O3Equilibria
Ozone (O3) aqueous dissolution equilibrium via temperature-dependent Henry's law. Migrated from Aerosol.jl@c8c640bb src/aqueous_equilibria.jl:589 (`O3Equilibria` @component). Implements Seinfeld & Pandis Ch 7 Table 7.3: K_H(O3, 298 K) = 1.1×10⁻² M/atm, ΔH_sol = −5.04 kcal/mol. O3 does not ionize in water; dissolution is purely described by Henry's law with van't Hoff temperature dependence.
Description
Ozone (O3) aqueous dissolution equilibrium via temperature-dependent Henry’s law. Migrated from Aerosol.jl@c8c640bb src/aqueous_equilibria.jl:589 (O3Equilibria @component). Implements Seinfeld & Pandis Ch 7 Table 7.3: K_H(O3, 298 K) = 1.1×10⁻² M/atm, ΔH_sol = −5.04 kcal/mol. O3 does not ionize in water; dissolution is purely described by Henry’s law with van’t Hoff temperature dependence.
Reference
_source_ref: Aerosol.jl@c8c640bb:src/aqueous_equilibria.jl:589
Upstream O3Equilibria is an MTK @component where T and p_O3 are @variables driven by a parent AqueousEquilibria system. For standalone serialization, T and p_O3 are declared as parameters here — matching the bead’s (S, observed-only) classification.
The Henry’s law constant H_O3_298 = 1.1×10⁻² M/atm is converted to SI (mol/m³/Pa): divide by 101325 Pa/atm and multiply by 1000 mol/m³ per M → 1.1e-2 / 101325 × 1000 ≈ 1.086×10⁻⁴ mol/(m³·Pa). The heat of dissolution dH_H_O3 = −5.04 kcal/mol × 4184 J/kcal = −21087.36 J/mol (S&P Table 7.3).
Van’t Hoff form: H_O3(T) = H_O3_298 × exp((dH_H_O3/R) × (1/T_ref − 1/T)). With dH_H_O3 < 0 (exothermic dissolution), H_O3 increases as T decreases — O3 is more soluble in cold clouds.
Tolerance rationale (rel=1e-6): purely algebraic observed-only system; 1e-6 covers float64 roundoff in the chained exp/multiply expressions across the atmospheric T range (273–318 K) and typical tropospheric p_O3 range._
Parameters
| Name | Units | Default | Description |
|---|---|---|---|
T | K | 298.0 | Temperature |
p_O3 | Pa | 0.004053 | Partial pressure of O3 (default ≈ 40 ppb at 1 atm) |
R_gas | J/mol/K | 8.314 | Gas constant |
T_ref | K | 298.0 | Reference temperature |
H_O3_298 | mol/m^3/Pa | 0.0001085615593387614 | Henry’s law constant for O3 at 298 K (1.1e-2 M/atm converted to mol/(m³·Pa)) |
dH_H_O3 | J/mol | -21087.36 | Heat of dissolution for O3 (−5.04 kcal/mol; S&P Table 7.3) |
Observed
| Name | Units | Default | Description |
|---|---|---|---|
H_O3 | mol/m^3/Pa | Temperature-dependent Henry’s law constant for O3 | |
O3_aq | mol/m^3 | Aqueous O3 concentration (Henry’s law: O3_aq = H_O3 × p_O3) |
Observed expressions
$$ H_{O3} = H_{O3\,298} \cdot e^{\frac{dH_{H\,O3} \cdot \left(\frac{1}{T_{ref}} + \frac{-1}{T}\right)}{R_{gas}}} $$Temperature-dependent Henry’s law constant for O3
$$ O3_{aq} = H_{O3} \cdot p_{O3} $$Aqueous O3 concentration (Henry’s law: O3_aq = H_O3 × p_O3)
Analyses
H_O3_vs_temperature
Van’t Hoff temperature dependence of the O3 Henry’s law constant (S&P Table 7.3). H_O3 increases by ~2.2× from 45°C to 0°C, reflecting the exothermic nature of O3 dissolution. Sweep T from 0°C to 45°C holding p_O3 fixed.
Time span: 0.0 → 1.0
Swept over: T
O3_aq_vs_p_O3
Henry’s law linearity: O3_aq = H_O3 × p_O3 at 298 K. Sweep p_O3 over three decades (0.001 to 1.0 Pa, covering sub-ppb to ~10 ppm O3) and verify the linear relationship.
