H2O2Equilibria

{
  "reference": {
    "notes": "source_ref: Aerosol.jl@c8c640bb:src/aqueous_equilibria.jl:519\n\nUpstream `H2O2Equilibria` is an MTK `@component` where T, H_plus, and p_H2O2 are `@variables` driven by a parent `AqueousEquilibria` system. For standalone serialization (and to make the component well-posed in isolation), T, H_plus, and p_H2O2 are declared as parameters here — matching the bead's `(S, observed-only)` classification. The six algebraic equations are unchanged from upstream.\n\nKey difference from SO2/CO2/NH3: K_h1 is temperature-independent (upstream `K_h1 ~ K_h1_298` with no van't Hoff correction). H2O2 is a very weak acid (pKa ≈ 11.6 at 298 K), so dissociation is negligible at typical atmospheric pH 3–7 (K_h1/H_plus ≤ 2.2×10⁻⁵ at pH 7, rising to 2.2 at pH 11).\n\nH_H2O2_298 = 1.0×10⁵ M/atm × 1000 mol·m⁻³/M ÷ 101325 Pa/atm = 986.9233 mol/(m³·Pa). K_h1_298 = 2.2×10⁻¹² M × 1000 = 2.2×10⁻⁹ mol/m³.\n\nTolerance rationale (model-level rel=1e-6): observed-only algebraic system (no ODE integration); 1e-6 covers float64 roundoff in the exp/multiply expression of the van't Hoff H_H2O2(T) closed form. K_h1 is constant; the dissociation and totals are simple products/sums."
  },
  "tolerance": {
    "rel": 1e-06
  },
  "variables": {
    "T": {
      "type": "parameter",
      "units": "K",
      "default": 298.0,
      "description": "Temperature"
    },
    "H_plus": {
      "type": "parameter",
      "units": "mol/m^3",
      "default": 0.0001,
      "description": "Hydrogen ion concentration (1e-4 mol/m³ = pH 7 in pure water at 298 K)"
    },
    "p_H2O2": {
      "type": "parameter",
      "units": "Pa",
      "default": 1.0,
      "description": "Partial pressure of H2O2"
    },
    "R_gas": {
      "type": "parameter",
      "units": "J/mol/K",
      "default": 8.314,
      "description": "Gas constant"
    },
    "T_ref": {
      "type": "parameter",
      "units": "K",
      "default": 298.0,
      "description": "Reference temperature"
    },
    "H_H2O2_298": {
      "type": "parameter",
      "units": "mol/m^3/Pa",
      "default": 986.9232667160128,
      "description": "Henry's law constant for H2O2 at 298 K (1.0×10⁵ M/atm converted to mol/(m³·Pa): 1.0e5 / 101325.0 * 1000.0)"
    },
    "dH_H_H2O2": {
      "type": "parameter",
      "units": "J/mol",
      "default": -60668.0,
      "description": "Heat of dissolution for H2O2 (-14.5 kcal/mol converted to J/mol; Seinfeld & Pandis Table 7.4)"
    },
    "K_h1_298": {
      "type": "parameter",
      "units": "mol/m^3",
      "default": 2.2e-09,
      "description": "Dissociation constant for H2O2 → H⁺ + HO2⁻ at 298 K (2.2×10⁻¹² M converted to mol/m³; very weak, temperature-independent in upstream source)"
    },
    "H_H2O2": {
      "type": "unknown",
      "units": "mol/m^3/Pa",
      "description": "Temperature-dependent Henry's law constant for H2O2"
    },
    "K_h1": {
      "type": "unknown",
      "units": "mol/m^3",
      "description": "Dissociation constant H2O2 → H⁺ + HO2⁻ (temperature-independent: K_h1 = K_h1_298)"
    },
    "H2O2_aq": {
      "type": "unknown",
      "units": "mol/m^3",
      "description": "Aqueous H2O2 concentration"
    },
    "HO2_minus": {
      "type": "unknown",
      "units": "mol/m^3",
      "description": "Hydroperoxide anion concentration [HO2-]"
    },
    "H2O2_total": {
      "type": "unknown",
      "units": "mol/m^3",
      "description": "Total dissolved hydrogen peroxide: [H2O2(aq)] + [HO2-]"
    },
    "H_H2O2_eff": {
      "type": "unknown",
      "units": "mol/m^3/Pa",
      "description": "Effective Henry's law constant for H2O2 accounting for dissociation: H_H2O2 × (1 + K_h1/[H+])"
    }
  },
  "equations": [
    {
      "lhs": "H_H2O2",
      "rhs": {
        "op": "*",
        "args": [
          "H_H2O2_298",
          {
            "op": "exp",
            "args": [
              {
                "op": "*",
                "args": [
                  {
                    "op": "/",
                    "args": [
                      "dH_H_H2O2",
                      "R_gas"
                    ]
                  },
                  {
                    "op": "+",
                    "args": [
                      {
                        "op": "/",
                        "args": [
                          1,
