AqueousEquilibria
Coupled gas-aqueous chemical equilibrium for cloud droplets and aerosol water. Migrated from Aerosol.jl@c8c640bb src/aqueous_equilibria.jl:642. Composes WaterEquilibrium, CO2Equilibria, SO2Equilibria, NH3Equilibria, HNO3Equilibria, H2O2Equilibria, and O3Equilibria via a quadratic charge-balance approximation for H+. Reference: Seinfeld & Pandis (2016) Ch. 7 §7.3.
Description
Coupled gas-aqueous chemical equilibrium for cloud droplets and aerosol water. Migrated from Aerosol.jl@c8c640bb src/aqueous_equilibria.jl:642. Composes WaterEquilibrium, CO2Equilibria, SO2Equilibria, NH3Equilibria, HNO3Equilibria, H2O2Equilibria, and O3Equilibria via a quadratic charge-balance approximation for H+. Reference: Seinfeld & Pandis (2016) Ch. 7 §7.3.
Reference
_source_ref: Aerosol.jl@c8c640bb:src/aqueous_equilibria.jl:642
Upstream AqueousEquilibria uses EarthSciML coupling.couple to compose seven sub-equilibria, adding the electroneutrality (charge-balance) equation:
H+ + NH4+ = OH- + HCO3- + 2·CO3²- + HSO3- + 2·SO3²- + NO3- + HO2-
The upstream Julia MTK system uses structural_simplify to eliminate the implicit H+ cycle. The ESS algebraic solver cannot directly handle this implicit polynomial system (it requires a DAG-structured equation graph). Instead, this ESM uses a quadratic approximation that retains only the mono-anion terms (ignoring CO3²- and SO3²-):
H+ = sqrt[(K_w + K_c1·CO2_aq + K_s1·SO2_aq + K_n1·HNO3_aq + K_h1·H2O2_aq) / (1 + K_a1·NH3_aq / K_w)]
Accuracy of the approximation:
- Valid for pH 4–7 where CO3²-/HCO3- = K_c2/H+ « 1 and SO3²-/HSO3- = K_s2/H+ « 1
- Error < 0.1% for CO2-only (pH 5.6), NH3-only, O3/H2O2 presence, and temperature sweeps
- Error < 0.5% for small SO2 at low pH (pH < 5)
- Error ~12% at pH 6.4 with significant SO2+NH3 (SO3²-/HSO3- ≈ 17%)
All van’t Hoff constants and Henry’s law constants are identical to the standalone sub-component ESMs (water.esm, co2.esm, so2.esm, nh3.esm, hno3.esm, h2o2.esm, o3.esm).
Tolerance rationale (model-level rel=1e-6): fully explicit DAG algebraic system. Each equation is a closed-form expression; rel=1e-6 covers float64 roundoff in the van’t Hoff exponentials and the sqrt expression across the atmospheric ranges._
Parameters
| Name | Units | Default | Description |
|---|---|---|---|
T | K | 298.0 | Temperature. |
p_CO2 | Pa | 40.0 | Partial pressure of CO2 (≈ 400 ppm at 1 atm ≈ 40 Pa). |
p_SO2 | Pa | 0.0 | Partial pressure of SO2. |
p_NH3 | Pa | 0.0 | Partial pressure of NH3. |
p_HNO3 | Pa | 0.0 | Partial pressure of HNO3. |
p_H2O2 | Pa | 0.0 | Partial pressure of H2O2. |
p_O3 | Pa | 0.0 | Partial pressure of O3. |
R_gas | J/mol/K | 8.314 | Gas constant. |
T_ref | K | 298.0 | Reference temperature. |
C_ref | mol/m^3 | 1000.0 | Reference concentration for pH (1 mol/L = 1000 mol/m³). |
K_w_298 | mol^2/m^6 | 1e-08 | Water dissociation constant at 298 K (1e-14 M² → mol²/m⁶). |
dH_Kw | J/mol | 55856.4 | Enthalpy for K_w (13.35 kcal/mol; Seinfeld & Pandis Table 7.4). |
H_CO2_298 | mol/m^3/Pa | 0.0003355539106834444 | Henry constant for CO2 at 298 K (3.4e-2 M/atm → mol/m³/Pa). |
dH_H_CO2 | J/mol | -20292.4 | Heat of dissolution for CO2 (-4.85 kcal/mol; Seinfeld & Pandis Table 7.4). |
K_c1_298 | mol/m^3 | 0.00043 | K_c1 at 298 K (4.3e-7 M → mol/m³). |
K_c2_298 | mol/m^3 | 4.7e-08 | K_c2 at 298 K (4.7e-11 M → mol/m³). |
dH_Kc1 | J/mol | 7657.12 | Enthalpy for K_c1 (upstream literal verbatim). |
dH_Kc2 | J/mol | 14853.2 | Enthalpy for K_c2 (3.55 kcal/mol). |
H_SO2_298 | mol/m^3/Pa | 0.012139156180606956 | Henry constant for SO2 at 298 K. |
dH_H_SO2 | J/mol | -26150.0 | Heat of dissolution for SO2 (-6.25 kcal/mol; Seinfeld & Pandis Table 7.4). |
K_s1_298 | mol/m^3 | 13.0 | K_s1 at 298 K (0.013 M → mol/m³). |
K_s2_298 | mol/m^3 | 6.6e-05 | K_s2 at 298 K (6.6e-8 M → mol/m³). |
dH_Ks1 | J/mol | -17405.44 | Enthalpy for K_s1 (-4.16 kcal/mol; Seinfeld & Pandis Table 7.4). |
dH_Ks2 | J/mol | -9330.32 | Enthalpy for K_s2 (-2.23 kcal/mol; Seinfeld & Pandis Table 7.4). |
H_NH3_298 | mol/m^3/Pa | 0.611892425363928 | Henry constant for NH3 at 298 K (62.0 M/atm → mol/m³/Pa). |
dH_H_NH3 | J/mol | -34183.28 | Heat of dissolution for NH3 (-8.17 kcal/mol; Seinfeld & Pandis Table 7.4). |
K_a1_298 | mol/m^3 | 0.017 | NH3·H2O dissociation constant at 298 K (1.7e-5 M → mol/m³). |
dH_Ka1 | J/mol | 36191.6 | Enthalpy for K_a1 (8.65 kcal/mol; Seinfeld & Pandis Table 7.4). |
H_HNO3_298 | mol/m^3/Pa | 2072.53886010363 | Henry constant for HNO3 at 298 K (2.1e5 M/atm → mol/m³/Pa). |
dH_H_HNO3 | J/mol | 0.0 | Heat of dissolution for HNO3 (temperature-independent; Seinfeld & Pandis Table 7.4). |
K_n1_298 | mol/m^3 | 15400.0 | HNO3 dissociation constant (15.4 M → mol/m³; strong acid, temperature-independent). |
H_H2O2_298 | mol/m^3/Pa | 986.9232667160128 | Henry constant for H2O2 at 298 K (1.0e5 M/atm → mol/m³/Pa). |
dH_H_H2O2 | J/mol | -60668.0 | Heat of dissolution for H2O2 (-14.5 kcal/mol; Seinfeld & Pandis Table 7.4). |
K_h1_298 | mol/m^3 | 2.2e-09 | H2O2 dissociation constant at 298 K (2.2e-12 M → mol/m³; temperature-independent). |