Time span: 0.0 → 1.0
Swept over: p_O3
Raw .esm
Raw .esm JSON (this component)
{
"reference": {
"notes": "source_ref: Aerosol.jl@c8c640bb:src/aqueous_equilibria.jl:589\n\nUpstream `O3Equilibria` is an MTK `@component` where T and p_O3 are `@variables` driven by a parent `AqueousEquilibria` system. For standalone serialization, T and p_O3 are declared as parameters here — matching the bead's (S, observed-only) classification.\n\nThe Henry's law constant H_O3_298 = 1.1×10⁻² M/atm is converted to SI (mol/m³/Pa): divide by 101325 Pa/atm and multiply by 1000 mol/m³ per M → 1.1e-2 / 101325 × 1000 ≈ 1.086×10⁻⁴ mol/(m³·Pa). The heat of dissolution dH_H_O3 = −5.04 kcal/mol × 4184 J/kcal = −21087.36 J/mol (S&P Table 7.3).\n\nVan't Hoff form: H_O3(T) = H_O3_298 × exp((dH_H_O3/R) × (1/T_ref − 1/T)). With dH_H_O3 < 0 (exothermic dissolution), H_O3 increases as T decreases — O3 is more soluble in cold clouds.\n\nTolerance rationale (rel=1e-6): purely algebraic observed-only system; 1e-6 covers float64 roundoff in the chained exp/multiply expressions across the atmospheric T range (273–318 K) and typical tropospheric p_O3 range."
},
"tolerance": {
"rel": 1e-06
},
"variables": {
"T": {
"type": "parameter",
"units": "K",
"default": 298.0,
"description": "Temperature"
},
"p_O3": {
"type": "parameter",
"units": "Pa",
"default": 0.004053,
"description": "Partial pressure of O3 (default ≈ 40 ppb at 1 atm)"
},
"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_O3_298": {
"type": "parameter",
"units": "mol/m^3/Pa",
"default": 0.0001085615593387614,
"description": "Henry's law constant for O3 at 298 K (1.1e-2 M/atm converted to mol/(m³·Pa))"
},
"dH_H_O3": {
"type": "parameter",
"units": "J/mol",
"default": -21087.36,
"description": "Heat of dissolution for O3 (−5.04 kcal/mol; S&P Table 7.3)"
},
"H_O3": {
"type": "unknown",
"units": "mol/m^3/Pa",
"description": "Temperature-dependent Henry's law constant for O3"
},
"O3_aq": {
"type": "unknown",
"units": "mol/m^3",
"description": "Aqueous O3 concentration (Henry's law: O3_aq = H_O3 × p_O3)"
}
},
"equations": [
{
"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"
]
}
}
],
"tests": [
{
"id": "reference_298K",
"description": "At T_ref = 298 K the van't Hoff exponent is zero, so H_O3 must equal H_O3_298 exactly. With p_O3 = 1 Pa, O3_aq = H_O3_298 × 1 Pa. Validates the reference-condition identity.",
"parameter_overrides": {
"T": 298.0,
"p_O3": 1.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "H_O3",
"time": 0.0,
"expected": 0.0001085615593387614
},
{
"variable": "O3_aq",
"time": 0.0,
"expected": 0.0001085615593387614
}
]
},
{
"id": "henry_law_linearity_298K",
"description": "At 298 K with p_O3 = 101.325 Pa (= 1 mbar), O3_aq = H_O3_298 × 101.325 = 1.1e-2 M/atm × 1e-3 atm × 1000 mol/m³/M = 0.011 mol/m³. Validates Henry's law proportionality and the unit conversion.",
"parameter_overrides": {
"T": 298.0,
"p_O3": 101.325
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "H_O3",
"time": 0.0,
"expected": 0.0001085615593387614
},
{
"variable": "O3_aq",
"time": 0.0,
"expected": 0.011
}
]
},
{
"id": "cold_cloud_273K",
"description": "Cold cloud at 273.15 K (0°C). With dH_H_O3 < 0 (exothermic dissolution), H_O3 increases as T decreases — O3 is ~2.17× more soluble at 0°C than at 25°C. Validates the sign and magnitude of the van't Hoff temperature correction.",
"parameter_overrides": {
"T": 273.15,
"p_O3": 1.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "H_O3",
"time": 0.0,
"expected": 0.00023548295179912852
},
{
"variable": "O3_aq",
"time": 0.0,
"expected": 0.00023548295179912852
}
]
},
{
"id": "warm_atmosphere_310K",
