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      "sources",
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  "assumptions": [
    "Monoprotic B + H2O ⇌ BH+ + OH−",
    "Activity coefficients ≈ 1",
    "Kw = 1e-14 at 25 °C when mode=ice",
    "Not Henderson–Hasselbalch",
    "Not weak-acid ICE",
    "Not pH = −log10[H+] identities",
    "Not polyprotic, not titration"
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  "limitations": [
    "Monoprotic B only; not polyprotic, not a weak acid, not activity coefficients",
    "Not Henderson–Hasselbalch (buffer pair as given)",
    "Not weak-acid ICE HA ⇌ H+ + A−",
    "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 Kb ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "pKb and Kb together, or Ka/pKa, or HA/A → MIXED_INPUT_ENCODING",
    "hh_ph is not a mode on this page"
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  "sources": [
    {
      "title": "OpenStax Chemistry 2e — Weak Bases",
      "section": "Equilibrium of a weak base",
      "url": "https://openstax.org/books/chemistry-2e/pages/14-3-relative-strengths-of-acids-and-bases",
      "supports": "Kb = [BH+][OH−]/[B]; ICE from formal C; dilute water may include Kw",
      "kind": "reference"
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    {
      "title": "IUPAC Gold Book — basicity constant",
      "section": "basicity constant",
      "url": "https://goldbook.iupac.org/terms/view/B00618",
      "supports": "Kb is the equilibrium constant for B + H2O ⇌ BH+ + OH−",
      "kind": "standard"
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        "Kb": 0.000018,
        "mode": "ice_no_water"
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        "BH": 0.001332670973077975,
        "model": "weak_base_ice",
        "include_water": false
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      "expectWarning": null,
      "actual": {
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        "pH": 11.124722938776406,
        "pOH": 2.8752770612235934,
        "h": 7.503727622568977e-12,
        "oh": 0.00133267097408,
        "B": 0.09866732902592,
        "BH": 0.00133267097408,
        "C": 0.1,
        "Kb": 0.000018,
        "pKb": 4.7447274948966935,
        "fraction_ionized": 0.0133267097408,
        "Kw": 1e-14,
        "pKw": 14,
        "T_C": 25,
        "model": "weak_base_ice",
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          "residual": 2.68775200867e-15
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        "Kb": 0.000018
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        "pH": 11.124723226136462,
        "pOH": 2.875276773863538,
        "h": 7.503722657571816e-12,
        "oh": 0.00133267185587,
        "B": 0.09866732815163373,
        "BH": 0.0013326718483662773,
        "C": 0.1,
        "Kb": 0.000018,
        "pKb": 4.7447274948966935,
        "fraction_ionized": 0.013326718483662773,
        "Kw": 1e-14,
        "pKw": 14,
        "T_C": 25,
        "model": "weak_base_ice",
        "include_water": true,
        "solver": {
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          "iterations": 24,
          "residual": 3.14336051842e-15
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      "tol": 1e-8
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    {
      "id": "boundary-base-pkb",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "C": 0.1,
        "pKb": 5
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      "expect": {
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        "model": "weak_base_ice"
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      "actual": {
        "mode": "ice",
        "pH": 10.997829246869566,
        "pOH": 3.0021707531304345,
        "h": 1.0050108563577444e-11,
        "oh": 0.000995014127135,
        "B": 0.09900498588291512,
        "BH": 0.0009950141170848915,
        "C": 0.1,
        "Kb": 0.000009999999999999999,
        "pKb": 5,
        "fraction_ionized": 0.009950141170848914,
        "Kw": 1e-14,
        "pKw": 14,
        "T_C": 25,
        "model": "weak_base_ice",
        "include_water": true,
        "solver": {
          "method": "bisection",
          "iterations": 23,
          "residual": 3.22819381151e-15
        }
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      "tol": 1e-8
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    {
      "id": "boundary-base-missing",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "Kb": 0.00001
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      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "C is required"
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    {
      "id": "boundary-base-c",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "C": 0,
        "Kb": 0.00001
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      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
      "error": "C must be greater than zero"
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    {
      "id": "boundary-base-mixed",
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        "pKb": 5,
        "Kb": 0.00001
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      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Use pKb or Kb, not both encodings"
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    {
      "id": "boundary-base-ka",
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        "Ka": 0.00001
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      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Use Kb or pKb, not Ka/pKa — this is not a weak-acid ICE"
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        "Kb": 0.00001,
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      "id": "property-base-charge",
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      "detail": "pKb encoding",
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