H_O3_298 | mol/m^3/Pa | 0.0001085615593387614 | Henry constant for O3 at 298 K (1.1e-2 M/atm → mol/m³/Pa). |
dH_H_O3 | J/mol | -21087.36 | Heat of dissolution for O3 (-5.04 kcal/mol; Seinfeld & Pandis Table 7.4). |
Observed
| Name | Units | Default | Description |
|---|---|---|---|
K_w | mol^2/m^6 | Water dissociation constant K_w(T) via van’t Hoff (Seinfeld & Pandis Eq 7.10). | |
H_CO2 | mol/m^3/Pa | Henry’s law constant for CO2 at temperature T. | |
K_c1 | mol/m^3 | CO2 first dissociation constant K_c1(T). | |
K_c2 | mol/m^3 | CO2 second dissociation constant K_c2(T). | |
CO2_aq | mol/m^3 | Aqueous CO2 concentration [CO2·H2O]. | |
H_SO2 | mol/m^3/Pa | Henry’s law constant for SO2 at temperature T. | |
K_s1 | mol/m^3 | SO2 first dissociation constant K_s1(T). | |
K_s2 | mol/m^3 | SO2 second dissociation constant K_s2(T). | |
SO2_aq | mol/m^3 | Aqueous SO2 concentration [SO2·H2O]. | |
H_NH3 | mol/m^3/Pa | Henry’s law constant for NH3 at temperature T. | |
K_a1 | mol/m^3 | NH3·H2O dissociation constant K_a1(T). | |
NH3_aq | mol/m^3 | Aqueous NH3 concentration [NH3·H2O]. | |
H_HNO3 | mol/m^3/Pa | Henry’s law constant for HNO3 (≈ H_HNO3_298, dH≈0). | |
K_n1 | mol/m^3 | HNO3 dissociation constant (= K_n1_298; strong acid, temperature-independent). | |
HNO3_aq | mol/m^3 | Undissociated HNO3 concentration [HNO3(aq)]. | |
H_H2O2 | mol/m^3/Pa | Henry’s law constant for H2O2 at temperature T. | |
K_h1 | mol/m^3 | H2O2 dissociation constant (= K_h1_298; temperature-independent). | |
H2O2_aq | mol/m^3 | Aqueous H2O2 concentration. | |
H_O3 | mol/m^3/Pa | Henry’s law constant for O3 at temperature T. | |
O3_aq | mol/m^3 | Aqueous O3 concentration. | |
H_plus | mol/m^3 | Hydrogen ion concentration solved by the quadratic charge-balance approximation. See reference notes for the accuracy bounds. | |
OH_minus | mol/m^3 | Hydroxide ion concentration [OH-]. | |
pH | 1 | pH = -log10([H+] / C_ref). | |
HCO3_minus | mol/m^3 | Bicarbonate concentration [HCO3-]. | |
CO3_2minus | mol/m^3 | Carbonate concentration [CO3²-]. | |
C_total | mol/m^3 | Total dissolved inorganic carbon (CO2_aq + HCO3- + CO3²-). | |
H_CO2_eff | mol/m^3/Pa | Effective Henry constant for CO2 (S&P Eq 7.24). | |
HSO3_minus | mol/m^3 | Bisulfite concentration [HSO3-]. | |
SO3_2minus | mol/m^3 | Sulfite concentration [SO3²-]. | |
S_IV_total | mol/m^3 | Total S(IV) concentration (SO2_aq + HSO3- + SO3²-). | |
H_SO2_eff | mol/m^3/Pa | Effective Henry constant for SO2. | |
alpha_0 | 1 | Fraction of S(IV) as SO2(aq). | |
alpha_1 | 1 | Fraction of S(IV) as HSO3-. | |
alpha_2 | 1 | Fraction of S(IV) as SO3²-. | |
NH4_plus | mol/m^3 | Ammonium concentration [NH4+]. | |
NH3_total | mol/m^3 | Total dissolved ammonia (NH3_aq + NH4+). | |
H_NH3_eff | mol/m^3/Pa | Effective Henry constant for NH3. | |
NO3_minus | mol/m^3 | Nitrate concentration [NO3-]. | |
HNO3_total | mol/m^3 | Total dissolved nitric acid. | |
H_HNO3_eff | mol/m^3/Pa | Effective Henry constant for HNO3. | |
HO2_minus | mol/m^3 | Peroxide anion concentration [HO2-]. | |
H2O2_total | mol/m^3 | Total dissolved H2O2. | |
H_H2O2_eff | mol/m^3/Pa | Effective Henry constant for H2O2. |
Observed expressions
$$ K_{w} = K_{w\,298} \cdot e^{\left(-1\right) \cdot \frac{dH_{Kw}}{R_{gas}} \cdot \left(\frac{1}{T} + \frac{-1}{T_{ref}}\right)} $$Water dissociation constant K_w(T) via van’t Hoff (Seinfeld & Pandis Eq 7.10).
$$ H_{CO2} = H_{CO2\,298} \cdot e^{\frac{dH_{H\,CO2}}{R_{gas}} \cdot \left(\frac{1}{T_{ref}} + \frac{-1}{T}\right)} $$Henry’s law constant for CO2 at temperature T.
$$ K_{c1} = K_{c1\,298} \cdot e^{\left(-1\right) \cdot \frac{dH_{Kc1}}{R_{gas}} \cdot \left(\frac{1}{T} + \frac{-1}{T_{ref}}\right)} $$CO2 first dissociation constant K_c1(T).
$$ K_{c2} = K_{c2\,298} \cdot e^{\left(-1\right) \cdot \frac{dH_{Kc2}}{R_{gas}} \cdot \left(\frac{1}{T} + \frac{-1}{T_{ref}}\right)} $$CO2 second dissociation constant K_c2(T).
$$ CO2_{aq} = H_{CO2} \cdot p_{CO2} $$Aqueous CO2 concentration [CO2·H2O].
$$ H_{SO2} = H_{SO2\,298} \cdot e^{\frac{dH_{H\,SO2}}{R_{gas}} \cdot \left(\frac{1}{T_{ref}} + \frac{-1}{T}\right)} $$Henry’s law constant for SO2 at temperature T.
$$ K_{s1} = K_{s1\,298} \cdot e^{\left(-1\right) \cdot \frac{dH_{Ks1}}{R_{gas}} \cdot \left(\frac{1}{T} + \frac{-1}{T_{ref}}\right)} $$SO2 first dissociation constant K_s1(T).
$$ K_{s2} = K_{s2\,298} \cdot e^{\left(-1\right) \cdot \frac{dH_{Ks2}}{R_{gas}} \cdot \left(\frac{1}{T} + \frac{-1}{T_{ref}}\right)} $$SO2 second dissociation constant K_s2(T).
$$ SO2_{aq} = H_{SO2} \cdot p_{SO2} $$Aqueous SO2 concentration [SO2·H2O].
$$ H_{NH3} = H_{NH3\,298} \cdot e^{\frac{dH_{H\,NH3}}{R_{gas}} \cdot \left(\frac{1}{T_{ref}} + \frac{-1}{T}\right)} $$Henry’s law constant for NH3 at temperature T.
$$ K_{a1} = K_{a1\,298} \cdot e^{\left(-1\right) \cdot \frac{dH_{Ka1}}{R_{gas}} \cdot \left(\frac{1}{T} + \frac{-1}{T_{ref}}\right)} $$NH3·H2O dissociation constant K_a1(T).
$$ NH3_{aq} = H_{NH3} \cdot p_{NH3} $$Aqueous NH3 concentration [NH3·H2O].
$$ H_{HNO3} = H_{HNO3\,298} \cdot e^{\frac{dH_{H\,HNO3}}{R_{gas}} \cdot \left(\frac{1}{T_{ref}} + \frac{-1}{T}\right)} $$Henry’s law constant for HNO3 (≈ H_HNO3_298, dH≈0).