                          "T_ref"
                        ]
                      },
                      {
                        "op": "/",
                        "args": [
                          -1,
                          "T"
                        ]
                      }
                    ]
                  }
                ]
              }
            ]
          }
        ]
      }
    },
    {
      "lhs": "K_h1",
      "rhs": "K_h1_298"
    },
    {
      "lhs": "H2O2_aq",
      "rhs": {
        "op": "*",
        "args": [
          "H_H2O2",
          "p_H2O2"
        ]
      }
    },
    {
      "lhs": "HO2_minus",
      "rhs": {
        "op": "/",
        "args": [
          {
            "op": "*",
            "args": [
              "K_h1",
              "H2O2_aq"
            ]
          },
          "H_plus"
        ]
      }
    },
    {
      "lhs": "H2O2_total",
      "rhs": {
        "op": "+",
        "args": [
          "H2O2_aq",
          "HO2_minus"
        ]
      }
    },
    {
      "lhs": "H_H2O2_eff",
      "rhs": {
        "op": "*",
        "args": [
          "H_H2O2",
          {
            "op": "+",
            "args": [
              1,
              {
                "op": "/",
                "args": [
                  "K_h1",
                  "H_plus"
                ]
              }
            ]
          }
        ]
      }
    }
  ],
  "tests": [
    {
      "id": "reference_298K_pH7",
      "description": "Reference state at 298 K (T_ref) with neutral water (pH 7) and 1 Pa H2O2. At T=T_ref the van't Hoff exponent is zero so H_H2O2 = H_H2O2_298. K_h1 is temperature-independent and equals K_h1_298. The dissociation correction K_h1/H_plus = 2.2e-9/1e-4 = 2.2e-5 is negligible — HO2_minus is ~0.002% of H2O2_aq.",
      "parameter_overrides": {
        "T": 298.0,
        "H_plus": 0.0001,
        "p_H2O2": 1.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "H_H2O2",
          "time": 0.0,
          "expected": 986.9232667160128
        },
        {
          "variable": "K_h1",
          "time": 0.0,
          "expected": 2.2e-09
        },
        {
          "variable": "H2O2_aq",
          "time": 0.0,
          "expected": 986.9232667160128
        },
        {
          "variable": "HO2_minus",
          "time": 0.0,
          "expected": 0.02171231186775228
        },
        {
          "variable": "H2O2_total",
          "time": 0.0,
          "expected": 986.9449790278805
        },
        {
          "variable": "H_H2O2_eff",
          "time": 0.0,
          "expected": 986.9449790278805
        }
      ]
    },
    {
      "id": "cold_273K_pH7",
      "description": "Cold cloud water at 273.15 K (0°C), pH 7. H2O2 has a very large negative ΔH_sol (−14.5 kcal/mol = −60668 J/mol), so solubility increases sharply with cooling — H_H2O2 grows ~9.3× relative to 298 K. K_h1 is unchanged (temperature-independent).",
      "parameter_overrides": {
        "T": 273.15,
        "H_plus": 0.0001,
        "p_H2O2": 1.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "H_H2O2",
          "time": 0.0,
          "expected": 9157.256660439376
        },
        {
          "variable": "K_h1",
          "time": 0.0,
          "expected": 2.2e-09
        },
        {
          "variable": "H2O2_aq",
          "time": 0.0,
          "expected": 9157.256660439376
        },
        {
          "variable": "HO2_minus",
          "time": 0.0,
          "expected": 0.20145964652966625
        },
        {
          "variable": "H2O2_total",
          "time": 0.0,
          "expected": 9157.458120085907
        },
        {
          "variable": "H_H2O2_eff",
          "time": 0.0,
          "expected": 9157.458120085905
        }
      ]
    },
    {
      "id": "cold_280K_pH7",
      "description": "Intermediate cold-water reference (280 K), pH 7. H_H2O2 ≈ 4763.6 mol/(m³·Pa), roughly 4.8× the 298 K value.",
      "parameter_overrides": {
        "T": 280.0,
        "H_plus": 0.0001,
        "p_H2O2": 1.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "H_H2O2",
          "time": 0.0,
          "expected": 4763.550867474284
        },
        {
          "variable": "H2O2_aq",
          "time": 0.0,
          "expected": 4763.550867474284
        }
      ]
    },
    {
      "id": "warm_310K_pH7",
