and M2 are molar masses in the same units, conventionally g/mol; any parsed chemical formulas must use a defined atomic-weights table and a stated rounding convention.
• Rate1 and rate2 must use the same rate units before applying the ratio; unit conversion is not supplied by Graham's law itself.
• Times must use the same time units, and the time relationship assumes equal quantities of gas are being compared.
• The gases are compared under sufficiently similar temperature, pressure, and apparatus conditions.
• Formula-derived molar masses assume neutral molecular formulas and require unambiguous formula parsing.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "gas1": "H2",
    "M1_g_per_mol": 2,
    "gas2": "O2",
    "M2_g_per_mol": 32,
    "known_rate1_L_per_s": 8,
    "known_time1_s": 10
  },
  "expected_outputs": {
    "rate_ratio_rate1_over_rate2": 4,
    "rate2_L_per_s": 2,
    "time2_s": 40
  },
  "working": "M2/M1 = 32/2 = 16; sqrt(16) = 4, so rate1/rate2 = 4. rate2 = rate1/4 = 8/4 = 2 L/s. For equal gas quantities, t2 = t1*sqrt(M2/M1) = 10*4 = 40 s."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The specification permits an input with zero molar mass even though it makes the square-root argument undefined, so the calculator requires explicit domain rejection. It also leaves the direction of the reported rate ratio dependent on gas labeling, creating a convention hazard.

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