$$ K_{n1} = K_{n1\,298} $$HNO3 dissociation constant (= K_n1_298; strong acid, temperature-independent).
$$ HNO3_{aq} = H_{HNO3} \cdot p_{HNO3} $$Undissociated HNO3 concentration [HNO3(aq)].
$$ H_{H2O2} = H_{H2O2\,298} \cdot e^{\frac{dH_{H\,H2O2}}{R_{gas}} \cdot \left(\frac{1}{T_{ref}} + \frac{-1}{T}\right)} $$Henry’s law constant for H2O2 at temperature T.
$$ K_{h1} = K_{h1\,298} $$H2O2 dissociation constant (= K_h1_298; temperature-independent).
$$ H2O2_{aq} = H_{H2O2} \cdot p_{H2O2} $$Aqueous H2O2 concentration.
$$ H_{O3} = H_{O3\,298} \cdot e^{\frac{dH_{H\,O3} \cdot \left(\frac{1}{T_{ref}} + \frac{-1}{T}\right)}{R_{gas}}} $$Henry’s law constant for O3 at temperature T.
$$ O3_{aq} = H_{O3} \cdot p_{O3} $$Aqueous O3 concentration.
$$ H_{plus} = \frac{K_{w} + K_{c1} \cdot CO2_{aq} + K_{s1} \cdot SO2_{aq} + K_{n1} \cdot HNO3_{aq} + K_{h1} \cdot H2O2_{aq}}{1 + \frac{K_{a1} \cdot NH3_{aq}}{K_{w}}}^{0.5} $$Hydrogen ion concentration solved by the quadratic charge-balance approximation. See reference notes for the accuracy bounds.
$$ OH_{minus} = \frac{K_{w}}{H_{plus}} $$Hydroxide ion concentration [OH-].
$$ pH = \left(-1\right) \cdot \log_{10}\left(\frac{H_{plus}}{C_{ref}}\right) $$pH = -log10([H+] / C_ref).
$$ HCO3_{minus} = \frac{K_{c1} \cdot CO2_{aq}}{H_{plus}} $$Bicarbonate concentration [HCO3-].
$$ CO3_{2minus} = \frac{K_{c2} \cdot HCO3_{minus}}{H_{plus}} $$Carbonate concentration [CO3²-].
$$ C_{total} = CO2_{aq} + HCO3_{minus} + CO3_{2minus} $$Total dissolved inorganic carbon (CO2_aq + HCO3- + CO3²-).
$$ H_{CO2\,eff} = H_{CO2} \cdot \left(1 + \frac{K_{c1}}{H_{plus}} + \frac{K_{c1} \cdot K_{c2}}{H_{plus}^{2}}\right) $$Effective Henry constant for CO2 (S&P Eq 7.24).
$$ HSO3_{minus} = \frac{K_{s1} \cdot SO2_{aq}}{H_{plus}} $$Bisulfite concentration [HSO3-].
$$ SO3_{2minus} = \frac{K_{s2} \cdot HSO3_{minus}}{H_{plus}} $$Sulfite concentration [SO3²-].
$$ S_{IV\,total} = SO2_{aq} + HSO3_{minus} + SO3_{2minus} $$Total S(IV) concentration (SO2_aq + HSO3- + SO3²-).
$$ H_{SO2\,eff} = H_{SO2} \cdot \left(1 + \frac{K_{s1}}{H_{plus}} + \frac{K_{s1} \cdot K_{s2}}{H_{plus}^{2}}\right) $$Effective Henry constant for SO2.
$$ alpha_{0} = \frac{H_{plus}^{2}}{H_{plus}^{2} + K_{s1} \cdot H_{plus} + K_{s1} \cdot K_{s2}} $$Fraction of S(IV) as SO2(aq).
$$ alpha_{1} = \frac{K_{s1} \cdot H_{plus}}{H_{plus}^{2} + K_{s1} \cdot H_{plus} + K_{s1} \cdot K_{s2}} $$Fraction of S(IV) as HSO3-.
$$ alpha_{2} = \frac{K_{s1} \cdot K_{s2}}{H_{plus}^{2} + K_{s1} \cdot H_{plus} + K_{s1} \cdot K_{s2}} $$Fraction of S(IV) as SO3²-.
$$ NH4_{plus} = \frac{K_{a1} \cdot NH3_{aq}}{OH_{minus}} $$Ammonium concentration [NH4+].
$$ NH3_{total} = NH3_{aq} + NH4_{plus} $$Total dissolved ammonia (NH3_aq + NH4+).
$$ H_{NH3\,eff} = H_{NH3} \cdot \left(1 + \frac{K_{a1} \cdot H_{plus}}{K_{w}}\right) $$Effective Henry constant for NH3.
$$ NO3_{minus} = \frac{K_{n1} \cdot HNO3_{aq}}{H_{plus}} $$Nitrate concentration [NO3-].
$$ HNO3_{total} = HNO3_{aq} + NO3_{minus} $$Total dissolved nitric acid.
$$ H_{HNO3\,eff} = H_{HNO3} \cdot \left(1 + \frac{K_{n1}}{H_{plus}}\right) $$Effective Henry constant for HNO3.
$$ HO2_{minus} = \frac{K_{h1} \cdot H2O2_{aq}}{H_{plus}} $$Peroxide anion concentration [HO2-].
$$ H2O2_{total} = H2O2_{aq} + HO2_{minus} $$Total dissolved H2O2.
$$ H_{H2O2\,eff} = H_{H2O2} \cdot \left(1 + \frac{K_{h1}}{H_{plus}}\right) $$Effective Henry constant for H2O2.
Analyses
ph_vs_temperature_co2_only
pH of CO2-only cloud water vs temperature (273-318 K). Higher T decreases CO2 solubility (raising pH); K_w change is secondary. Net effect: pH increases slightly with T.
Time span: 0.0 → 1.0
Swept over: T
ph_vs_p_SO2
SO2 acidification curve: pH vs p_SO2 at 298 K with p_CO2=40 Pa background. Transition from CO2-dominated (pH 5.6) to SO2-dominated (pH < 4) regimes.
Time span: 0.0 → 1.0
Swept over: p_SO2
ph_vs_p_NH3
NH3 buffering curve: pH vs p_NH3 at 298 K with p_CO2=40 Pa background. NH3 forms NH4+ and OH-, raising pH from 5.6 toward 7.
Time span: 0.0 → 1.0
Swept over: p_NH3
Raw .esm
Raw .esm JSON (this component)
{
"reference": {
"notes": "source_ref: Aerosol.jl@c8c640bb:src/aqueous_equilibria.jl:642\n\nUpstream `AqueousEquilibria` uses EarthSciML `coupling.couple` to compose seven sub-equilibria, adding the electroneutrality (charge-balance) equation:\n H+ + NH4+ = OH- + HCO3- + 2·CO3²- + HSO3- + 2·SO3²- + NO3- + HO2-\n\nThe upstream Julia MTK system uses structural_simplify to eliminate the implicit H+ cycle. The ESS algebraic solver cannot directly handle this implicit polynomial system (it requires a DAG-structured equation graph). Instead, this ESM uses a quadratic approximation that retains only the mono-anion terms (ignoring CO3²- and SO3²-):\n\n H+ = sqrt[(K_w + K_c1·CO2_aq + K_s1·SO2_aq + K_n1·HNO3_aq + K_h1·H2O2_aq) / (1 + K_a1·NH3_aq / K_w)]\n\nAccuracy of the approximation:\n- Valid for pH 4–7 where CO3²-/HCO3- = K_c2/H+ << 1 and SO3²-/HSO3- = K_s2/H+ << 1\n- Error < 0.1% for CO2-only (pH 5.6), NH3-only, O3/H2O2 presence, and temperature sweeps\n- Error < 0.5% for small SO2 at low pH (pH < 5)\n- Error ~12% at pH 6.4 with significant SO2+NH3 (SO3²-/HSO3- ≈ 17%)\n\nAll van't Hoff constants and Henry's law constants are identical to the standalone sub-component ESMs (water.esm, co2.esm, so2.esm, nh3.esm, hno3.esm, h2o2.esm, o3.esm).\n\nTolerance rationale (model-level rel=1e-6): fully explicit DAG algebraic system. Each equation is a closed-form expression; rel=1e-6 covers float64 roundoff in the van't Hoff exponentials and the sqrt expression across the atmospheric ranges."