      "description": "Warm-cloud reference (310 K), pH 7. H2O2 solubility falls with warming (large negative ΔH_sol): H_H2O2 ≈ 382.5 mol/(m³·Pa), about 0.39× the 298 K value.",
      "parameter_overrides": {
        "T": 310.0,
        "H_plus": 0.0001,
        "p_H2O2": 1.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "H_H2O2",
          "time": 0.0,
          "expected": 382.4940875002585
        },
        {
          "variable": "H2O2_aq",
          "time": 0.0,
          "expected": 382.4940875002585
        },
        {
          "variable": "HO2_minus",
          "time": 0.0,
          "expected": 0.008414869925005687
        },
        {
          "variable": "H_H2O2_eff",
          "time": 0.0,
          "expected": 382.5025023701835
        }
      ]
    },
    {
      "id": "hot_318K_pH7",
      "description": "Upper-range reference (318 K, 45°C) for warm aqueous-phase chemistry.",
      "parameter_overrides": {
        "T": 318.0,
        "H_plus": 0.0001,
        "p_H2O2": 1.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "H_H2O2",
          "time": 0.0,
          "expected": 211.56603164215167
        },
        {
          "variable": "H2O2_aq",
          "time": 0.0,
          "expected": 211.56603164215167
        }
      ]
    },
    {
      "id": "van_t_hoff_ratio_check",
      "description": "Explicit van't Hoff ratio: H_H2O2(273.15) / H_H2O2(298) = exp((-60668/8.314) × (1/298 - 1/273.15)) ≈ 9.27. Verified via the ratio of the cold_273K and reference_298K test values: 9157.26/986.92 ≈ 9.27. States H_H2O2_eff matches H_H2O2 × (1 + K_h1/H_plus) at a p=2 Pa case.",
      "parameter_overrides": {
        "T": 273.15,
        "H_plus": 0.0001,
        "p_H2O2": 2.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "H_H2O2",
          "time": 0.0,
          "expected": 9157.256660439376
        },
        {
          "variable": "H2O2_aq",
          "time": 0.0,
          "expected": 18314.513320878752
        },
        {
          "variable": "HO2_minus",
          "time": 0.0,
          "expected": 0.4029192930593325
        }
      ]
    },
    {
      "id": "acidic_pH4_298K",
      "description": "Acidic cloud water (pH 4, [H+] = 0.1 mol/m³) at 298 K. K_h1/H_plus = 2.2e-9/0.1 = 2.2e-8 — even smaller fraction dissociated than at pH 7. H_H2O2_eff → H_H2O2 to excellent approximation.",
      "parameter_overrides": {
        "T": 298.0,
        "H_plus": 0.1,
        "p_H2O2": 1.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "H2O2_aq",
          "time": 0.0,
          "expected": 986.9232667160128
        },
        {
          "variable": "HO2_minus",
          "time": 0.0,
          "expected": 2.171231186775228e-05
        },
        {
          "variable": "H2O2_total",
          "time": 0.0,
          "expected": 986.9232884283247
        },
        {
          "variable": "H_H2O2_eff",
          "time": 0.0,
          "expected": 986.9232884283247
        }
      ]
    },
    {
      "id": "acidic_pH2_298K",
      "description": "Strongly acidic regime (pH 2, [H+] = 10 mol/m³) at 298 K. K_h1/H_plus = 2.2e-10 — dissociation completely negligible. Stress-tests the HO2_minus and H_H2O2_eff expressions at the far-acidic tail.",
      "parameter_overrides": {
        "T": 298.0,
        "H_plus": 10.0,
        "p_H2O2": 1.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "HO2_minus",
          "time": 0.0,
          "expected": 2.1712311867752282e-07
        },
        {
          "variable": "H_H2O2_eff",
          "time": 0.0,
          "expected": 986.9232669331359
        }
      ]
    },
    {
      "id": "basic_pH11_298K",
      "description": "Basic regime (pH 11, [H+] = 1e-8 mol/m³) at 298 K. K_h1/H_plus = 2.2e-9/1e-8 = 0.22 — dissociation is now ~22% of H2O2_aq, comparable. H_H2O2_eff is ~1.22× H_H2O2.",
      "parameter_overrides": {
        "T": 298.0,
        "H_plus": 1e-08,
        "p_H2O2": 1.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "H2O2_aq",
          "time": 0.0,
          "expected": 986.9232667160128
        },
        {
          "variable": "HO2_minus",
          "time": 0.0,
          "expected": 217.12311867752283
        },
        {
          "variable": "H2O2_total",
          "time": 0.0,
          "expected": 1204.0463853935357
        },
        {
          "variable": "H_H2O2_eff",