"description": "Warm atmosphere at 310 K (37°C). H_O3 decreases to ~0.72× its 298 K value — less O3 dissolves into warmer droplets. Validates the opposite temperature-dependence direction from the cold-cloud case.",
"parameter_overrides": {
"T": 310.0,
"p_O3": 1.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "H_O3",
"time": 0.0,
"expected": 7.808888111339828e-05
},
{
"variable": "O3_aq",
"time": 0.0,
"expected": 7.808888111339828e-05
}
]
},
{
"id": "ambient_o3_298K",
"description": "Typical tropospheric background O3 at ~40 ppb partial pressure (p_O3 = 40e-9 × 101325 Pa ≈ 4.053e-3 Pa) at 298 K. Validates the model at realistic atmospheric concentrations.",
"parameter_overrides": {
"T": 298.0,
"p_O3": 0.004053
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "H_O3",
"time": 0.0,
"expected": 0.0001085615593387614
},
{
"variable": "O3_aq",
"time": 0.0,
"expected": 4.400000000000001e-07
}
]
},
{
"id": "cold_ambient_o3_273K",
"description": "Cold cloud at 273.15 K with ambient O3 at ~40 ppb (p_O3 ≈ 4.053e-3 Pa). Cross-check combining van't Hoff temperature correction with realistic partial pressure: O3_aq = H_O3(273.15) × p_O3.",
"parameter_overrides": {
"T": 273.15,
"p_O3": 0.004053
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "H_O3",
"time": 0.0,
"expected": 0.00023548295179912852
},
{
"variable": "O3_aq",
"time": 0.0,
"expected": 9.54412403641868e-07
}
]
},
{
"id": "warm_high_o3_310K",
"description": "Warm droplet at 310 K with elevated O3 at p_O3 = 5.0 Pa (~50 ppm; pollution episode or high-altitude scenario). Exercises both temperature reduction in H_O3 and the Henry's law proportionality at an elevated partial pressure.",
"parameter_overrides": {
"T": 310.0,
"p_O3": 5.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "H_O3",
"time": 0.0,
"expected": 7.808888111339828e-05
},
{
"variable": "O3_aq",
"time": 0.0,
"expected": 0.0003904444055669914
}
]
},
{
"id": "van_t_hoff_ratio_cold",
"description": "Explicit ratio check: H_O3(273.15) / H_O3(298) should equal exp(dH/R × (1/298 − 1/273.15)) ≈ 2.169. This is confirmed by the pair of tests cold_cloud_273K and reference_298K, but this test states it explicitly at p_O3 = 10.0 Pa so H_O3 can be derived from O3_aq / p_O3.",
"parameter_overrides": {
"T": 273.15,
"p_O3": 10.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "H_O3",
"time": 0.0,
"expected": 0.00023548295179912852
},
{
"variable": "O3_aq",
"time": 0.0,
"expected": 0.0023548295179912854
}
]
}
],
"analyses": [
{
"id": "H_O3_vs_temperature",
"description": "Van't Hoff temperature dependence of the O3 Henry's law constant (S&P Table 7.3). H_O3 increases by ~2.2× from 45°C to 0°C, reflecting the exothermic nature of O3 dissolution. Sweep T from 0°C to 45°C holding p_O3 fixed.",
"initial_state": {},
"parameters": {
"p_O3": 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_O3_curve",
"type": "line",
"description": "H_O3 as a function of temperature (van't Hoff).",
"x": {
"variable": "T",
"label": "Temperature (K)"
},
"y": {
"variable": "H_O3",
"label": "H_O3 (mol/(m³·Pa))"
}
}
]
},
{
"id": "O3_aq_vs_p_O3",
"description": "Henry's law linearity: O3_aq = H_O3 × p_O3 at 298 K. Sweep p_O3 over three decades (0.001 to 1.0 Pa, covering sub-ppb to ~10 ppm O3) and verify the linear relationship.",
"initial_state": {},
"parameters": {
"T": 298.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"parameter_sweep": {
"type": "cartesian",
"dimensions": [
{
"parameter": "p_O3",
"range": {
"start": 0.001,
"stop": 1.0,
"count": 20,
"scale": "log"
}
}
]
},
"plots": [
{
"id": "O3_aq_vs_p_O3",
"type": "line",
"description": "Aqueous O3 concentration as a function of partial pressure at 298 K (linear Henry's law).",
"x": {
"variable": "p_O3",
"label": "p(O3) (Pa, log scale)"
},
"y": {
"variable": "O3_aq",
"label": "[O3_aq] (mol/m³, log scale)"
}
}
]
}
]
}