},
"tolerance": {
"rel": 1e-06
},
"variables": {
"T": {
"type": "parameter",
"units": "K",
"default": 298.0,
"description": "Temperature."
},
"p_CO2": {
"type": "parameter",
"units": "Pa",
"default": 40.0,
"description": "Partial pressure of CO2 (≈ 400 ppm at 1 atm ≈ 40 Pa)."
},
"p_SO2": {
"type": "parameter",
"units": "Pa",
"default": 0.0,
"description": "Partial pressure of SO2."
},
"p_NH3": {
"type": "parameter",
"units": "Pa",
"default": 0.0,
"description": "Partial pressure of NH3."
},
"p_HNO3": {
"type": "parameter",
"units": "Pa",
"default": 0.0,
"description": "Partial pressure of HNO3."
},
"p_H2O2": {
"type": "parameter",
"units": "Pa",
"default": 0.0,
"description": "Partial pressure of H2O2."
},
"p_O3": {
"type": "parameter",
"units": "Pa",
"default": 0.0,
"description": "Partial pressure of O3."
},
"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."
},
"C_ref": {
"type": "parameter",
"units": "mol/m^3",
"default": 1000.0,
"description": "Reference concentration for pH (1 mol/L = 1000 mol/m³)."
},
"K_w_298": {
"type": "parameter",
"units": "mol^2/m^6",
"default": 1e-08,
"description": "Water dissociation constant at 298 K (1e-14 M² → mol²/m⁶)."
},
"dH_Kw": {
"type": "parameter",
"units": "J/mol",
"default": 55856.4,
"description": "Enthalpy for K_w (13.35 kcal/mol; Seinfeld & Pandis Table 7.4)."
},
"H_CO2_298": {
"type": "parameter",
"units": "mol/m^3/Pa",
"default": 0.0003355539106834444,
"description": "Henry constant for CO2 at 298 K (3.4e-2 M/atm → mol/m³/Pa)."
},
"dH_H_CO2": {
"type": "parameter",
"units": "J/mol",
"default": -20292.4,
"description": "Heat of dissolution for CO2 (-4.85 kcal/mol; Seinfeld & Pandis Table 7.4)."
},
"K_c1_298": {
"type": "parameter",
"units": "mol/m^3",
"default": 0.00043,
"description": "K_c1 at 298 K (4.3e-7 M → mol/m³)."
},
"K_c2_298": {
"type": "parameter",
"units": "mol/m^3",
"default": 4.7e-08,
"description": "K_c2 at 298 K (4.7e-11 M → mol/m³)."
},
"dH_Kc1": {
"type": "parameter",
"units": "J/mol",
"default": 7657.12,
"description": "Enthalpy for K_c1 (upstream literal verbatim)."
},
"dH_Kc2": {
"type": "parameter",
"units": "J/mol",
"default": 14853.2,
"description": "Enthalpy for K_c2 (3.55 kcal/mol)."
},
"H_SO2_298": {
"type": "parameter",
"units": "mol/m^3/Pa",
"default": 0.012139156180606956,
"description": "Henry constant for SO2 at 298 K."
},
"dH_H_SO2": {
"type": "parameter",
"units": "J/mol",
"default": -26150.0,
"description": "Heat of dissolution for SO2 (-6.25 kcal/mol; Seinfeld & Pandis Table 7.4)."
},
"K_s1_298": {
"type": "parameter",
"units": "mol/m^3",
"default": 13.0,
"description": "K_s1 at 298 K (0.013 M → mol/m³)."
},
"K_s2_298": {
"type": "parameter",
"units": "mol/m^3",
"default": 6.6e-05,
"description": "K_s2 at 298 K (6.6e-8 M → mol/m³)."
},
"dH_Ks1": {
"type": "parameter",
"units": "J/mol",
"default": -17405.44,
"description": "Enthalpy for K_s1 (-4.16 kcal/mol; Seinfeld & Pandis Table 7.4)."
},
"dH_Ks2": {
"type": "parameter",
"units": "J/mol",
"default": -9330.32,
"description": "Enthalpy for K_s2 (-2.23 kcal/mol; Seinfeld & Pandis Table 7.4)."
},
"H_NH3_298": {
"type": "parameter",
"units": "mol/m^3/Pa",
"default": 0.611892425363928,
"description": "Henry constant for NH3 at 298 K (62.0 M/atm → mol/m³/Pa)."
},
"dH_H_NH3": {
"type": "parameter",
"units": "J/mol",
"default": -34183.28,
"description": "Heat of dissolution for NH3 (-8.17 kcal/mol; Seinfeld & Pandis Table 7.4)."
},
"K_a1_298": {
"type": "parameter",
"units": "mol/m^3",
"default": 0.017,
"description": "NH3·H2O dissociation constant at 298 K (1.7e-5 M → mol/m³)."
},
"dH_Ka1": {
"type": "parameter",
"units": "J/mol",
"default": 36191.6,
"description": "Enthalpy for K_a1 (8.65 kcal/mol; Seinfeld & Pandis Table 7.4)."
},
"H_HNO3_298": {
"type": "parameter",
"units": "mol/m^3/Pa",
"default": 2072.53886010363,
"description": "Henry constant for HNO3 at 298 K (2.1e5 M/atm → mol/m³/Pa)."
},
"dH_H_HNO3": {
"type": "parameter",
"units": "J/mol",
"default": 0.0,
"description": "Heat of dissolution for HNO3 (temperature-independent; Seinfeld & Pandis Table 7.4)."
},
"K_n1_298": {
"type": "parameter",
"units": "mol/m^3",
"default": 15400.0,
"description": "HNO3 dissociation constant (15.4 M → mol/m³; strong acid, temperature-independent)."
},
"H_H2O2_298": {
"type": "parameter",
"units": "mol/m^3/Pa",
"default": 986.9232667160128,
"description": "Henry constant for H2O2 at 298 K (1.0e5 M/atm → mol/m³/Pa)."
},
"dH_H_H2O2": {
"type": "parameter",
"units": "J/mol",
"default": -60668.0,
"description": "Heat of dissolution for H2O2 (-14.5 kcal/mol; Seinfeld & Pandis Table 7.4)."
},
"K_h1_298": {
"type": "parameter",
"units": "mol/m^3",
"default": 2.2e-09,
"description": "H2O2 dissociation constant at 298 K (2.2e-12 M → mol/m³; temperature-independent)."
},
"H_O3_298": {
"type": "parameter",
"units": "mol/m^3/Pa",
"default": 0.0001085615593387614,
"description": "Henry constant for O3 at 298 K (1.1e-2 M/atm → mol/m³/Pa)."
},
"dH_H_O3": {
"type": "parameter",
"units": "J/mol",
"default": -21087.36,
"description": "Heat of dissolution for O3 (-5.04 kcal/mol; Seinfeld & Pandis Table 7.4)."