          "time": 0.0,
          "expected": 1204.0463853935355
        }
      ]
    },
    {
      "id": "basic_pH12_298K",
      "description": "Basic regime (pH 12, [H+] = 1e-9 mol/m³) at 298 K. K_h1/H_plus = 2.2 — dissociation is now substantial: HO2_minus ≈ 2.2× H2O2_aq. H_H2O2_eff ≈ 3.2× H_H2O2. Exercises the high-pH enhancement of the effective Henry's constant.",
      "parameter_overrides": {
        "T": 298.0,
        "H_plus": 1e-09,
        "p_H2O2": 1.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "HO2_minus",
          "time": 0.0,
          "expected": 2171.2311867752283
        },
        {
          "variable": "H2O2_total",
          "time": 0.0,
          "expected": 3158.154453491241
        },
        {
          "variable": "H_H2O2_eff",
          "time": 0.0,
          "expected": 3158.1544534912405
        }
      ]
    },
    {
      "id": "high_p_H2O2",
      "description": "Henry's-law linearity check: 10× p_H2O2 at fixed T and H_plus scales H2O2_aq, HO2_minus, H2O2_total by 10× while leaving H_H2O2, K_h1, H_H2O2_eff unchanged.",
      "parameter_overrides": {
        "T": 298.0,
        "H_plus": 0.0001,
        "p_H2O2": 10.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "H2O2_aq",
          "time": 0.0,
          "expected": 9869.232667160128
        },
        {
          "variable": "HO2_minus",
          "time": 0.0,
          "expected": 0.2171231186775228
        },
        {
          "variable": "H2O2_total",
          "time": 0.0,
          "expected": 9869.449790278804
        },
        {
          "variable": "H_H2O2_eff",
          "time": 0.0,
          "expected": 986.9449790278805
        }
      ]
    },
    {
      "id": "low_p_H2O2",
      "description": "Henry's-law linearity check at low partial pressure: p_H2O2 = 0.01 Pa scales H2O2_aq by 0.01× from baseline. H_H2O2_eff is independent of p_H2O2.",
      "parameter_overrides": {
        "T": 298.0,
        "H_plus": 0.0001,
        "p_H2O2": 0.01
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "H2O2_aq",
          "time": 0.0,
          "expected": 9.869232667160128
        },
        {
          "variable": "H2O2_total",
          "time": 0.0,
          "expected": 9.869449790278805
        },
        {
          "variable": "H_H2O2_eff",
          "time": 0.0,
          "expected": 986.9449790278805
        }
      ]
    },
    {
      "id": "coupled_cold_acidic",
      "description": "Cross-check: cold (273.15 K) AND acidic (pH 4). Combines the van't Hoff temperature shift (H_H2O2 grows ~9.3×) with the acidic suppression of HO2_minus. Dissociation is negligible at pH 4 regardless of T.",
      "parameter_overrides": {
        "T": 273.15,
        "H_plus": 0.1,
        "p_H2O2": 1.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "H_H2O2",
          "time": 0.0,
          "expected": 9157.256660439376
        },
        {
          "variable": "H2O2_aq",
          "time": 0.0,
          "expected": 9157.256660439376
        },
        {
          "variable": "H2O2_total",
          "time": 0.0,
          "expected": 9157.256861899023
        },
        {
          "variable": "H_H2O2_eff",
          "time": 0.0,
          "expected": 9157.256861899023
        }
      ]
    },
    {
      "id": "coupled_warm_basic",
      "description": "Cross-check: warm (310 K) AND basic (pH 11). Reduced H_H2O2 (lower T reduces solubility) combined with elevated dissociation at high pH. K_h1/H_plus = 2.2e-9/1e-8 = 0.22 → HO2_minus ≈ 84 mol/m³, H_H2O2_eff ≈ 1.22× H_H2O2.",
      "parameter_overrides": {
        "T": 310.0,
        "H_plus": 1e-08,
        "p_H2O2": 1.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "H_H2O2",
          "time": 0.0,
          "expected": 382.4940875002585
        },
        {
          "variable": "H2O2_aq",
          "time": 0.0,
          "expected": 382.4940875002585
        },
        {
          "variable": "HO2_minus",
          "time": 0.0,
          "expected": 84.14869925005686
        },
        {
          "variable": "H_H2O2_eff",
          "time": 0.0,
          "expected": 466.64278675031534
        }
      ]
    }
  ],
  "analyses": [
    {
      "id": "H_H2O2_vs_temperature",
