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    "boundary": {
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    "property": {
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  "internally_reviewed": false,
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  "assumptions": [
    "Monoprotic HA ⇌ H+ + A−",
    "Activity coefficients ≈ 1",
    "Kw = 1e-14 at 25 °C when mode=ice",
    "Not Henderson–Hasselbalch",
    "Not pH = −log10[H+] identities",
    "Not polyprotic, not a weak base, not titration"
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  "limitations": [
    "Monoprotic HA only; not polyprotic, not a weak base, not activity coefficients",
    "Not Henderson–Hasselbalch (buffer pair as given)",
    "Not the water-ion identity page pH=−log10[H+]",
    "Kw = 1e-14 at 25 °C when mode=ice"
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  "boundary_conditions": [
    "missing C → MISSING_REQUIRED_INPUT",
    "C ≤ 0 or Ka ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "pKa and Ka together → MIXED_INPUT_ENCODING",
    "hh_ph is not a mode on this page"
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  "sources": [
    {
      "title": "OpenStax Chemistry 2e — Weak Acids",
      "section": "Equilibrium of a weak acid",
      "url": "https://openstax.org/books/chemistry-2e/pages/14-3-relative-strengths-of-acids-and-bases",
      "supports": "Ka = [H+][A−]/[HA]; ICE from formal C; dilute water may include Kw",
      "kind": "reference"
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    {
      "title": "IUPAC Gold Book — acid dissociation constant",
      "section": "acidity constant",
      "url": "https://goldbook.iupac.org/terms/view/A00080",
      "supports": "Ka is the equilibrium constant for HA ⇌ H+ + A−",
      "kind": "standard"
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  "fingerprint": "sha256:0487fdb858a23b1d782f18415e706a34132a45f9e48fe10d08e4dfbbf371dd0c",
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      "kind": "golden",
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        "Ka": 0.000018,
        "mode": "ice_no_water"
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        "A": 0.001332670973077975,
        "model": "weak_acid_ice",
        "include_water": false
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      "expectWarning": null,
      "actual": {
        "mode": "ice_no_water",
        "pH": 2.8752770612235934,
        "h": 0.00133267097408,
        "HA": 0.09866732902592,
        "A": 0.00133267097408,
        "oh": 7.503727622568977e-12,
        "C": 0.1,
        "Ka": 0.000018,
        "pKa": 4.7447274948966935,
        "fraction_dissociated": 0.0133267097408,
        "Kw": 1e-14,
        "pKw": 14,
        "T_C": 25,
        "model": "weak_acid_ice",
        "include_water": false,
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          "residual": 2.68775200867e-15
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      "tol": 1e-8
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      "ok": true,
      "kind": "golden",
      "inputs": {
        "C": 0.1,
        "Ka": 0.000018
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      "actual": {
        "mode": "ice",
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        "h": 0.00133267185587,
        "HA": 0.09866732815163373,
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        "oh": 7.503722657571816e-12,
        "C": 0.1,
        "Ka": 0.000018,
        "pKa": 4.7447274948966935,
        "fraction_dissociated": 0.013326718483662773,
        "Kw": 1e-14,
        "pKw": 14,
        "T_C": 25,
        "model": "weak_acid_ice",
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      "tol": 1e-8
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    {
      "id": "boundary-ice-pka",
      "ok": true,
      "kind": "boundary",
      "inputs": {
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        "pKa": 5
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      "expect": {
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        "model": "weak_acid_ice"
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      "actual": {
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        "pH": 3.0021707531304345,
        "h": 0.000995014127135,
        "HA": 0.09900498588291512,
        "A": 0.0009950141170848915,
        "oh": 1.0050108563577444e-11,
        "C": 0.1,
        "Ka": 0.000009999999999999999,
        "pKa": 5,
        "fraction_dissociated": 0.009950141170848914,
        "Kw": 1e-14,
        "pKw": 14,
        "T_C": 25,
        "model": "weak_acid_ice",
        "include_water": true,
        "solver": {
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          "residual": 3.22819381151e-15
        }
      },
      "tol": 1e-8
    },
    {
      "id": "boundary-ice-missing",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "Ka": 0.00001
      },
      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "C is required"
    },
    {
      "id": "boundary-ice-c",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "C": 0,
        "Ka": 0.00001
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      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
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    {
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        "pKa": 5,
        "Ka": 0.00001
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      "expectError": "MIXED_INPUT_ENCODING",
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