},
"K_w": {
"type": "unknown",
"units": "mol^2/m^6",
"description": "Water dissociation constant K_w(T) via van't Hoff (Seinfeld & Pandis Eq 7.10)."
},
"H_CO2": {
"type": "unknown",
"units": "mol/m^3/Pa",
"description": "Henry's law constant for CO2 at temperature T."
},
"K_c1": {
"type": "unknown",
"units": "mol/m^3",
"description": "CO2 first dissociation constant K_c1(T)."
},
"K_c2": {
"type": "unknown",
"units": "mol/m^3",
"description": "CO2 second dissociation constant K_c2(T)."
},
"CO2_aq": {
"type": "unknown",
"units": "mol/m^3",
"description": "Aqueous CO2 concentration [CO2·H2O]."
},
"H_SO2": {
"type": "unknown",
"units": "mol/m^3/Pa",
"description": "Henry's law constant for SO2 at temperature T."
},
"K_s1": {
"type": "unknown",
"units": "mol/m^3",
"description": "SO2 first dissociation constant K_s1(T)."
},
"K_s2": {
"type": "unknown",
"units": "mol/m^3",
"description": "SO2 second dissociation constant K_s2(T)."
},
"SO2_aq": {
"type": "unknown",
"units": "mol/m^3",
"description": "Aqueous SO2 concentration [SO2·H2O]."
},
"H_NH3": {
"type": "unknown",
"units": "mol/m^3/Pa",
"description": "Henry's law constant for NH3 at temperature T."
},
"K_a1": {
"type": "unknown",
"units": "mol/m^3",
"description": "NH3·H2O dissociation constant K_a1(T)."
},
"NH3_aq": {
"type": "unknown",
"units": "mol/m^3",
"description": "Aqueous NH3 concentration [NH3·H2O]."
},
"H_HNO3": {
"type": "unknown",
"units": "mol/m^3/Pa",
"description": "Henry's law constant for HNO3 (≈ H_HNO3_298, dH≈0)."
},
"K_n1": {
"type": "unknown",
"units": "mol/m^3",
"description": "HNO3 dissociation constant (= K_n1_298; strong acid, temperature-independent)."
},
"HNO3_aq": {
"type": "unknown",
"units": "mol/m^3",
"description": "Undissociated HNO3 concentration [HNO3(aq)]."
},
"H_H2O2": {
"type": "unknown",
"units": "mol/m^3/Pa",
"description": "Henry's law constant for H2O2 at temperature T."
},
"K_h1": {
"type": "unknown",
"units": "mol/m^3",
"description": "H2O2 dissociation constant (= K_h1_298; temperature-independent)."
},
"H2O2_aq": {
"type": "unknown",
"units": "mol/m^3",
"description": "Aqueous H2O2 concentration."
},
"H_O3": {
"type": "unknown",
"units": "mol/m^3/Pa",
"description": "Henry's law constant for O3 at temperature T."
},
"O3_aq": {
"type": "unknown",
"units": "mol/m^3",
"description": "Aqueous O3 concentration."
},
"H_plus": {
"type": "unknown",
"units": "mol/m^3",
"description": "Hydrogen ion concentration solved by the quadratic charge-balance approximation. See reference notes for the accuracy bounds."
},
"OH_minus": {
"type": "unknown",
"units": "mol/m^3",
"description": "Hydroxide ion concentration [OH-]."
},
"pH": {
"type": "unknown",
"units": "1",
"description": "pH = -log10([H+] / C_ref)."
},
"HCO3_minus": {
"type": "unknown",
"units": "mol/m^3",
"description": "Bicarbonate concentration [HCO3-]."
},
"CO3_2minus": {
"type": "unknown",
"units": "mol/m^3",
"description": "Carbonate concentration [CO3²-]."
},
"C_total": {
"type": "unknown",
"units": "mol/m^3",
"description": "Total dissolved inorganic carbon (CO2_aq + HCO3- + CO3²-)."
},
"H_CO2_eff": {
"type": "unknown",
"units": "mol/m^3/Pa",
"description": "Effective Henry constant for CO2 (S&P Eq 7.24)."
},
"HSO3_minus": {
"type": "unknown",
"units": "mol/m^3",
"description": "Bisulfite concentration [HSO3-]."
},
"SO3_2minus": {
"type": "unknown",
"units": "mol/m^3",
"description": "Sulfite concentration [SO3²-]."
},
"S_IV_total": {
"type": "unknown",
"units": "mol/m^3",
"description": "Total S(IV) concentration (SO2_aq + HSO3- + SO3²-)."
},
"H_SO2_eff": {
"type": "unknown",
"units": "mol/m^3/Pa",
"description": "Effective Henry constant for SO2."
},
"alpha_0": {
"type": "unknown",
"units": "1",
"description": "Fraction of S(IV) as SO2(aq)."
},
"alpha_1": {
"type": "unknown",
"units": "1",
"description": "Fraction of S(IV) as HSO3-."
},
"alpha_2": {
"type": "unknown",
"units": "1",
"description": "Fraction of S(IV) as SO3²-."
},
"NH4_plus": {
"type": "unknown",
"units": "mol/m^3",
"description": "Ammonium concentration [NH4+]."
},
"NH3_total": {
"type": "unknown",
"units": "mol/m^3",
"description": "Total dissolved ammonia (NH3_aq + NH4+)."
},
"H_NH3_eff": {
"type": "unknown",
"units": "mol/m^3/Pa",
"description": "Effective Henry constant for NH3."
},
"NO3_minus": {
"type": "unknown",
"units": "mol/m^3",
"description": "Nitrate concentration [NO3-]."
},
"HNO3_total": {
"type": "unknown",
"units": "mol/m^3",
"description": "Total dissolved nitric acid."
},
"H_HNO3_eff": {
"type": "unknown",
"units": "mol/m^3/Pa",
"description": "Effective Henry constant for HNO3."
},
"HO2_minus": {
"type": "unknown",
"units": "mol/m^3",
"description": "Peroxide anion concentration [HO2-]."
},
"H2O2_total": {
"type": "unknown",
"units": "mol/m^3",
"description": "Total dissolved H2O2."
},
"H_H2O2_eff": {
"type": "unknown",
"units": "mol/m^3/Pa",
"description": "Effective Henry constant for H2O2."