      "description": "Van't Hoff temperature dependence of the H2O2 Henry's law constant (S&P Table 7.3). With ΔH_sol = −14.5 kcal/mol, H2O2 is one of the most strongly temperature-sensitive atmospheric gases — H_H2O2 increases ~43× from 45°C (318 K) to 0°C (273 K), much larger than SO2 (~2.6×) or CO2 (~2.1×). This strong temperature sensitivity controls H2O2 partitioning between gas and cloud-droplet phases.",
      "initial_state": {},
      "parameters": {
        "H_plus": 0.0001,
        "p_H2O2": 1.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "parameter_sweep": {
        "type": "cartesian",
        "dimensions": [
          {
            "parameter": "T",
            "range": {
              "start": 273.15,
              "stop": 318.0,
              "count": 20,
              "scale": "linear"
            }
          }
        ]
      },
      "plots": [
        {
          "id": "H_H2O2_curve",
          "type": "line",
          "description": "H_H2O2(T) — van't Hoff curve showing steep increase of H2O2 solubility at low T.",
          "x": {
            "variable": "T",
            "label": "Temperature (K)"
          },
          "y": {
            "variable": "H_H2O2",
            "label": "H_H2O2 (mol/(m³·Pa))"
          }
        },
        {
          "id": "H2O2_aq_curve",
          "type": "line",
          "description": "Aqueous H2O2 concentration vs temperature at 1 Pa partial pressure.",
          "x": {
            "variable": "T",
            "label": "Temperature (K)"
          },
          "y": {
            "variable": "H2O2_aq",
            "label": "[H2O2(aq)] (mol/m³)"
          }
        }
      ]
    },
    {
      "id": "H_H2O2_eff_vs_pH",
      "description": "Effective Henry's law constant H*_H2O2 = H_H2O2 × (1 + K_h1/[H+]) vs [H+] at 298 K. H2O2 pKa ≈ 11.6, so the dissociation enhancement is negligible below pH 10 and only becomes noticeable above pH 11. At pH 12, H*_H2O2 ≈ 3.2× H_H2O2. This is in stark contrast to SO2 (pKa1 ≈ 1.9) where dissociation enhances H*_SO2 by many orders of magnitude across the atmospheric pH range.",
      "initial_state": {},
      "parameters": {
        "T": 298.0,
        "p_H2O2": 1.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "parameter_sweep": {
        "type": "cartesian",
        "dimensions": [
          {
            "parameter": "H_plus",
            "range": {
              "start": 1e-10,
              "stop": 1.0,
              "count": 25,
              "scale": "log"
            }
          }
        ]
      },
      "plots": [
        {
          "id": "Hstar_curve",
          "type": "line",
          "description": "H*_H2O2 vs [H+] — flat until pH > 10, then rises steeply above the pKa ≈ 11.6.",
          "x": {
            "variable": "H_plus",
            "label": "[H⁺] (mol/m³, log scale)"
          },
          "y": {
            "variable": "H_H2O2_eff",
            "label": "H*_H2O2 (mol/(m³·Pa), log scale)"
          }
        }
      ]
    },
    {
      "id": "coupled_T_p_sweep",
      "description": "Henry's law: aqueous H2O2 concentration as a function of both temperature (van't Hoff) and partial pressure (linearity). Sweeping T from 273 K to 318 K and p_H2O2 from 1e-5 to 1.0 Pa shows the joint T-p surface that determines cloud-droplet H2O2 in atmospheric models.",
      "initial_state": {},
      "parameters": {
        "H_plus": 0.0001
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "parameter_sweep": {
        "type": "cartesian",
        "dimensions": [
          {
            "parameter": "T",
            "range": {
              "start": 273.15,
              "stop": 318.0,
              "count": 10,
              "scale": "linear"
            }
          },
          {
            "parameter": "p_H2O2",
            "range": {
              "start": 1e-05,
              "stop": 1.0,
              "count": 15,
              "scale": "log"
            }
          }
        ]
      },
      "plots": [
        {
          "id": "H2O2_aq_heatmap",
          "type": "heatmap",
          "description": "[H2O2(aq)] as a function of T and p_H2O2.",
          "x": {
            "variable": "T",
            "label": "Temperature (K)"
          },
          "y": {
            "variable": "p_H2O2",
            "label": "p(H2O2) (Pa, log scale)"
          },
          "value": {
            "variable": "H2O2_aq",
            "reduce": "final"
          }
        }
      ]
    }
  ]
}