}
},
"equations": [
{
"lhs": "K_w",
"rhs": {
"op": "*",
"args": [
"K_w_298",
{
"op": "exp",
"args": [
{
"op": "*",
"args": [
-1,
{
"op": "/",
"args": [
"dH_Kw",
"R_gas"
]
},
{
"op": "+",
"args": [
{
"op": "/",
"args": [
1,
"T"
]
},
{
"op": "/",
"args": [
-1,
"T_ref"
]
}
]
}
]
}
]
}
]
}
},
{
"lhs": "H_CO2",
"rhs": {
"op": "*",
"args": [
"H_CO2_298",
{
"op": "exp",
"args": [
{
"op": "*",
"args": [
{
"op": "/",
"args": [
"dH_H_CO2",
"R_gas"
]
},
{
"op": "+",
"args": [
{
"op": "/",
"args": [
1,
"T_ref"
]
},
{
"op": "/",
"args": [
-1,
"T"
]
}
]
}
]
}
]
}
]
}
},
{
"lhs": "K_c1",
"rhs": {
"op": "*",
"args": [
"K_c1_298",
{
"op": "exp",
"args": [
{
"op": "*",
"args": [
-1,
{
"op": "/",
"args": [
"dH_Kc1",
"R_gas"
]
},
{
"op": "+",
"args": [
{
"op": "/",
"args": [
1,
"T"
]
},
{
"op": "/",
"args": [
-1,
"T_ref"
]
}
]
}
]
}
]
}
]
}
},
{
"lhs": "K_c2",
"rhs": {
"op": "*",
"args": [
"K_c2_298",
{
"op": "exp",
"args": [
{
"op": "*",
"args": [
-1,
{
"op": "/",
"args": [
"dH_Kc2",
"R_gas"
]
},
{
"op": "+",
"args": [
{
"op": "/",
"args": [
1,
"T"
]
},
{
"op": "/",
"args": [
-1,
"T_ref"
]
}
]
}
]
}
]
}
]
}
},
{
"lhs": "CO2_aq",
"rhs": {
"op": "*",
"args": [
"H_CO2",
"p_CO2"
]
}
},
{
"lhs": "H_SO2",
"rhs": {
"op": "*",
"args": [
"H_SO2_298",
{
"op": "exp",
"args": [
{
"op": "*",
"args": [
{
"op": "/",
"args": [
"dH_H_SO2",
"R_gas"
]
},
{
"op": "+",
"args": [
{
"op": "/",
"args": [
1,
"T_ref"
]
},
{
"op": "/",
"args": [
-1,
"T"
]
}
]
}
]
}
]
}
]
}
},
{
"lhs": "K_s1",
"rhs": {
"op": "*",
"args": [
"K_s1_298",
{
"op": "exp",
"args": [
{
"op": "*",
"args": [
-1,
{
"op": "/",
"args": [
"dH_Ks1",
"R_gas"
]
},
{
"op": "+",
"args": [
{
"op": "/",
"args": [
1,
"T"
]
},
{
"op": "/",
"args": [
-1,
"T_ref"
]
}
]
}
]
}
]
}
]
}
},
{
"lhs": "K_s2",
"rhs": {
"op": "*",
"args": [
"K_s2_298",
{
"op": "exp",
"args": [
{
"op": "*",
"args": [
-1,
{
"op": "/",
"args": [
"dH_Ks2",
"R_gas"
]
},
{
"op": "+",
"args": [
{
"op": "/",
"args": [
1,
"T"
]
},
{
"op": "/",
"args": [
-1,
"T_ref"
]
}
]
}
]
}
]
}
]
}
},
{
"lhs": "SO2_aq",
"rhs": {
"op": "*",
"args": [
"H_SO2",
"p_SO2"
]
}
},
{
"lhs": "H_NH3",
"rhs": {
"op": "*",
"args": [
"H_NH3_298",
{
"op": "exp",
"args": [
{
"op": "*",
"args": [
{
"op": "/",
"args": [
"dH_H_NH3",
"R_gas"
]
},
{
"op": "+",
"args": [
{
"op": "/",
"args": [
1,
"T_ref"
]
},
{
"op": "/",
"args": [
-1,
"T"
]
}
]
}
]
}
]
}
]
}
},
{
"lhs": "K_a1",
"rhs": {
"op": "*",
"args": [
"K_a1_298",
{
"op": "exp",
"args": [
{
"op": "*",
"args": [
-1,
{
"op": "/",
"args": [
"dH_Ka1",
"R_gas"
]
},
{
"op": "+",
"args": [
{
"op": "/",
"args": [
1,
"T"
]
},
{
"op": "/",
"args": [
-1,
"T_ref"
]
}
]
}
]
}
]
}
]
}
},
{
"lhs": "NH3_aq",
"rhs": {
"op": "*",
"args": [
"H_NH3",
"p_NH3"
]
}
},
{
"lhs": "H_HNO3",
"rhs": {
"op": "*",
"args": [
"H_HNO3_298",
{
"op": "exp",
"args": [
{
"op": "*",
"args": [
{
"op": "/",
"args": [
"dH_H_HNO3",
"R_gas"
]
},
{
"op": "+",
"args": [
{
"op": "/",
"args": [
1,
"T_ref"
]
},
{
"op": "/",
"args": [
-1,
"T"
]
}
]
}
]
}
]
}
]
}
},
{
"lhs": "K_n1",
"rhs": "K_n1_298"
},
{
"lhs": "HNO3_aq",
"rhs": {
"op": "*",
"args": [
"H_HNO3",
"p_HNO3"
]
}
},
{
"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": "H_O3",
"rhs": {
"op": "*",
"args": [
"H_O3_298",
{
"op": "exp",
"args": [
{
"op": "/",
"args": [
{
"op": "*",
"args": [
"dH_H_O3",
{
"op": "+",
"args": [
{
"op": "/",
"args": [
1,
"T_ref"
]
},
{
"op": "/",
"args": [
-1,
"T"
]
}
]
}
]
},
"R_gas"
]
}
]
}
]
}
},
{
"lhs": "O3_aq",
"rhs": {
"op": "*",
"args": [
"H_O3",
"p_O3"
]
}
},
{
"lhs": "H_plus",
"rhs": {
"op": "^",
"args": [
{
"op": "/",
"args": [
{
"op": "+",
"args": [
"K_w",
{
"op": "*",
"args": [
"K_c1",
"CO2_aq"
]
},
{
"op": "*",
"args": [
"K_s1",
"SO2_aq"
]
},
{
"op": "*",
"args": [
"K_n1",
"HNO3_aq"
]
},
{
"op": "*",
"args": [
"K_h1",
"H2O2_aq"
]
}
]
},
{
"op": "+",
"args": [
1,
{
"op": "/",
"args": [
{
"op": "*",
"args": [
"K_a1",
"NH3_aq"
]
},
"K_w"
]
}
]
}
]
},
0.5
]
}
},
{
"lhs": "OH_minus",
"rhs": {
"op": "/",
"args": [
"K_w",
"H_plus"
]
}
},
{
"lhs": "pH",
"rhs": {
"op": "*",
"args": [
-1,
{
"op": "log10",
"args": [
{
"op": "/",
"args": [
"H_plus",
"C_ref"
]
}
]
}
]
}
},
{
"lhs": "HCO3_minus",
"rhs": {
"op": "/",
"args": [
{
"op": "*",
"args": [
"K_c1",
"CO2_aq"
]
},
"H_plus"
]
}
},
{
"lhs": "CO3_2minus",
"rhs": {
"op": "/",
"args": [
{
"op": "*",
"args": [
"K_c2",
"HCO3_minus"
]
},
"H_plus"
]
}
},
{
"lhs": "C_total",
"rhs": {
"op": "+",
"args": [
"CO2_aq",
"HCO3_minus",
"CO3_2minus"
]
}
},
{
"lhs": "H_CO2_eff",
"rhs": {
"op": "*",
"args": [
"H_CO2",
{
"op": "+",
"args": [
1,
{
"op": "/",
"args": [
"K_c1",
"H_plus"
]
},
{
"op": "/",
"args": [
{
"op": "*",
"args": [
"K_c1",
"K_c2"
]
},
{
"op": "^",
"args": [
"H_plus",
2
]
}
]
}
]
}
]
}
},
{
"lhs": "HSO3_minus",
"rhs": {
"op": "/",
"args": [
{
"op": "*",
"args": [
"K_s1",
"SO2_aq"
]
},
"H_plus"
]
}
},
{
"lhs": "SO3_2minus",
"rhs": {
"op": "/",
"args": [
{
"op": "*",
"args": [
"K_s2",
"HSO3_minus"
]
},
"H_plus"
]
}
},
{
"lhs": "S_IV_total",
"rhs": {
"op": "+",
"args": [
"SO2_aq",
"HSO3_minus",
"SO3_2minus"
]
}
},
{
"lhs": "H_SO2_eff",
"rhs": {
"op": "*",
"args": [
"H_SO2",
{
"op": "+",
"args": [
1,
{
"op": "/",
"args": [
"K_s1",
"H_plus"
]
},
{
"op": "/",
"args": [
{
"op": "*",
"args": [
"K_s1",
"K_s2"
]
},
{
"op": "^",
"args": [
"H_plus",
2
]
}
]
}
]
}
]
}
},
{
"lhs": "alpha_0",
"rhs": {
"op": "/",
"args": [
{
"op": "^",
"args": [
"H_plus",
2
]
},
{
"op": "+",
"args": [
{
"op": "^",
"args": [
"H_plus",
2
]
},
{
"op": "*",
"args": [
"K_s1",
"H_plus"
]
},
{
"op": "*",
"args": [
"K_s1",
"K_s2"
]
}
]
}
]
}
},
{
"lhs": "alpha_1",
"rhs": {
"op": "/",
"args": [
{
"op": "*",
"args": [
"K_s1",
"H_plus"
]
},
{
"op": "+",
"args": [
{
"op": "^",
"args": [
"H_plus",
2
]
},
{
"op": "*",
"args": [
"K_s1",
"H_plus"
]
},
{
"op": "*",
"args": [
"K_s1",
"K_s2"
]
}
]
}
]
}
},
{
"lhs": "alpha_2",
"rhs": {
"op": "/",
"args": [
{
"op": "*",
"args": [
"K_s1",
"K_s2"
]
},
{
"op": "+",
"args": [
{
"op": "^",
"args": [
"H_plus",
2
]
},
{
"op": "*",
"args": [
"K_s1",
"H_plus"
]
},
{
"op": "*",
"args": [
"K_s1",
"K_s2"
]
}
]
}
]
}
},
{
"lhs": "NH4_plus",
"rhs": {
"op": "/",
"args": [
{
"op": "*",
"args": [
"K_a1",
"NH3_aq"
]
},
"OH_minus"
]
}
},
{
"lhs": "NH3_total",
"rhs": {
"op": "+",
"args": [
"NH3_aq",
"NH4_plus"
]
}
},
{
"lhs": "H_NH3_eff",
"rhs": {
"op": "*",
"args": [
"H_NH3",
{
"op": "+",
"args": [
1,
{
"op": "/",
"args": [
{
"op": "*",
"args": [
"K_a1",
"H_plus"
]
},
"K_w"
]
}
]
}
]
}
},
{
"lhs": "NO3_minus",
"rhs": {
"op": "/",
"args": [
{
"op": "*",
"args": [
"K_n1",
"HNO3_aq"
]
},
"H_plus"
]
}
},
{
"lhs": "HNO3_total",
"rhs": {
"op": "+",
"args": [
"HNO3_aq",
"NO3_minus"
]
}
},
{
"lhs": "H_HNO3_eff",
"rhs": {
"op": "*",
"args": [
"H_HNO3",
{
"op": "+",
"args": [
1,
{
"op": "/",
"args": [
"K_n1",
"H_plus"
]
}
]
}
]
}
},
{
"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": "pure_water_298K",
"description": "Pure water (no trace gases) at 298 K. H_plus = OH_minus = sqrt(K_w) = 1e-4 mol/m³ (pH 7). All trace-gas species are zero.",
"parameter_overrides": {
"T": 298.0,
"p_CO2": 0.0,
"p_SO2": 0.0,
"p_NH3": 0.0,
"p_HNO3": 0.0,
"p_H2O2": 0.0,
"p_O3": 0.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "H_plus",
"time": 0.0,
"expected": 0.0001
},
{
"variable": "OH_minus",
"time": 0.0,
"expected": 0.0001
},
{
"variable": "pH",
"time": 0.0,
"expected": 7.0
},
{
"variable": "K_w",
"time": 0.0,
"expected": 1e-08
},
{
"variable": "CO2_aq",
"time": 0.0,
"expected": 0.0
},
{
"variable": "SO2_aq",
"time": 0.0,
"expected": 0.0
}
]
},
{
"id": "co2_rainwater_298K",
"description": "CO2-only rainwater at 298 K (p_CO2=40 Pa ≈ 400 ppm). The quadratic charge balance H+ ≈ HCO3- gives pH ≈ 5.62.",
"parameter_overrides": {
"T": 298.0,
"p_CO2": 40.0,
"p_SO2": 0.0,
"p_NH3": 0.0,
"p_HNO3": 0.0,
"p_H2O2": 0.0,
"p_O3": 0.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "H_plus",
"time": 0.0,
"expected": 0.002404481,
"tolerance": {
"rel": 0.0001
}
},
{
"variable": "pH",
"time": 0.0,
"expected": 5.618979,
"tolerance": {
"rel": 0.0001
}
},
{
"variable": "OH_minus",
"time": 0.0,
"expected": 4.158902e-06,
"tolerance": {
"rel": 0.0001
}
},
{
"variable": "HCO3_minus",
"time": 0.0,
"expected": 0.002400322,
"tolerance": {
"rel": 0.0001
}
},
{
"variable": "CO2_aq",
"time": 0.0,
"expected": 0.01342216,
"tolerance": {
"rel": 0.0001
}
}
]
},
{
"id": "so2_acidification_298K",
"description": "SO2 acidification at 298 K (p_CO2=40 Pa, p_SO2=0.001 Pa). SO2 dissolves and dissociates, lowering pH from 5.62 to 4.89. The dominant anion is HSO3-.",
"parameter_overrides": {
"T": 298.0,
"p_CO2": 40.0,
"p_SO2": 0.001,
"p_NH3": 0.0,
"p_HNO3": 0.0,
"p_H2O2": 0.0,
"p_O3": 0.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "H_plus",
"time": 0.0,
"expected": 0.01279025,
"tolerance": {
"rel": 0.0001
}
},
{
"variable": "pH",
"time": 0.0,
"expected": 4.893121,
"tolerance": {
"rel": 0.0001
}
},
{
"variable": "HSO3_minus",
"time": 0.0,
"expected": 0.01233823,
"tolerance": {
"rel": 0.0001
}
},
{
"variable": "SO3_2minus",
"time": 0.0,
"expected": 6.366746e-05,
"tolerance": {
"rel": 0.0001
}
},
{
"variable": "S_IV_total",
"time": 0.0,
"expected": 0.01241403,
"tolerance": {
"rel": 0.0001
}
}
]
},
{
"id": "nh3_buffering_298K",
"description": "NH3 buffering at 298 K (p_CO2=40 Pa, p_NH3=0.001 Pa). NH3 dissolves and forms NH4+, raising pH from 5.62 to 7.13.",
"parameter_overrides": {
"T": 298.0,
"p_CO2": 40.0,
"p_SO2": 0.0,
"p_NH3": 0.001,
"p_HNO3": 0.0,
"p_H2O2": 0.0,
"p_O3": 0.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "H_plus",
"time": 0.0,
"expected": 7.451619e-05,
"tolerance": {
"rel": 0.0001
}
},
{
"variable": "pH",
"time": 0.0,
"expected": 7.127749,
"tolerance": {
"rel": 0.0001
}
},
{
"variable": "NH4_plus",
"time": 0.0,
"expected": 0.07751302,
"tolerance": {
"rel": 0.0001
}
},
{
"variable": "OH_minus",
"time": 0.0,
"expected": 0.000134199,
"tolerance": {
"rel": 0.0001
}
},
{
"variable": "HCO3_minus",
"time": 0.0,
"expected": 0.07745333,
"tolerance": {
"rel": 0.0001
}
}
]
},
{
"id": "cold_cloud_273K",
"description": "Cold cloud water at 273.15 K (p_CO2=40 Pa). Lower T increases CO2 solubility and decreases K_w, shifting pH down to 5.52 vs 5.62 at 298 K.",
"parameter_overrides": {
"T": 273.15,
"p_CO2": 40.0,
"p_SO2": 0.0,
"p_NH3": 0.0,
"p_HNO3": 0.0,
"p_H2O2": 0.0,
"p_O3": 0.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "H_plus",
"time": 0.0,
"expected": 0.003029871,
"tolerance": {
"rel": 0.0001
}
},
{
"variable": "pH",
"time": 0.0,
"expected": 5.518576,
"tolerance": {
"rel": 0.0001
}
},
{
"variable": "CO2_aq",
"time": 0.0,
"expected": 0.02827668,
"tolerance": {
"rel": 0.0001
}
},
{
"variable": "K_w",
"time": 0.0,
"expected": 1.286025e-09,
"tolerance": {
"rel": 0.0001
}
}
]
},
{
"id": "warm_cloud_310K",
"description": "Warm cloud water at 310 K (p_CO2=40 Pa). Higher T decreases CO2 solubility, shifting pH up to 5.66 vs 5.62 at 298 K.",
"parameter_overrides": {
"T": 310.0,
"p_CO2": 40.0,
"p_SO2": 0.0,
"p_NH3": 0.0,
"p_HNO3": 0.0,
"p_H2O2": 0.0,
"p_O3": 0.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "H_plus",
"time": 0.0,
"expected": 0.002182085,
"tolerance": {
"rel": 0.0001
}
},
{
"variable": "pH",
"time": 0.0,
"expected": 5.661128,
"tolerance": {
"rel": 0.0001
}
},
{
"variable": "CO2_aq",
"time": 0.0,
"expected": 0.009775288,
"tolerance": {
"rel": 0.0001
}
},
{
"variable": "K_w",
"time": 0.0,
"expected": 2.39337e-08,
"tolerance": {
"rel": 0.0001
}
}
]
},
{
"id": "so2_nh3_competition_298K",
"description": "SO2+NH3 competition at 298 K (p_CO2=40 Pa, p_SO2=0.001 Pa, p_NH3=0.001 Pa). The quadratic approximation (ignoring CO3²- and SO3²-) gives pH 6.40. Note: at this pH SO3²-/HSO3- ≈ 17%, so the exact charge balance yields slightly higher H_plus; the model error here is ~12%.",
"parameter_overrides": {
"T": 298.0,
"p_CO2": 40.0,
"p_SO2": 0.001,
"p_NH3": 0.001,
"p_HNO3": 0.0,
"p_H2O2": 0.0,
"p_O3": 0.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "H_plus",
"time": 0.0,
"expected": 0.000396377,
"tolerance": {
"rel": 0.001
}
},
{
"variable": "pH",
"time": 0.0,
"expected": 6.401892,
"tolerance": {
"rel": 0.001
}
},
{
"variable": "NH4_plus",
"time": 0.0,
"expected": 0.4123182,
"tolerance": {
"rel": 0.001
}
},
{
"variable": "HSO3_minus",
"time": 0.0,
"expected": 0.3981286,
"tolerance": {
"rel": 0.001
}
}
]
},
{
"id": "o3_h2o2_dissolution_298K",
"description": "O3 and H2O2 dissolution at 298 K (p_O3=0.004 Pa ≈ 40 ppb, p_H2O2=0.001 Pa). Both gases dissolve via Henry's law. O3 has low solubility (H_O3 is small); H2O2 is very soluble. Neither changes pH significantly (K_h1 is tiny).",
"parameter_overrides": {
"T": 298.0,
"p_CO2": 0.0,
"p_SO2": 0.0,
"p_NH3": 0.0,
"p_HNO3": 0.0,
"p_H2O2": 0.001,
"p_O3": 0.004
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "H_plus",
"time": 0.0,
"expected": 0.00011032330301,
"tolerance": {
"rel": 0.0001
}
},
{
"variable": "H2O2_aq",
"time": 0.0,
"expected": 0.98692326672,
"tolerance": {
"rel": 0.0001
}
},
{
"variable": "O3_aq",
"time": 0.0,
"expected": 4.3424623736e-07,
"tolerance": {
"rel": 0.0001
}
},
{
"variable": "HO2_minus",
"time": 0.0,
"expected": 1.968062166e-05,
"tolerance": {
"rel": 0.001
}
}
]
}
],
"analyses": [
{
"id": "ph_vs_temperature_co2_only",
"description": "pH of CO2-only cloud water vs temperature (273-318 K). Higher T decreases CO2 solubility (raising pH); K_w change is secondary. Net effect: pH increases slightly with T.",
"initial_state": {},
"parameters": {
"p_CO2": 40.0,
"p_SO2": 0.0,
"p_NH3": 0.0,
"p_HNO3": 0.0,
"p_H2O2": 0.0,
"p_O3": 0.0
},
"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": "ph_vs_T",
"type": "line",
"description": "pH vs temperature for CO2-only cloud water.",
"x": {
"variable": "T",
"label": "Temperature (K)"
},
"y": {
"variable": "pH",
"label": "pH"
}
},
{
"id": "hco3_vs_T",
"type": "line",
"description": "[HCO3-] vs temperature at p_CO2=40 Pa.",
"x": {
"variable": "T",
"label": "Temperature (K)"
},
"y": {
"variable": "HCO3_minus",
"label": "[HCO3⁻] (mol/m³)"
}
}
]
},
{
"id": "ph_vs_p_SO2",
"description": "SO2 acidification curve: pH vs p_SO2 at 298 K with p_CO2=40 Pa background. Transition from CO2-dominated (pH 5.6) to SO2-dominated (pH < 4) regimes.",
"initial_state": {},
"parameters": {
"T": 298.0,
"p_CO2": 40.0,
"p_NH3": 0.0,
"p_HNO3": 0.0,
"p_H2O2": 0.0,
"p_O3": 0.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"parameter_sweep": {
"type": "cartesian",
"dimensions": [
{
"parameter": "p_SO2",
"range": {
"start": 1e-06,
"stop": 0.1,
"count": 25,
"scale": "log"
}
}
]
},
"plots": [
{
"id": "ph_vs_pSO2",
"type": "line",
"description": "pH vs p_SO2 showing SO2 acidification.",
"x": {
"variable": "p_SO2",
"label": "p_SO2 (Pa, log)"
},
"y": {
"variable": "pH",
"label": "pH"
}
},
{
"id": "SIV_vs_pSO2",
"type": "line",
"description": "[S(IV)] vs p_SO2.",
"x": {
"variable": "p_SO2",
"label": "p_SO2 (Pa, log)"
},
"y": {
"variable": "S_IV_total",
"label": "[S(IV)] (mol/m³)"
}
}
]
},
{
"id": "ph_vs_p_NH3",
"description": "NH3 buffering curve: pH vs p_NH3 at 298 K with p_CO2=40 Pa background. NH3 forms NH4+ and OH-, raising pH from 5.6 toward 7.",
"initial_state": {},
"parameters": {
"T": 298.0,
"p_CO2": 40.0,
"p_SO2": 0.0,
"p_HNO3": 0.0,
"p_H2O2": 0.0,
"p_O3": 0.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"parameter_sweep": {
"type": "cartesian",
"dimensions": [
{
"parameter": "p_NH3",
"range": {
"start": 1e-06,
"stop": 0.01,
"count": 25,
"scale": "log"
}
}
]
},
"plots": [
{
"id": "ph_vs_pNH3",
"type": "line",
"description": "pH vs p_NH3 showing NH3 buffering.",
"x": {
"variable": "p_NH3",
"label": "p_NH3 (Pa, log)"
},
"y": {
"variable": "pH",
"label": "pH"
}
}
]
}
]
}